- Business Essentials
- Leadership & Management
- Credential of Leadership, Impact, and Management in Business (CLIMB)
- Entrepreneurship & Innovation
- Digital Transformation
- Finance & Accounting
- Business in Society
- For Organizations
- Support Portal
- Media Coverage
- Founding Donors
- Leadership Team

- Harvard Business School →
- HBS Online →
- Business Insights →

## Business Insights

Harvard Business School Online's Business Insights Blog provides the career insights you need to achieve your goals and gain confidence in your business skills.

- Career Development
- Communication
- Decision-Making
- Earning Your MBA
- Negotiation
- News & Events
- Productivity
- Staff Spotlight
- Student Profiles
- Work-Life Balance
- AI Essentials for Business
- Alternative Investments
- Business Analytics
- Business Strategy
- Business and Climate Change
- Creating Brand Value
- Design Thinking and Innovation
- Digital Marketing Strategy
- Disruptive Strategy
- Economics for Managers
- Entrepreneurship Essentials
- Financial Accounting
- Global Business
- Launching Tech Ventures
- Leadership Principles
- Leadership, Ethics, and Corporate Accountability
- Leading Change and Organizational Renewal
- Leading with Finance
- Management Essentials
- Negotiation Mastery
- Organizational Leadership
- Power and Influence for Positive Impact
- Strategy Execution
- Sustainable Business Strategy
- Sustainable Investing
- Winning with Digital Platforms

## 17 Data Visualization Techniques All Professionals Should Know

- 17 Sep 2019

There’s a growing demand for business analytics and data expertise in the workforce. But you don’t need to be a professional analyst to benefit from data-related skills.

Becoming skilled at common data visualization techniques can help you reap the rewards of data-driven decision-making , including increased confidence and potential cost savings. Learning how to effectively visualize data could be the first step toward using data analytics and data science to your advantage to add value to your organization.

Several data visualization techniques can help you become more effective in your role. Here are 17 essential data visualization techniques all professionals should know, as well as tips to help you effectively present your data.

Access your free e-book today.

## What Is Data Visualization?

Data visualization is the process of creating graphical representations of information. This process helps the presenter communicate data in a way that’s easy for the viewer to interpret and draw conclusions.

There are many different techniques and tools you can leverage to visualize data, so you want to know which ones to use and when. Here are some of the most important data visualization techniques all professionals should know.

## Data Visualization Techniques

The type of data visualization technique you leverage will vary based on the type of data you’re working with, in addition to the story you’re telling with your data .

Here are some important data visualization techniques to know:

- Gantt Chart
- Box and Whisker Plot
- Waterfall Chart
- Scatter Plot
- Pictogram Chart
- Highlight Table
- Bullet Graph
- Choropleth Map
- Network Diagram
- Correlation Matrices

## 1. Pie Chart

Pie charts are one of the most common and basic data visualization techniques, used across a wide range of applications. Pie charts are ideal for illustrating proportions, or part-to-whole comparisons.

Because pie charts are relatively simple and easy to read, they’re best suited for audiences who might be unfamiliar with the information or are only interested in the key takeaways. For viewers who require a more thorough explanation of the data, pie charts fall short in their ability to display complex information.

## 2. Bar Chart

The classic bar chart , or bar graph, is another common and easy-to-use method of data visualization. In this type of visualization, one axis of the chart shows the categories being compared, and the other, a measured value. The length of the bar indicates how each group measures according to the value.

One drawback is that labeling and clarity can become problematic when there are too many categories included. Like pie charts, they can also be too simple for more complex data sets.

## 3. Histogram

Unlike bar charts, histograms illustrate the distribution of data over a continuous interval or defined period. These visualizations are helpful in identifying where values are concentrated, as well as where there are gaps or unusual values.

Histograms are especially useful for showing the frequency of a particular occurrence. For instance, if you’d like to show how many clicks your website received each day over the last week, you can use a histogram. From this visualization, you can quickly determine which days your website saw the greatest and fewest number of clicks.

## 4. Gantt Chart

Gantt charts are particularly common in project management, as they’re useful in illustrating a project timeline or progression of tasks. In this type of chart, tasks to be performed are listed on the vertical axis and time intervals on the horizontal axis. Horizontal bars in the body of the chart represent the duration of each activity.

Utilizing Gantt charts to display timelines can be incredibly helpful, and enable team members to keep track of every aspect of a project. Even if you’re not a project management professional, familiarizing yourself with Gantt charts can help you stay organized.

## 5. Heat Map

A heat map is a type of visualization used to show differences in data through variations in color. These charts use color to communicate values in a way that makes it easy for the viewer to quickly identify trends. Having a clear legend is necessary in order for a user to successfully read and interpret a heatmap.

There are many possible applications of heat maps. For example, if you want to analyze which time of day a retail store makes the most sales, you can use a heat map that shows the day of the week on the vertical axis and time of day on the horizontal axis. Then, by shading in the matrix with colors that correspond to the number of sales at each time of day, you can identify trends in the data that allow you to determine the exact times your store experiences the most sales.

## 6. A Box and Whisker Plot

A box and whisker plot , or box plot, provides a visual summary of data through its quartiles. First, a box is drawn from the first quartile to the third of the data set. A line within the box represents the median. “Whiskers,” or lines, are then drawn extending from the box to the minimum (lower extreme) and maximum (upper extreme). Outliers are represented by individual points that are in-line with the whiskers.

This type of chart is helpful in quickly identifying whether or not the data is symmetrical or skewed, as well as providing a visual summary of the data set that can be easily interpreted.

## 7. Waterfall Chart

A waterfall chart is a visual representation that illustrates how a value changes as it’s influenced by different factors, such as time. The main goal of this chart is to show the viewer how a value has grown or declined over a defined period. For example, waterfall charts are popular for showing spending or earnings over time.

## 8. Area Chart

An area chart , or area graph, is a variation on a basic line graph in which the area underneath the line is shaded to represent the total value of each data point. When several data series must be compared on the same graph, stacked area charts are used.

This method of data visualization is useful for showing changes in one or more quantities over time, as well as showing how each quantity combines to make up the whole. Stacked area charts are effective in showing part-to-whole comparisons.

## 9. Scatter Plot

Another technique commonly used to display data is a scatter plot . A scatter plot displays data for two variables as represented by points plotted against the horizontal and vertical axis. This type of data visualization is useful in illustrating the relationships that exist between variables and can be used to identify trends or correlations in data.

Scatter plots are most effective for fairly large data sets, since it’s often easier to identify trends when there are more data points present. Additionally, the closer the data points are grouped together, the stronger the correlation or trend tends to be.

## 10. Pictogram Chart

Pictogram charts , or pictograph charts, are particularly useful for presenting simple data in a more visual and engaging way. These charts use icons to visualize data, with each icon representing a different value or category. For example, data about time might be represented by icons of clocks or watches. Each icon can correspond to either a single unit or a set number of units (for example, each icon represents 100 units).

In addition to making the data more engaging, pictogram charts are helpful in situations where language or cultural differences might be a barrier to the audience’s understanding of the data.

## 11. Timeline

Timelines are the most effective way to visualize a sequence of events in chronological order. They’re typically linear, with key events outlined along the axis. Timelines are used to communicate time-related information and display historical data.

Timelines allow you to highlight the most important events that occurred, or need to occur in the future, and make it easy for the viewer to identify any patterns appearing within the selected time period. While timelines are often relatively simple linear visualizations, they can be made more visually appealing by adding images, colors, fonts, and decorative shapes.

## 12. Highlight Table

A highlight table is a more engaging alternative to traditional tables. By highlighting cells in the table with color, you can make it easier for viewers to quickly spot trends and patterns in the data. These visualizations are useful for comparing categorical data.

Depending on the data visualization tool you’re using, you may be able to add conditional formatting rules to the table that automatically color cells that meet specified conditions. For instance, when using a highlight table to visualize a company’s sales data, you may color cells red if the sales data is below the goal, or green if sales were above the goal. Unlike a heat map, the colors in a highlight table are discrete and represent a single meaning or value.

## 13. Bullet Graph

A bullet graph is a variation of a bar graph that can act as an alternative to dashboard gauges to represent performance data. The main use for a bullet graph is to inform the viewer of how a business is performing in comparison to benchmarks that are in place for key business metrics.

In a bullet graph, the darker horizontal bar in the middle of the chart represents the actual value, while the vertical line represents a comparative value, or target. If the horizontal bar passes the vertical line, the target for that metric has been surpassed. Additionally, the segmented colored sections behind the horizontal bar represent range scores, such as “poor,” “fair,” or “good.”

## 14. Choropleth Maps

A choropleth map uses color, shading, and other patterns to visualize numerical values across geographic regions. These visualizations use a progression of color (or shading) on a spectrum to distinguish high values from low.

Choropleth maps allow viewers to see how a variable changes from one region to the next. A potential downside to this type of visualization is that the exact numerical values aren’t easily accessible because the colors represent a range of values. Some data visualization tools, however, allow you to add interactivity to your map so the exact values are accessible.

## 15. Word Cloud

A word cloud , or tag cloud, is a visual representation of text data in which the size of the word is proportional to its frequency. The more often a specific word appears in a dataset, the larger it appears in the visualization. In addition to size, words often appear bolder or follow a specific color scheme depending on their frequency.

Word clouds are often used on websites and blogs to identify significant keywords and compare differences in textual data between two sources. They are also useful when analyzing qualitative datasets, such as the specific words consumers used to describe a product.

## 16. Network Diagram

Network diagrams are a type of data visualization that represent relationships between qualitative data points. These visualizations are composed of nodes and links, also called edges. Nodes are singular data points that are connected to other nodes through edges, which show the relationship between multiple nodes.

There are many use cases for network diagrams, including depicting social networks, highlighting the relationships between employees at an organization, or visualizing product sales across geographic regions.

## 17. Correlation Matrix

A correlation matrix is a table that shows correlation coefficients between variables. Each cell represents the relationship between two variables, and a color scale is used to communicate whether the variables are correlated and to what extent.

Correlation matrices are useful to summarize and find patterns in large data sets. In business, a correlation matrix might be used to analyze how different data points about a specific product might be related, such as price, advertising spend, launch date, etc.

## Other Data Visualization Options

While the examples listed above are some of the most commonly used techniques, there are many other ways you can visualize data to become a more effective communicator. Some other data visualization options include:

- Bubble clouds
- Circle views
- Dendrograms
- Dot distribution maps
- Open-high-low-close charts
- Polar areas
- Radial trees
- Ring Charts
- Sankey diagram
- Span charts
- Streamgraphs
- Wedge stack graphs
- Violin plots

## Tips For Creating Effective Visualizations

Creating effective data visualizations requires more than just knowing how to choose the best technique for your needs. There are several considerations you should take into account to maximize your effectiveness when it comes to presenting data.

Related : What to Keep in Mind When Creating Data Visualizations in Excel

One of the most important steps is to evaluate your audience. For example, if you’re presenting financial data to a team that works in an unrelated department, you’ll want to choose a fairly simple illustration. On the other hand, if you’re presenting financial data to a team of finance experts, it’s likely you can safely include more complex information.

Another helpful tip is to avoid unnecessary distractions. Although visual elements like animation can be a great way to add interest, they can also distract from the key points the illustration is trying to convey and hinder the viewer’s ability to quickly understand the information.

Finally, be mindful of the colors you utilize, as well as your overall design. While it’s important that your graphs or charts are visually appealing, there are more practical reasons you might choose one color palette over another. For instance, using low contrast colors can make it difficult for your audience to discern differences between data points. Using colors that are too bold, however, can make the illustration overwhelming or distracting for the viewer.

Related : Bad Data Visualization: 5 Examples of Misleading Data

## Visuals to Interpret and Share Information

No matter your role or title within an organization, data visualization is a skill that’s important for all professionals. Being able to effectively present complex data through easy-to-understand visual representations is invaluable when it comes to communicating information with members both inside and outside your business.

There’s no shortage in how data visualization can be applied in the real world. Data is playing an increasingly important role in the marketplace today, and data literacy is the first step in understanding how analytics can be used in business.

Are you interested in improving your analytical skills? Learn more about Business Analytics , our eight-week online course that can help you use data to generate insights and tackle business decisions.

This post was updated on January 20, 2022. It was originally published on September 17, 2019.

## About the Author

## Learning Through Visuals

Visual imagery in the classroom.

Posted July 20, 2012

A large body of research indicates that visual cues help us to better retrieve and remember information. The research outcomes on visual learning make complete sense when you consider that our brain is mainly an image processor (much of our sensory cortex is devoted to vision), not a word processor. In fact, the part of the brain used to process words is quite small in comparison to the part that processes visual images.

Words are abstract and rather difficult for the brain to retain, whereas visuals are concrete and, as such, more easily remembered. To illustrate, think about your past school days of having to learn a set of new vocabulary words each week. Now, think back to the first kiss you had or your high school prom date. Most probably, you had to put forth great effort to remember the vocabulary words. In contrast, when you were actually having your first kiss or your prom date, I bet you weren’t trying to commit them to memory . Yet, you can quickly and effortlessly visualize these experiences (now, even years later). You can thank your brain’s amazing visual processor for your ability to easily remember life experiences. Your brain memorized these events for you automatically and without you even realizing what it was doing.

There are countless studies that have confirmed the power of visual imagery in learning. For instance, one study asked students to remember many groups of three words each, such as dog, bike, and street. Students who tried to remember the words by repeating them over and over again did poorly on recall. In comparison, students who made the effort to make visual associations with the three words, such as imagining a dog riding a bike down the street, had significantly better recall.

Various types of visuals can be effective learning tools: photos, illustrations, icons, symbols, sketches, figures, and concept maps, to name only a few. Consider how memorable the visual graphics are in logos, for example. You recognize the brand by seeing the visual graphic, even before reading the name of the brand. This type of visual can be so effective that earlier this year Starbucks simplified their logo by dropping their printed name and keeping only the graphic image of the popularly referred to mermaid (technically, it’s a siren). I think we can safely assume that Starbucks Corporation must be keenly aware of how our brains have automatically and effortlessly committed their graphic image to memory.

So powerful is visual learning that I embrace it in my teaching and writing. Each page in the psychology textbooks I coauthor has been individually formatted to maximize visual learning. Each lecture slide I use in class is presented in a way to make the most of visual learning. I believe the right visuals can help make abstract and difficult concepts more tangible and welcoming, as well as make learning more effective and long lasting. This is why I scrutinize every visual I use in my writing and teaching to make sure it is paired with content in a clear, meaningful manner.

Based upon research outcomes, the effective use of visuals can decrease learning time, improve comprehension, enhance retrieval, and increase retention. In addition, the many testimonials I hear from my students and readers weigh heavily in my mind as support for the benefits of learning through visuals. I hear it often and still I can’t hear it enough times . . . by retrieving a visual cue presented on the pages of a book or on the slides of a lecture presentation, a learner is able to accurately retrieve the content associated with the visual.

McDaniel, M. A., & Einstein, G. O. (1986). Bizarre imagery as an effective memory aid: The importance of distinctiveness. Journal of Experimental Psychology: Learning, Memory, and Cognition , 12(1), 54-65.

Meier, D. (2000). The accelerated learning handbook. NY: McGraw-Hill.

Patton, W. W. (1991). Opening students’ eyes: Visual learning theory in the Socratic classroom. Law and Psychology Review, 15, 1-18.

Schacter, D.L. (1966). Searching for memory. NY: Basic Books.

Verdi, M. P., Johnson, J. T., Stock, W. A., Kulhavy, R. W., Whitman-Ahern, P. (1997). Organized spatial displays and texts: Effects of presentation order and display type on learning outcomes. Journal of Experimental Education , 65, 303-317.

Haig Kouyoumdjian, Ph.D. , is a clinical psychologist and coauthor of Introduction to Psychology , 9th ed. and the innovative Discovery Series: Introduction to Psychology.

- Find a Therapist
- Find a Treatment Center
- Find a Psychiatrist
- Find a Support Group
- Find Online Therapy
- United States
- Brooklyn, NY
- Chicago, IL
- Houston, TX
- Los Angeles, CA
- New York, NY
- Portland, OR
- San Diego, CA
- San Francisco, CA
- Seattle, WA
- Washington, DC
- Asperger's
- Bipolar Disorder
- Chronic Pain
- Eating Disorders
- Passive Aggression
- Personality
- Goal Setting
- Positive Psychology
- Stopping Smoking
- Low Sexual Desire
- Relationships
- Child Development
- Self Tests NEW
- Therapy Center
- Diagnosis Dictionary
- Types of Therapy

Sticking up for yourself is no easy task. But there are concrete skills you can use to hone your assertiveness and advocate for yourself.

- Emotional Intelligence
- Gaslighting
- Affective Forecasting
- Neuroscience

## Visual Representations for Science Teaching and Learning

- First Online: 17 April 2024

## Cite this chapter

- Eduardo Ravanal Moreno ORCID: orcid.org/0000-0003-2763-9237 12 ,
- Elías Francisco Amórtegui Cedeño 13 &
- Diego Armando Retana Alvarado 14

Part of the book series: Contemporary Trends and Issues in Science Education ((CTISE,volume 59))

100 Accesses

In this chapter, we present the tendency to focus science teaching in the classroom as a descriptive accumulation of phenomena, and how to move toward more discursive practices that recognize elaboration processes and a socially contextualized vision of science. From a vision where science is imagined and drawn as part of human activity, we promote drawing as a school scientific activity, recovering places from the history of science (1852–1934). Finally, we collect different experiences that highlight drawing in the classroom to represent science, science reasoning, and verbal and visual communication, improving participation by shaping student ideas toward the visual organization of their knowledge.

This is a preview of subscription content, log in via an institution to check access.

## Access this chapter

Subscribe and save.

- Get 10 units per month
- Download Article/Chapter or eBook
- 1 Unit = 1 Article or 1 Chapter
- Cancel anytime
- Available as PDF
- Read on any device
- Instant download
- Own it forever
- Available as EPUB and PDF
- Durable hardcover edition
- Dispatched in 3 to 5 business days
- Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Aguilar, J. (2016). Las serpientes no son como las pintan [Snakes are not as they are portrayed] (pp. 6–13). Comunicaciones libres.

Google Scholar

Ainsworth, S., Prain, V., & Tytler, R. (2011). Drawing to learn in Science. Science Education, 333 , 1096–1097. https://doi.org/10.1126/science.1204153

Article Google Scholar

Anderson, E., & Kim, D. (2006). Increasing the success of minority students in science and technology . American Council on Education. Retrieved from: https://vtechworks.lib.vt.edu/handle/10919/86900

Bermudez, G., & Longhi, L. (2008). La Educación Ambiental y la Ecología como ciencia. Una discusión necesaria para la enseñanza [Environmental education and ecology as a science. A necessary discussion for teaching]. Revista Electrónica de Enseñanza de las Ciencias, 7 (2), 275–297.

Bistoni, M., Hued, A., Sironi, M., & Torres, R. (2015). Diversidad de vertebrados de la provincia de Córdoba. Aportes para su conocimiento y conservación [Diversity of vertebrates in the province of Córdoba. Contributions for its knowledge and conservation]. In I. G. M. Bermúdez & A. L. De Longhi (Eds.), Retos para la enseñanza de la biodiversiad hoy (pp. 165–197). Universidad Nacional de Córdoba.

Bonil, J., & Pujol, R. M. (2008a). El paradigma de la complejidad, un marco referencial para el diseño de un instrumento de evaluación de programas en la formación inicial de profesores [The paradigm of complexity, a frame of reference for the design of a program evaluation instrument in initial teacher training]. Enseñanza de las Ciencias, 26 (1), 5–22.

Bonil, J., & Pujol, R. M. (2008b). Orientaciones didácticas para favorecer la presencia del modelo conceptual complejo de ser vivo en la formación inicial de profesorado de educación primaria [Didactical orientations to favor the presence of the complex conceptual model of living being in the initial training of primary education teachers]. Enseñanza de las Ciencias, 26 (3), 403–418.

Braaten, M., & Windschitl, M. (2011). Working toward a stronger conceptualization of scientific explanation for science education. Science Education, 95 (4), 639–669. https://doi.org/10.1002/sce.20449

Brooks, M. (2009). Drawing, visualization and young children’s exploration of “big ideas”. International Journal of Science Education, 31 (3), 319–341.

Casas Andreu, G. (2000). Mitos, leyendas y realidades de los reptiles en México [Myths, legends and realities of reptiles in Mexico]. Ciencia Ergo Sum, 7 (3), 286–291.

Chi-Yan, T., & Treagust, D. (2013). Introduction to multiple representations: Their importance in biology and biological education. In C. Y. Tsui & D. F. Treagust (Eds.), Multiple representations in biological education (pp. 3–18). Springer.

Christidou, V., Katzinikita, V., & Dimitriou, A. (2009). Children’s drawings about environmental phenomena: The use of visual codes. The International Journal of Science in Society, 1 (1), 107–108.

Couso, D., & Garrido-Espeja, A. (2015). Models and modelling in pre-service teacher education: Why we need both. In K. Hahl, K. Juuti, J. Lampiselkä, A. Uitto, & J. Lavoven (Eds.), Cognitive and affective aspects in Science Education Research (pp. 245–261). Springer.

Couso, D., & Grimalt-Alvaro, C. (2020). ¿Qué es STEM y STEAM y por qué ponerse a ello? [What is STEAM and STEAM and why get in on it?]. Aula de Innovación Educativa, 290 , 71–72.

Cunningham, C. M. (2018). Engineering in elementary STEM education: Curriculum design, instruction, learning, and assessment . Teachers College Press and Museum of Science Driveway.

Daugherty, M., Carter, V., & Swagerty, L. (2014). Elementary STEM education: The future for technology and engineering education? Journal of STEM Teacher Education, 49 (1), 45–55. https://doi.org/10.30707/JSTE49.1Daugherty

Dávila, M. A., Borrachero, A., Cañada, F., Martínez, G., & Sánchez, J. (2015). Evolución de las emociones que experimentan los estudiantes del grado de maestro en educación primaria, en didáctica de la materia y la energía [Evolution of the emotions experienced by students of the master’s degree in primary education, in didactics of matter and energy]. Revista Eureka sobre Enseñanza y Divulgación de las Ciencias, 12 (3), 550–564.

Domènech-Casal, J. (2018). Aprendizaje Basado en Proyectos en el marco STEM. Componentes didácticos para la Competencia Científica [Project Based Learning in the STEM framework. Didactical components for Scientific Competence.] Ápice. Revista de Educación Científica, 2 (2), 29–42. https://doi.org/10.17979/arec.2018.2.2.4524

Duschl, R. A., & Grandy, R. E. (2008). Teaching scientific inquiry: Recommendations for research and implementation . Sense Publishers.

Book Google Scholar

Eilam, B. (2013). Possible constraints of visualization in biology: Challenges in learning with multiple representations. In C. Y. Tsui & D. F. Treagust (Eds.), Multiple representations in biological education (pp. 55–73). Springer.

Chapter Google Scholar

Eilam, B., & Gilbert, J. (2014). The significance of visual representations in the teaching of science. In B. Eilam & J. Gilbert (Eds.), Science teachers’ use of visual representations (pp. 3–28). Springer.

Fiorella, L., & Mayer, R. (2015). Eight ways to promote generative learning. Educational Psychology Review, 28 , 717–741.

Flórez, J., & Gaitán, E. (2015). Enseñanza de la Avifauna a través de salidas de campo en estudiantes de cuarto y quinto de primaria de la Institución Educativa Guacirco, Sede 301 Peñas Blancas, Vereda Peñas Blancas (Neiva, Huila, Colombia) [Teaching of Avifauna through field trips in fourth and fifth grade students of the Guacirco Educational Institution, Headquarters 301 Peñas Blancas, Vereda Peñas Blancas, (Neiva, Huila, Colombia)]. Universidad Surcolombiana.

Forbus, K., & Ainsworth, S. (2017). Editors’ introduction: Sketching and cognition. Topics in Cognitive Science, 9 (4), 864–865. https://doi.org/10.1111/tops.12299

García-Barros, S., Fuentes, M. J., Rivadulla-López, J. C., & Vásquez-Ben, L. (2021). La adaptación de los animales al medio. Qué aspectos consideran los estudiantes de Primaria y Secundaria [The adaptation of animals to the environment. What aspects Primary and Secondary students consider]. Revista Eureka sobre Enseñanza y Divulgación de las Ciencias, 18 (3), 3106. https://doi.org/10.25267/Rev_Eureka_ensen_divulg_cienc.2021.v18.i3.3106

Genek, S., & Küçük, Z. (2020). Investigation of scientific creativity levels of elementary school students who enrolled in a STEM program. Ilkogretim Online – Elementary Education Online, 19 , 1715–1728. https://doi.org/10.17051/ilkonline.2020.734849

Gess-Newsome, J. (2015). A model of teacher professional knowledge and skill including PCK: Results of the thinking from the PCK Summit. In A. Berry, P. Friedrichsen, & J. Loughran (Eds.), Re-examining pedagogical content knowledge in science education (pp. 28–42). Routledge.

Gómez, D., & Herrera, J. (2018). Enseñanza-aprendizaje sobre conservación de la ofidiofauna con estudiantes de octavo grado de la Institución Educativa Núcleo Escolar “El Guadual” Rivera-Huila (tesis de pregrado) [Teaching-learning on conservation of the ophidiofauna with eighth grade students of the Educational Institution School Nucleus “El Guadual” Rivera-Huila (undergraduate thesis)]. Universidad Surcolombiana, Neiva, Huila, Colombia.

Guevara, S., & Quiroga, A. D. (2017). Enseñanza y aprendizaje de conceptos, procedimientos y actitudes ecológicas a través del uso de arañas en estudiantes de sexto grado de la Institución Educativa José Reinel Cerquera del municipio de Palermo, Huila. (Tesis de pregado) [Teaching and learning of concepts, procedures and ecological attitudes through the use of spiders in sixth grade students of the José Reinel Cerquera Educational Institution in the municipality of Palermo, Huila. (undegraduate thesis)] Universidad Surcolombiana, Neiva, Huila, Colombia.

Hasanah, U. (2020). Key definitions of STEM education: Literature review. Interdisciplinary Journal of Environmental and Science Education, 16 , 1–7. https://doi.org/10.29333/ijese/8336

Hodges, C., Moore, S., Lockee, B., Trust, T., & Bond, A. (2020). The difference between emergency remote teaching and online learning . Educause Review. Retrieved from https://er.educause.edu/articles/2020/3/the-difference-between-emergency-remote-teaching-and-online-learning

Izquierdo, M. (2007). Enseñar ciencias, una nueva ciencia [Teaching science, a new science]. Enseñanza de las Ciencias Sociales, 6 , 125–138.

Kitano, H. (2002). System biology: A brief overview. Science, 295 , 1662–1664.

Lardi, C., & Leopold, C. (2022). Effects of interactive teacher-generated drawings on students’ understanding of plate tectonic. Instructional Science, 50 , 273–302. https://doi.org/10.1007/s11251-021-09567-0

Leopold, C., & Leutner, D. (2012). Science text comprehension: Drawing, main idea selection, and summarizing as learning strategies. Learning and Instruction, 22 , 16–26. https://doi.org/10.1016/j_learninstruc.2011.05.005

Llombart, V., & Gavidia, V. (2015). Describir y dibujar en ciencias. La importancia del dibujo en las representaciones mentales del alumnado [Describe and draw in science. The importance of drawing in the mental representations of students]. Revista Eureka sobre Enseñanza y Divulgación de las Ciencias, 12 (3), 441–455.

López, V., Couso, D., & Simarro, C. (2020). STEM Education in and for the digital world. Distance Education Journal, 20 (62), 1–29. https://doi.org/10.6018/red.410011

López, F., Ravanal, E., Palma, C., & Merino, C. (2021). Representaciones de estudiantes de Educación Secundaria sobre la división celular mitótica: una experiencia con realidad aumentada [Representations of secondary school students about mitotic cell division: An experience with augmented reality]. Pixel-Bit. Revista de Medios y Educación, 62 , 7–37. https://doi.org/10.12795/pixelbit.84491

Lynch, J. D. (2012). El contexto de las serpientes en Colombia con un análisis de las amenazas en contra de su conservación [The context of snakes in Colombia with an analysis of the threats against their conservation]. Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales, 36 , 435.

Márquez, C. (2002). Dibujar en las clases de Ciencias [Drawing in Science classes]. Aula de Innovación Educativa, 117 , 54–57.

Martin-Lopez, B., Montes, C., & Benayas, J. (2007). The non-economic motives behind the willingness to pay for biodiversity conservation. Biological Conservation, 139 , 67–82.

Mendoza, J. (2015). El reto de la conservación de serpientes en Colombia [The challenge of snake conservation in Colombia]. Hipótesis, Apuntes científicos uniandinos , 36–47. Retrieved from http://hipotesis.uniandes.edu.co/hipotesis/images/stories/ed19pdf/Conservacionserpientes-19.pdf

Mercer, N., Hennessy, S., & Warwick, P. (2019). Dialogue, thinking together and digital technology in the classroom: Some educational implications of a continuing line of inquiry. International Journal of Educational Research, 97 , 187–199. https://doi.org/10.1016/j.ijer.2017.08.007

Öhman, A., & Mineka, S. (2003). The malicious serpent: Snakes as a prototypical stimulus for an evolved module of fear. Current Directions in Psychological Science, 12 (1), 5–9.

Perales, F., & Aguilera, D. (2020). Ciencia-Tecnología-Sociedad vs. STEM: ¿evolución, revolución o disyunción? [Science-Technology-Society vs. STEM: Evolution, revolution, or disjunction?]. Ápice. Revista de Educación Científica, 4 (1), 1–15. https://doi.org/10.17979/arec.2020.4.1.5826

Pough, F. H., Andrews, R. M., Cadle, J. E., Crump, M. L., Savitzky, A. H., & Wells, K. D. (1998). Herpetology . Prentice-Hall.

Prokop, P; Ozel, M & Usak, M. (2009). Cross-cultural comparison of student attitudes toward snakes. Society and Animals, 224-240.

Pujalte, A., Adúriz-Bravo, A., & Porro, S. (2015). Del discurso a la práctica de aula: Imágenes de ciencia en profesores y profesoras de Biología [From discourse to classroom practice: Science images in biology teachers]. Revista de Educación en Biología, 18 (2), 11–19.

Ravanal, E. (2023). Dibujando seres vivos “imaginados” para aprender [Drawing “imagined” living beings to learn]. Alambique, 112 , 64–70.

Ravanal, E., Quintanilla, M., & Labarrere, A. (2012). Concepciones epistemológicas del profesorado de Biología en ejercicio sobre la enseñanza de la Biología [Epistemological conceptions of in-service teachers about the teaching of Biology]. Ciência & Educação, 18 (4), 875–895.

Ravanal, E., López-Cortés, F., Amórtegui, E., & Joglar, C. (2021). Preocupaciones docentes y las Etapas de desarrollo de profesores chilenos de Biología [Teaching concerns and the stages of development of Chilean teachers of Biology]. Revista de Estudios y Experiencias en Educación, 20 (42), 213–232.

Retana-Alvarado, D. A., de las Heras Pérez, M. Á., Vázquez-Bernal, B., & Jiménez-Pérez, R. (2018). El cambio en las emociones de maestros en formación inicial hacia el clima de aula en una intervención basada en investigación escolar [The shift in the emotions of teachers in initial training towards classroom climate in an intervention based on school research]. Revista Eureka sobre Enseñanza y Divulgación de las Ciencias, 15 (2), 2602. https://doi.org/10.25267/Rev_Eureka_ensen_divulg_cienc.2018.v15.i2.2602

Rivera, S. (2016). Enseñanza y Aprendizaje de la Quiropterofauna a través del diseño y aplicación de una unidad didáctica dirigida a estudiantes de octavo grado de la institución educativa técnico superior [Teaching and Learning of Chiroptero fauna through the design and application of a didactical unit aimed at eighth grade students of the higher technical educational institution]. Universidad Surcolombiana.

Rivero, A., Martín del Pozo, R., Solís, E., & Porlán, R. (2017). Didáctica de las ciencias experimentales en educación primaria [Didactics of experimental sciences in primary education]. Editorial Síntesis.

Tamayo, O., & Sanmartí, N. (2003). Estudio multidimensional de las representaciones mentales de los estudiantes. Aplicación al concepto de respiración [Multidimensional study of students’ mental representations. Application to the concept of breathing]. Revista Latinoamericana de Ciencias Sociales, Niñez y Juventud, 1 (1), 181–205.

Toma, R. B. (2020). STEM education in elementary grades: Design of an effective framework for improving attitudes towards school science . University of Burgos.

Toma, R. B., & García-Carmona, A. (2021). «De STEM nos gusta todo menos STEM». Análisis crítico de una tendencia educativa de moda. Enseñanza de las Ciencias [“We like everything about STEM except STEM.” Critical analysis of a fashionable educational trend]. Revista de Investigación y Experiencias Didácticas, 39 (1), 65–80. https://doi.org/10.5565/rev/ensciencias.3093

Toma, R. B., & Retana-Alvarado, D. A. (2021). Mejora de las concepciones de maestros en formación de la educación STEM [Improvement of the conceptions of teachers in STEM education training]. Revista Iberoamericana de Educación, 87 (1), 15–33. https://doi.org/10.35362/rie8714538

Tsui, C.-Y., & Treagust, D. (2013). Introduction to multiple representations; their importance in biology and biological education. In D. Treagust & C.-Y. Tsui (Eds.), Multiple representations in biological education (pp. 3–18). Springer.

Tytler, R., Prain, V., Aranda, G., Ferguson, J., & Gorur, R. (2020). Drawing to reason and learn in science. Journal of Research in Science Teaching, 57 (2), 209–231. https://doi.org/10.1002/tea.21590

Uetz, P., & Hallerman, J. (2017). The reptile database . Retrieved on October 20, 2018, from the reptile database: http://reptiledatabase.reptarium.cz/species? genus=Bothrocophias&species=colombianus

Velasco, S., & Navarro, M. (2014). El papel de la imagen en la enseñanza. Análisis de las ilustraciones del proceso de la meiosis en fuentes de consulta utilizadas por alumnos de biología del CCH Vallejo [The role of the image in teaching. Analysis of the illustrations of the meiosis process in reference sources used by biology students of the CCH Vallejo]. Nuevos Cuadernos del Colegio, 3 , 1–10.

Vergara, C., & Cofré, H. (2012). La Indagación Científica: Un concepto esquivo, pero necesario [Scientific inquiry: An elusive but necessary concept]. Revista Chilena de Educación Científica, 11 (1), 30–38.

Watson, S., Duncan, O., & Peters, M. (2020). School administrators’ awareness of parental STEM knowledge, strategies to promote STEM knowledge, and student STEM preparation. Research in Science & Technological Education, 1–20 . https://doi.org/10.1080/02635143.2020.17774747

Wittrock, M. C. (1989). Learning as a generative process. Educational Psychologist, 11 (2), 87–95. https://doi.org/10.1080/00461520903433554

Wittrock, M. C. (2010). Learning as a generative process. Educational Psychologist, 45 (1), 40–45. https://doi.org/10.1080/00461520903433554

Download references

## Author information

Authors and affiliations.

Universidad Santo Tomás, Santiago, Chile

Eduardo Ravanal Moreno

Universidad Surcolombiana, Neiva, Colombia

Elías Francisco Amórtegui Cedeño

University of Costa Rica, San José, Costa Rica

Diego Armando Retana Alvarado

You can also search for this author in PubMed Google Scholar

## Corresponding author

Correspondence to Eduardo Ravanal Moreno .

## Editor information

Editors and affiliations.

Pontificia Universidad Católica de Chile, Santiago, Chile

Ainoa Marzabal

Pontificia Universidad Católica de Valparaíso, Curauma, Chile

Cristian Merino

## Rights and permissions

Reprints and permissions

## Copyright information

© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG

## About this chapter

Moreno, E.R., Cedeño, E.F.A., Alvarado, D.A.R. (2024). Visual Representations for Science Teaching and Learning. In: Marzabal, A., Merino, C. (eds) Rethinking Science Education in Latin-America. Contemporary Trends and Issues in Science Education, vol 59. Springer, Cham. https://doi.org/10.1007/978-3-031-52830-9_14

## Download citation

DOI : https://doi.org/10.1007/978-3-031-52830-9_14

Published : 17 April 2024

Publisher Name : Springer, Cham

Print ISBN : 978-3-031-52829-3

Online ISBN : 978-3-031-52830-9

eBook Packages : Education Education (R0)

## Share this chapter

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

- Publish with us

Policies and ethics

- Find a journal
- Track your research

## Initial Thoughts

Perspectives & resources, what is high-quality mathematics instruction and why is it important.

- Page 1: The Importance of High-Quality Mathematics Instruction
- Page 2: A Standards-Based Mathematics Curriculum
- Page 3: Evidence-Based Mathematics Practices

## What evidence-based mathematics practices can teachers employ?

- Page 4: Explicit, Systematic Instruction

## Page 5: Visual Representations

- Page 6: Schema Instruction
- Page 7: Metacognitive Strategies
- Page 8: Effective Classroom Practices
- Page 9: References & Additional Resources
- Page 10: Credits

## Research Shows

- Students who use accurate visual representations are six times more likely to correctly solve mathematics problems than are students who do not use them. However, students who use inaccurate visual representations are less likely to correctly solve mathematics problems than those who do not use visual representations at all. (Boonen, van Wesel, Jolles, & van der Schoot, 2014)
- Students with a learning disability (LD) often do not create accurate visual representations or use them strategically to solve problems. Teaching students to systematically use a visual representation to solve word problems has led to substantial improvements in math achievement for students with learning disabilities. (van Garderen, Scheuermann, & Jackson, 2012; van Garderen, Scheuermann, & Poch, 2014)
- Students who use visual representations to solve word problems are more likely to solve the problems accurately. This was equally true for students who had LD, were low-achieving, or were average-achieving. (Krawec, 2014)

Visual representations are flexible; they can be used across grade levels and types of math problems. They can be used by teachers to teach mathematics facts and by students to learn mathematics content. Visual representations can take a number of forms. Click on the links below to view some of the visual representations most commonly used by teachers and students.

## How does this practice align?

High-leverage practice (hlp).

- HLP15 : Provide scaffolded supports

## CCSSM: Standards for Mathematical Practice

- MP1 : Make sense of problems and persevere in solving them.

Number Lines

Definition : A straight line that shows the order of and the relation between numbers.

Common Uses : addition, subtraction, counting

Strip Diagrams

Definition : A bar divided into rectangles that accurately represent quantities noted in the problem.

Common Uses : addition, fractions, proportions, ratios

Definition : Simple drawings of concrete or real items (e.g., marbles, trucks).

Common Uses : counting, addition, subtraction, multiplication, division

Graphs/Charts

Definition : Drawings that depict information using lines, shapes, and colors.

Common Uses : comparing numbers, statistics, ratios, algebra

Graphic Organizers

Definition : Visual that assists students in remembering and organizing information, as well as depicting the relationships between ideas (e.g., word webs, tables, Venn diagrams).

Common Uses : algebra, geometry

Triangles | ||
---|---|---|

equilateral | – all sides are same length – all angles 60° | |

isosceles | – two sides are same length – two angles are the same | |

scalene | – no sides are the same length – no angles are the same | |

right | – one angle is 90°(right angle) – opposite side of right angle is longest side (hypotenuse) | |

obtuse | – one angle is greater than 90° | |

acute | – all angles are less than 90° |

Before they can solve problems, however, students must first know what type of visual representation to create and use for a given mathematics problem. Some students—specifically, high-achieving students, gifted students—do this automatically, whereas others need to be explicitly taught how. This is especially the case for students who struggle with mathematics and those with mathematics learning disabilities. Without explicit, systematic instruction on how to create and use visual representations, these students often create visual representations that are disorganized or contain incorrect or partial information. Consider the examples below.

## Elementary Example

Mrs. Aldridge ask her first-grade students to add 2 + 4 by drawing dots.

Notice that Talia gets the correct answer. However, because Colby draws his dots in haphazard fashion, he fails to count all of them and consequently arrives at the wrong solution.

## High School Example

Mr. Huang asks his students to solve the following word problem:

The flagpole needs to be replaced. The school would like to replace it with the same size pole. When Juan stands 11 feet from the base of the pole, the angle of elevation from Juan’s feet to the top of the pole is 70 degrees. How tall is the pole?

Compare the drawings below created by Brody and Zoe to represent this problem. Notice that Brody drew an accurate representation and applied the correct strategy. In contrast, Zoe drew a picture with partially correct information. The 11 is in the correct place, but the 70° is not. As a result of her inaccurate representation, Zoe is unable to move forward and solve the problem. However, given an accurate representation developed by someone else, Zoe is more likely to solve the problem correctly.

## Manipulatives

Some students will not be able to grasp mathematics skills and concepts using only the types of visual representations noted in the table above. Very young children and students who struggle with mathematics often require different types of visual representations known as manipulatives. These concrete, hands-on materials and objects—for example, an abacus or coins—help students to represent the mathematical idea they are trying to learn or the problem they are attempting to solve. Manipulatives can help students develop a conceptual understanding of mathematical topics. (For the purpose of this module, the term concrete objects refers to manipulatives and the term visual representations refers to schematic diagrams.)

It is important that the teacher make explicit the connection between the concrete object and the abstract concept being taught. The goal is for the student to eventually understand the concepts and procedures without the use of manipulatives. For secondary students who struggle with mathematics, teachers should show the abstract along with the concrete or visual representation and explicitly make the connection between them.

A move from concrete objects or visual representations to using abstract equations can be difficult for some students. One strategy teachers can use to help students systematically transition among concrete objects, visual representations, and abstract equations is the Concrete-Representational-Abstract (CRA) framework.

If you would like to learn more about this framework, click here.

## Concrete-Representational-Abstract Framework

- Concrete —Students interact and manipulate three-dimensional objects, for example algebra tiles or other algebra manipulatives with representations of variables and units.
- Representational — Students use two-dimensional drawings to represent problems. These pictures may be presented to them by the teacher, or through the curriculum used in the class, or students may draw their own representation of the problem.
- Abstract — Students solve problems with numbers, symbols, and words without any concrete or representational assistance.

CRA is effective across all age levels and can assist students in learning concepts, procedures, and applications. When implementing each component, teachers should use explicit, systematic instruction and continually monitor student work to assess their understanding, asking them questions about their thinking and providing clarification as needed. Concrete and representational activities must reflect the actual process of solving the problem so that students are able to generalize the process to solve an abstract equation. The illustration below highlights each of these components.

## For Your Information

One promising practice for moving secondary students with mathematics difficulties or disabilities from the use of manipulatives and visual representations to the abstract equation quickly is the CRA-I strategy . In this modified version of CRA, the teacher simultaneously presents the content using concrete objects, visual representations of the concrete objects, and the abstract equation. Studies have shown that this framework is effective for teaching algebra to this population of students (Strickland & Maccini, 2012; Strickland & Maccini, 2013; Strickland, 2017).

Kim Paulsen discusses the benefits of manipulatives and a number of things to keep in mind when using them (time: 2:35).

Kim Paulsen, EdD Associate Professor, Special Education Vanderbilt University

View Transcript

Transcript: Kim Paulsen, EdD

Manipulatives are a great way of helping kids understand conceptually. The use of manipulatives really helps students see that conceptually, and it clicks a little more with them. Some of the things, though, that we need to remember when we’re using manipulatives is that it is important to give students a little bit of free time when you’re using a new manipulative so that they can just explore with them. We need to have specific rules for how to use manipulatives, that they aren’t toys, that they really are learning materials, and how students pick them up, how they put them away, the right time to use them, and making sure that they’re not distracters while we’re actually doing the presentation part of the lesson. One of the important things is that we don’t want students to memorize the algorithm or the procedures while they’re using the manipulatives. It really is just to help them understand conceptually. That doesn’t mean that kids are automatically going to understand conceptually or be able to make that bridge between using the concrete manipulatives into them being able to solve the problems. For some kids, it is difficult to use the manipulatives. That’s not how they learn, and so we don’t want to force kids to have to use manipulatives if it’s not something that is helpful for them. So we have to remember that manipulatives are one way to think about teaching math.

I think part of the reason that some teachers don’t use them is because it takes a lot of time, it takes a lot of organization, and they also feel that students get too reliant on using manipulatives. One way to think about using manipulatives is that you do it a couple of lessons when you’re teaching a new concept, and then take those away so that students are able to do just the computation part of it. It is true we can’t walk around life with manipulatives in our hands. And I think one of the other reasons that a lot of schools or teachers don’t use manipulatives is because they’re very expensive. And so it’s very helpful if all of the teachers in the school can pool resources and have a manipulative room where teachers can go check out manipulatives so that it’s not so expensive. Teachers have to know how to use them, and that takes a lot of practice.

- Reviews / Why join our community?
- For companies
- Frequently asked questions

## Information Visualization

What is information visualization.

Information visualization is the process of representing data in a visual and meaningful way so that a user can better understand it. Dashboards and scatter plots are common examples of information visualization. Via its depicting an overview and showing relevant connections, information visualization allows users to draw insights from abstract data in an efficient and effective manner.

Information visualization plays an important role in making data digestible and turning raw information into actionable insights. It draws from the fields of human-computer interaction, visual design, computer science, and cognitive science, among others. Examples include world map-style representations, line graphs, and 3-D virtual building or town plan designs.

The process of creating information visualization typically starts with understanding the information needs of the target user group. Qualitative research (e.g., user interviews) can reveal how, when, and where the visualization will be used. Taking these insights, a designer can determine which form of data organization is needed for achieving the users’ goals. Once information is organized in a way that helps users understand it better—and helps them apply it so as to reach their goals—visualization techniques are the next tools a designer brings out to use. Visual elements (e.g., maps and graphs) are created, along with appropriate labels, and visual parameters such as color, contrast, distance, and size are used to create an appropriate visual hierarchy and a visual path through the information.

Information visualization is becoming increasingly interactive, especially when used in a website or application. Being interactive allows for manipulation of the visualization by users, making it highly effective in catering to their needs. With interactive information visualization, users are able to view topics from different perspectives, and manipulate their visualizations of these until they reach the desired insights. This is especially useful if users require an explorative experience.

## Questions related to Information Visualization

There are many types of information visualization . And different types cater to diverse needs. The most common forms include charts, graphs, diagrams, and maps. Charts, like bar graphs, succinctly display data trends. Diagrams, such as flowcharts, convey processes. Maps visually represent spatial information, enhancing geographical insights.

Each type serves a unique purpose, offering a comprehensive toolkit for effective information representation.

Information visualization and data visualization share a connection but diverge in scope. Data visualization centers on graphically representing raw data using charts or graphs. Information visualization extends beyond raw data, embracing a comprehensive array of contextual details and intricate datasets. It strives for a complete presentation, often employing interactivity to convey insights.

Data visualization concentrates on visually representing data points. Conversely, information visualization adopts a holistic approach. It considers the context for deeper comprehension and decision-making.

This video illustrates this concept using a routine example. It highlights the creative process and the importance of capturing and structuring ideas for effective communication.

- Transcript loading…

Information visualization and infographics play unique roles. Human memory is visual, often remembering images and patterns more than raw data. Information visualization capitalizes on this aspect. It simplifies complex data through graphics for better understanding.

This article gives valuable insights into the properties of human memory and their significance for information visualization .

Infographics portray information in engaging formats, often for storytelling or marketing. Both use visuals, but information visualization prioritizes clarity for users and turning data into usable insights. However, the latter focuses on effective communication and engagement.

No, Information Design and data visualization are distinctive in their objectives and applications. Information Design is a broader concept. It helps organize and present information to improve communication in the bigger picture. It considers the text, images, and layout to convey information effectively.

On the other hand, data visualization translates raw data into graphical representations. It extracts meaningful insights and patterns. The approach focuses on visual elements to simplify the analysis of complex datasets.

Information visualization is a process that transforms complex data into easy-to-understand visuals. The seven stages include:

Data collection: Gathering relevant data from diverse sources to form the basis for visualization.

Data analysis: Examining and processing the collected data to identify patterns, trends, and insights.

Data pre-processing: Cleaning and organizing the data to make it suitable for visualization.

Visual representation: Choosing appropriate visualization techniques to represent data accurately and effectively.

Interaction design: Developing user-friendly interfaces that allow meaningful interaction with the visualized data.

Interpretation: Enabling users to interpret and derive insights from the visualized information.

Evaluation: Assessing the effectiveness of the visualization in conveying information and meeting objectives.

This article provides a comprehensive overview of the data analysis process and explores key techniques for analysis.

Information visualization helps people understand data and make decisions. It turns complicated data into easy-to-understand visuals. This makes it easier to see patterns and get a good overall picture. It also helps people communicate by showing information in a visually exciting way. Visualizations empower individuals to interact with data, enhancing engagement and enabling deeper exploration. Additionally, visual representations facilitate easier retention and recall of information.

Data visualization has advantages and disadvantages. One big challenge is misinterpretation. The visualization of data can be misleading if presented inappropriately. It can also lead to false conclusions, especially for those who do not understand the information.

Another major problem is too much information, as this article explains: Information Overload, Why it Matters, and How to Combat It . A crowded or complex visualization can overwhelm users and make communicating difficult.

Also, making good visualizations takes time and skill. This can sometimes be challenging for newbies.

Data visualization is a powerful tool. Creating valuable and impactful visualizations requires a combination of skills. You must understand the data, choose suitable visualization methods, and tell a compelling story . All this requires a good understanding of data and design, as explained in this video.

Interpreting complex data and choosing compelling visualizations can be challenging for beginners. However, leveraging available resources and enhancing skills can simplify data visualization despite the occasional difficulty.

Check out this course to learn more about Information Visualization . The course also explains the connection between the eye and the brain in creating images. It looks at the history of information visualization, how it has evolved, and common mistakes that you must avoid in visual perception.

It will teach you how to design compelling information visualizations and use various techniques for your projects.

## Literature on Information Visualization

Here’s the entire UX literature on Information Visualization by the Interaction Design Foundation, collated in one place:

## Learn more about Information Visualization

Take a deep dive into Information Visualization with our course Information Visualization .

Information visualization skills are in high demand, partly thanks to the rise in big data. Tech research giant Gartner Inc. observed that digital transformation has put data at the center of every organization. With the ever-increasing amount of information being gathered and analyzed, there’s an increasing need to present data in meaningful and understandable ways.

In fact, even if you are not involved in big data, information visualization will be able to help in your work processes as a designer. This is because many design processes—including conducting user interviews and analyzing user flows and sales funnels—involve the collation and presentation of information. Information visualization turns raw data into meaningful patterns, which will help you find actionable insights. From designing meaningful interfaces, to processing your own UX research, information visualization is an indispensable tool in your UX design kit.

This course is presented by Alan Dix, a former professor at Lancaster University in the UK. A world-renowned authority in the field of human-computer interaction, Alan is the author of the university-level textbook Human-Computer Interaction . “Information Visualization” is full of simple but practical lessons to guide your development in information visualization. We start with the basics of what information visualization is, including its history and necessity, and then walk you through the initial steps in creating your own information visualizations. While there’s plenty of theory here, we’ve got plenty of practice for you, too.

## All open-source articles on Information Visualization

Information overload, why it matters and how to combat it.

- 1.1k shares
- 4 years ago

## Visual Representation

## How to Design an Information Visualization

## How to Visualize Your Qualitative User Research Results for Maximum Impact

- 3 years ago

## Preattentive Visual Properties and How to Use Them in Information Visualization

- 5 years ago

## How to Conduct Focus Groups

## The Properties of Human Memory and Their Importance for Information Visualization

- 7 years ago

## Information Visualization – A Brief Introduction

## Visual Mapping – The Elements of Information Visualization

## Guidelines for Good Visual Information Representations

## How to Show Hierarchical Data with Information Visualization

## Information Visualization – An Introduction to Multivariate Analysis

- 8 years ago

## Information Visualization – Who Needs It?

## How to Display Complex Network Data with Information Visualization

## Vision and Visual Perception Challenges

## Information Visualization an Introduction to Transformable Information Representations

## The Principles of Information Visualization for Basic Network Data

## The Continuum of Understanding and Information Visualization

- 6 years ago

## Information Visualization – A Brief Pre-20th Century History

## Information Visualization an Introduction to Manipulable Information Representations

## Open Access—Link to us!

We believe in Open Access and the democratization of knowledge . Unfortunately, world-class educational materials such as this page are normally hidden behind paywalls or in expensive textbooks.

If you want this to change , cite this page , link to us, or join us to help us democratize design knowledge !

## Privacy Settings

Our digital services use necessary tracking technologies, including third-party cookies, for security, functionality, and to uphold user rights. Optional cookies offer enhanced features, and analytics.

Experience the full potential of our site that remembers your preferences and supports secure sign-in.

Governs the storage of data necessary for maintaining website security, user authentication, and fraud prevention mechanisms.

## Enhanced Functionality

Saves your settings and preferences, like your location, for a more personalized experience.

## Referral Program

We use cookies to enable our referral program, giving you and your friends discounts.

## Error Reporting

We share user ID with Bugsnag and NewRelic to help us track errors and fix issues.

Optimize your experience by allowing us to monitor site usage. You’ll enjoy a smoother, more personalized journey without compromising your privacy.

## Analytics Storage

Collects anonymous data on how you navigate and interact, helping us make informed improvements.

Differentiates real visitors from automated bots, ensuring accurate usage data and improving your website experience.

Lets us tailor your digital ads to match your interests, making them more relevant and useful to you.

## Advertising Storage

Stores information for better-targeted advertising, enhancing your online ad experience.

## Personalization Storage

Permits storing data to personalize content and ads across Google services based on user behavior, enhancing overall user experience.

## Advertising Personalization

Allows for content and ad personalization across Google services based on user behavior. This consent enhances user experiences.

Enables personalizing ads based on user data and interactions, allowing for more relevant advertising experiences across Google services.

Receive more relevant advertisements by sharing your interests and behavior with our trusted advertising partners.

Enables better ad targeting and measurement on Meta platforms, making ads you see more relevant.

Allows for improved ad effectiveness and measurement through Meta’s Conversions API, ensuring privacy-compliant data sharing.

## LinkedIn Insights

Tracks conversions, retargeting, and web analytics for LinkedIn ad campaigns, enhancing ad relevance and performance.

## LinkedIn CAPI

Enhances LinkedIn advertising through server-side event tracking, offering more accurate measurement and personalization.

## Google Ads Tag

Tracks ad performance and user engagement, helping deliver ads that are most useful to you.

## Share Knowledge, Get Respect!

or copy link

## Cite according to academic standards

Simply copy and paste the text below into your bibliographic reference list, onto your blog, or anywhere else. You can also just hyperlink to this page.

## New to UX Design? We’re Giving You a Free ebook!

Download our free ebook The Basics of User Experience Design to learn about core concepts of UX design.

In 9 chapters, we’ll cover: conducting user interviews, design thinking, interaction design, mobile UX design, usability, UX research, and many more!

- Our Mission

## The Power of Visualization in Math

Creating visual representations for math students can open up understanding. We have resources you can use in class tomorrow.

When do you know it’s time to try something different in your math lesson?

For me, I knew the moment I read this word problem to my fifth-grade summer school students: “On average, the sun’s energy density reaching Earth’s upper atmosphere is 1,350 watts per square meter. Assume the incident, monochromatic light has a wavelength of 800 nanometers (each photon has an energy of 2.48 × 10 -19 joules at this wavelength). How many photons are incident on the Earth’s upper atmosphere in one second?”

My students couldn’t get past the language, the sizes of the different numbers, or the science concepts addressed in the question. In short, I had effectively shut them down, and I needed a new approach to bring them back to their learning. So I started drawing on the whiteboard and created something with a little whimsy, a cartoon photon asking how much energy a photon has.

Immediately, students started yelling out, “2.48 × 10 -19 joules,” and they could even cite the text where they had learned the information. I knew I was on to something, so the next thing I drew was a series of boxes with our friend the photon.

If all of the photons in the image below were to hit in one second, how much energy is represented in the drawing?

Students realized that we were just adding up all the individual energy from each photon and then quickly realized that this was multiplication. And then they knew that the question we were trying to answer was just figuring out the number of photons, and since we knew the total energy in one second, we could compute the number of photons by division.

The point being, we reached a place where my students were able to process the learning. The power of the visual representation made all the difference for these students, and being able to sequence through the problem using the visual supports completely changed the interactions they were having with the problem.

If you’re like me, you’re thinking, “So the visual representations worked with this problem, but what about other types of problems? Surely there isn’t a visual model for every problem!”

The power of this moment, the change in the learning environment, and the excitement of my fifth graders as they could not only understand but explain to others what the problem was about convinced me it was worth the effort to pursue visualization and try to answer these questions: Is there a process to unlock visualizations in math? And are there resources already available to help make mathematics visual?

I realized that the first step in unlocking visualization as a scaffold for students was to change the kind of question I was asking myself. A powerful question to start with is: “How might I represent this learning target in a visual way?” This reframing opens a world of possible representations that we might not otherwise have considered. Thinking about many possible visual representations is the first step in creating a good one for students.

The Progressions published in tandem with the Common Core State Standards for mathematics are one resource for finding specific visual models based on grade level and standard. In my fifth-grade example, what I constructed was a sequenced process to develop a tape diagram—a type of visual model that uses rectangles to represent the parts of a ratio. I didn’t realize it, but to unlock my thinking I had to commit to finding a way to represent the problem in a visual way. Asking yourself a very simple series of questions leads you down a variety of learning paths, and primes you for the next step in the sequence—finding the right resources to complete your visualization journey.

Posing the question of visualization readies your brain to identify the right tool for the desired learning target and your students. That is, you’ll more readily know when you’ve identified the right tool for the job for your students. There are many, many resources available to help make this process even easier, and I’ve created a matrix of clickable tools, articles, and resources .

The process to visualize your math instruction is summarized at the top of my Visualizing Math graphic; below that is a mix of visualization strategies and resources you can use tomorrow in your classroom.

Our job as educators is to set a stage that maximizes the amount of learning done by our students, and teaching students mathematics in this visual way provides a powerful pathway for us to do our job well. The process of visualizing mathematics tests your abilities at first, and you’ll find that it makes both you and your students learn.

- Architecture and Design
- Asian and Pacific Studies
- Business and Economics
- Classical and Ancient Near Eastern Studies
- Computer Sciences
- Cultural Studies
- Engineering
- General Interest
- Geosciences
- Industrial Chemistry
- Islamic and Middle Eastern Studies
- Jewish Studies
- Library and Information Science, Book Studies
- Life Sciences
- Linguistics and Semiotics
- Literary Studies
- Materials Sciences
- Mathematics
- Social Sciences
- Sports and Recreation
- Theology and Religion
- Publish your article
- The role of authors
- Promoting your article
- Abstracting & indexing
- Publishing Ethics
- Why publish with De Gruyter
- How to publish with De Gruyter
- Our book series
- Our subject areas
- Your digital product at De Gruyter
- Contribute to our reference works
- Product information
- Tools & resources
- Product Information
- Promotional Materials
- Orders and Inquiries
- FAQ for Library Suppliers and Book Sellers
- Repository Policy
- Free access policy
- Open Access agreements
- Database portals
- For Authors
- Customer service
- People + Culture
- Journal Management
- How to join us
- Working at De Gruyter
- Mission & Vision
- De Gruyter Foundation
- De Gruyter Ebound
- Our Responsibility
- Partner publishers

Your purchase has been completed. Your documents are now available to view.

## 11. On the nature and role of visual representations in knowledge production and science communication

From the book science communication.

- Luc Pauwels

This chapter presents a conceptual framework for a more thorough and conscious investigation of visual representational practices within the different discourses of scientific data representation, conceptualization, and scholarly and public communication. While several scholars have pointed at the great diversity of visual representations and their uses, few systematic attempts have been made at devising a typology of uses or at producing an encompassing framework for increasing insight in this complex domain. Such a taxonomic attempt however may form the basis or starting point of a more conscious practice and an essential part of a program aimed at heightening both social and natural scientists’ visual literacy skills as well as those of science communicators.

- X / Twitter

## Supplementary Materials

Please login or register with De Gruyter to order this product.

## Chapters in this book (37)

## Why is Visualization Important for Learning Mathematics?

By charlene marchese.

How often do we ask students to show their mathematical thinking or explain an answer using words, pictures, or diagrams? If you’re like most of us, the answer to that question is probably “Very often”!

But what does it mean to express mathematical ideas and processes through these modalities? What is our expectation that students’ work contains language that connects to diagrams and pictures? Are representations of thinking created after a solution is found, or are pictures, diagrams, and language part of developing a solution? To explore these questions, let’s first take a close look at four mathematical tasks, each requiring increasingly complex conceptual understandings, and the visual representations and language that can support understanding these tasks.

## Examples in Action

Example 1: an early childhood story problem.

Many children are introduced to story problems like this. For young learners, adding one on to a number or collection of objects is a complex concept and tackling a solution using a concrete model is a natural place to start.

If given a container of red and blue bears, a student could line up three red bears, place one blue one at the end of the line, and then count the four bears. To describe how they came up with their solution, a student could say, “I took three red bears and then one blue bear. Now I have 4 bears.”

A semi-concrete representation of a solution could be a drawing of three red circles and one blue circle, and the student then counts the four circles. For older learners, a symbolic or abstract representation shows the solved equation 3 + 1 = 4.

Visual strategies can also be used to support solving more complex problems, as shown in the next several examples. As you read each one, take notice of the images that come to mind.

## Example 2 : An Elementary Grade Expression

One way to visualize this problem is to think about jumps on an open number line where a learner employs the critical understanding of decomposing numbers. Starting at 45, the larger number, and moving to the right, one could add 28 by jumping 2 tens (or 20) to land on 65. Next, one could jump 5 and land on the friendly number 70. Finally, one could jump 3 to land on 73. Landing on 73 means the sum of 45 and 28 is 73. In describing their work, a student could say, “I started with the higher number 45, jumped 20, then jumped 5, and then jumped 3, to get to 73. So 45 + 28 is equal to 73.”

## Example 3: A Middle School Exploration

Starting with the understanding that the square root of a number is the side length of its square, a learner can visualize the approximate square that is created with a non-perfect square number such as 72. Since arranging 72 tiles into a square is impossible, one could think about making one square with a number that is less than 72 and one that is greater than 72, such as 64 and 81. The square root of 64 is 8, and the square root of 81 is 9. Since 72 is about halfway between 64 and 81, one can approximate the side length or the square root of 72 to be about 8.5. A student could describe their work by saying, “I can use the two square numbers that 72 is in between to estimate the square root of 72.”

## Example 4: An 8th Grade or High School Exploration

For this question, we explore and apply the Pythagorean theorem, which states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse. By building a model of a triangle, either with tiles or by sketching one on graph paper, the student can visualize the right triangle and the squares that can be created by each side length. The leg with a length of 3 units would create a square with an area of 9 square tiles, and the leg with a length of 4 units would create an area of 16 square tiles. The sum of the two squares is 25 square tiles, which would have a side length (or square root) of 5 units. Therefore, a right triangle with leg lengths of 3 units and 4 units would have a hypotenuse of 5 units.

The Pythagorean theorem can be (1) demonstrated concretely using square tiles, (2) shown in a semi-concrete way by sketching and labeling shapes on graph paper, or (3) represented abstractly by the theorem, which can be used to solve for either the missing value of a leg or the hypotenuse of a right triangle.

Connecting both the concrete and semi-concrete models to the Pythagorean theorem deepens students’ understanding of the theorem and its relationship to the physical world. A student making the connection between the concrete and abstract could say, “I built a square for each side of the triangle and determined that the sum of the squares of the legs of the triangle was equal to the square of the hypotenuse.”

There are multiple ways of visualizing mathematics to solve the above questions. Did you use the same visual representations illustrated here, or did you have a different way of visualizing? Were you able to make sense of the visual representations shown here? How do these representations enhance the understanding of the mathematical concept?

The examples illustrate that visualizing mathematics is both a support for students who struggle with a range of math concepts and a critical component of learning mathematics. From young children using concrete objects, like their fingers, to understand counting to college students using representational graphs to grasp calculus, visualization provides an avenue to understand mathematics for all students.

## Developing Visualization Skills

How do we help students develop visualization skills, especially with those whose prior math classroom experience may not have included visualizing? In the book Routines for Reasoning (Kelemanik et al., 2016) the authors explore a Recognizing Repetition routine designed to develop this very skill. Students are asked to build or draw a sequence of figures and then to analyze how the figures are growing by focusing on the repetition, looking specifically at what changes and what stays the same. Students use their analysis to determine the number of tiles needed to build the 10th figure and then determine a mathematical rule that can be applied to determine the number of tiles for any figure number.

Here is an example of a growing pattern that students can explore.

There are multiple ways of visualizing mathematics to solve the above questions. Are you able to make sense of the visual representations shown? Do you use the same ones illustrated here, or do you have a different way of visualizing? How do these representations enhance one’s understanding of the mathematical concept?

Based on this visualization of the growing pattern, students could determine a relationship between each part of the shape and its figure number. For example, each section of pink tiles is one number less than the figure number. To determine how many tiles would be in the 10th figure, students would know that each section of pink tiles would have 9 tiles (one less than the Figure 10). With 2 sets of pink tiles (9 + 9), plus the blue tile that is constant in each figure (1), students could add 9 + 9 + 1 = 19. Making a generalized rule from this line of thinking, a student might say in words, “Take one away from the figure number, double it and add one,” and then connect their words to the rule written symbolically 2( x – 1) + 1, with x representing the figure number.

Another student might have said, “Double the figure number and subtract 1,” or write it symbolically as “2 x –1.” Can you visualize how they determined this rule from the model? Can you determine a general rule by visualizing the growing figures in a different way?

What about the students who initially cannot visualize how to determine the 10th figure? How can teachers support students who may not be able to initially see how the figure grows and/or how to state a generalization? To support this learner, it is necessary for the teacher to listen to students’ responses and be ready to ask questions based on responses. Questions like the ones below may be helpful to ask:

- Can you tell me how you built the first 4 figures that are displayed? Did you notice anything changing? Was there anything that stayed the same?
- Can you build what you think Figure 5 would look like and explain your thoughts?
- If we skip a few figures, can you use what you noticed about how the figures are growing to build Figure 10?
- Is there a way we can use the figure number to determine how many tiles it took to build Figure 3 and then 4? Could these ideas be used to determine how many tiles are in Figure 10 or Figure 100? Could it be sketched out?
- Could we describe the process to find the number of tiles in any figure?

Notice how the questions refer back to the concrete figures. That is, there is a relationship between the visuals made with materials and the language used . Teacher questioning can also enhance the mathematical practice of “Construct viable arguments and critique the reasoning of others” (Common Core State Standards Initiative, n.d.) and provide a vehicle for student-to-student engagement in mathematical discourse. A teacher could consider asking this series of questions: “Another group came up with the idea that if they doubled the figure number and subtracted 1, they would always get the number of tiles for that figure. Does that work? Will it always work? How do you think they determined this?”

The instructional goal of this routine is focused on students’ process of visualizing how the figures are growing, with an emphasis on what changes and what stays the same. Young children can begin to develop this ability by building and discussing age-appropriate pattern sequences with increasing complexity as they move through the grades. As students move into the upper elementary, middle, and high schools, they build on their ability to identify patterns and to generalize these patterns, which can be expressed in words and then with symbols. Explicitly making the connections between the physical pattern, the visualization of the changes in the pattern, and the symbolic representation of the pattern is a cycle that builds mathematical knowledge with understanding.

## Connecting the Concrete, Semi-Concrete, and Abstract

From teacher education courses in college to professional development sessions in the field, the message is that students learn mathematics by starting with the concrete and then moving to the abstract. While this is a powerful message, it is important to take a closer look at the learning process.

There is an important step of semi-concrete or visual representation between the concrete and the abstract. It could be argued that this is the step we are asking students to describe when we ask them to show their work with words, pictures, and diagrams. These three steps—concrete, semi-concrete (visual representations), and abstract or symbolic—are not linear. Rather they repeatedly interact. Throughout a unit of study, students’ experience should be one where they go back and forth among these phases of representation with a focus on making the connection between them. It is the students’ understanding of the connection between the concrete, semi-concrete, and abstract that allows for deep knowledge of the content. We each encounter a whole class of students with different learning styles and ways of thinking. Therefore, all three of these methods always need to be available to all students with a continued focus on their interconnectedness.

A plea to all teachers reading this: With the pressures of test scores, pacing charts, and unfinished learning from the pandemic, many times we feel pulled to emphasize the abstract and only use concrete representations for students who have perceived challenges in learning mathematics. This blog post is making the case to reimagine the idea of moving from the concrete to the abstract to not only include the semi-concrete visual representation but to reconceptualize mathematics instruction as a continual interplay of the concrete, semi-concrete, and abstract representations of mathematical ideas for all students.

Here are a few suggestions:

- Be sure that concrete materials are always present and available for student use.
- Refer to concrete materials and connect them to the visual representations and abstract thinking of all students throughout the unit of study.
- Have an expectation that “show your work” goes beyond the symbolic representation to include pictures, a model, and/or words to explain solutions.
- As teachers, complete the mathematical tasks yourselves, a key component of Math for All, to explore and understand the various physical models, visual representations, and symbolic processes that can be developed in support of the mathematical content.
- Value the concrete models and pictures of the mathematical content in a similar way to how science classes value the physical materials and pictures of the science content.
- Provide opportunities for students to explore mathematics visually.

COMMON CORE STATE STANDARDS FOR MATHEMATICS . (n.d.).

Kelemanik, G., Lucenta, A., Janssen Creighton, S., & Lampert, M. (2016). Routines for reasoning: fostering the mathematical practices in all students . Heinemann.

The contents of this blog post were developed under a grant from the Department of Education. However, those contents do not necessarily represent the policy of the Department of Education, and you should not assume endorsement by the Federal Government.

Math for All is a professional development program that brings general and special education teachers together to enhance their skills in planning and adapting mathematics lessons to ensure that all students achieve high-quality learning outcomes in mathematics.

## Our Newsletter Provides Ideas for Making High-Quality Mathematics Instruction Accessible to All Students

Sign up for our newsletter, recent blogs.

- Social Justice in the Math Classroom May 30, 2024
- Parents and Teachers as Co-Constructors of Children’s Success as Mathematical Learners May 1, 2024
- The Problem with Word Problems March 11, 2024
- Honoring Diversity: What, why, and how? February 22, 2024
- Looking at a Student at Work January 3, 2024

Team & Partners

Testimonials

Newsletter Signup

## Using Visual Representations in Mathematics

On this page:, drawing on technology tools, in the classroom, online resources for visual representations, introduction.

All students can benefit from using visual representations, although struggling students may require additional, focused support and practice. Visual representations are a powerful way for students to access abstract mathematical ideas. To be college and career ready, students need to be able to draw a situation, graph lists of data, or place numbers on a number line. Developing this strategy early during the elementary grades gives students tools for engaging with—and ways of thinking about—increasingly abstract concepts. Over time, they will work toward developing Common Core Standards for Mathematical Practice:

- CCSS.Math.Practice.MP2 (opens in a new window) Reason abstractly and quantitatively.
- CCSS.Math.Practice.MP4 (opens in a new window) Model with mathematics.
- CCSS.Math.Practice.MP5 (opens in a new window) Use appropriate tools strategically.

WAYS TO SUPPORT STUDENTS

Helping students choose the “right” visual representation often depends on content and context. In some contexts, there are multiple ways to represent the same idea. Show your students a variety of examples in order to demonstrate when (and why) they should choose each one (see UDL Checkpoint 2.5: Illustrate through multiple media (opens in a new window) ). Consider how you could use the following strategies to support your students:

- Check for understanding to determine a starting point. For example, you could ask the following questions: Why do you think that? How do you know that is correct? How does that picture represent the problem? Can you explain your answer? Is there another way you could do that?
- Ask students about features of the visual representation (including labels and scales, when appropriate).
- As students create visual representations, ask questions to ensure that they understand all the features of the representations. Prompt students to focus on the information the visual representations provide.
- When possible, include alternative visual representations and discuss the similarities and differences between them.
- Vary the shapes and orientations of representations so that students focus only on the important features as they learn about the objects and situations represented.
- Show your students a specific representation—a graph or a table—that is missing an important feature. Ask them to identify the missing feature.

New technologies are constantly expanding our ability to visualize data and explain mathematical concepts. For teachers looking to incorporate technology into the classroom, using virtual manipulatives (instead of physical ones) can be a good start. Students can begin with simple graphical representations of mathematical concepts and then work toward more complex modules that require them to create the data or work within a system of rules, like a game. Infographics (opens in a new window) —visualizations that are designed to communicate complex information effectively—have become increasingly popular. They can be used to “tell a story” with numbers, such as international democracy rankings (opens in a new window) or climate change impacts (opens in a new window) . Learning to create infographics gives students additional tools to communicate data and other quantitative information.

3D printing is a technology that, until recently, has been too expensive to make use of in a classroom. However, thanks to falling prices, they have now started to appear in high schools and it may not be long before elementary schools and middle schools also embrace this technology. 3D printing allows you to create solid, three-dimensional models from a digital design. You can explore what others have created (opens in a new window) to get a sense of what is possible. Imagine having students design and create their own mathematical models and manipulatives!

For more ideas on using technology to create visual representations, visit the Tech Matters blog (opens in a new window) or PowerUp’s Pinterest page (opens in a new window) . You can also check out the “ Virtual Manipulatives (opens in a new window) ” video, which supports students’ use of visual representations.

Geometry lends itself naturally to teaching with visual representations, as can be seen in Ms. Richardson’s Grade 6 class. So far, students have learned how to classify different quadrilaterals and triangles, and they are beginning to decompose polygons. They have also started using software (e.g., GeoGebra (opens in a new window) ) that can support their understanding by emphasizing the connections between mathematical language and visualization.

Ms. Richardson’s lesson objective is to have students decompose polygons into triangles, rectangles, and trapezoids. She will address two s Common Core State in this lesson:

- CCSS Math 6.G.1 (opens in a new window) Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
- CCSS Math MP4 (opens in a new window) Model with mathematics.

Ms. Richardson has students work on these standards within the context of a real-world example—a painting by the artist Sol LeWitt.

Sol LeWitt. Wall Drawing #1113. On a wall, a triangle within a rectangle, each with broken bands of color, 2003. Hirshhorn Museum and Sculpture Garden, Smithsonian Institution.

Students will build on their existing technology skills and create a model of this work, decomposing polygons and creating their own virtual LeWitt in the process. Ms. Richardson’s lesson plan is organized into three sections: a warm-up exercise to review concepts, the main learning task, and a closing discussion and assessment.

## Lesson plan

Launch | |
---|---|

Learning Task | |

Closure |

This article draws from the PowerUp WHAT WORKS (opens in a new window) website, particularly the Visual Representations Instructional Strategy Guide (opens in a new window) . PowerUp is a free, teacher-friendly website that requires no log-in or registration. The Instructional Strategy Guide on visual representations includes a brief overview with an accompanying slide show; a list of the relevant mathematics Common Core State Standards; evidence-based teaching strategies to differentiate instruction using technology; short videos; and links to resources that will help you use technology to support mathematics instruction. If you want to dig deeper into the research foundation behind best practices in the use of virtual manipulatives, take a look at our Tech Research Brief (opens in a new window) on the topic. If you are responsible for professional development, the PD Support Materials (opens in a new window) provide helpful ideas and materials for using the resources. Want more information? See PowerUp WHAT WORKS (opens in a new window) .

## Liked it? Share it!

Visit our sister websites:, reading rockets launching young readers (opens in a new window), start with a book read. explore. learn (opens in a new window), colorín colorado helping ells succeed (opens in a new window), adlit all about adolescent literacy (opens in a new window), reading universe all about teaching reading and writing (opens in a new window).

An official website of the United States government

The .gov means it’s official. Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

The site is secure. The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

- Publications
- Account settings

Preview improvements coming to the PMC website in October 2024. Learn More or Try it out now .

- Advanced Search
- Journal List
- HHS Author Manuscripts

## The Role of Visual Representations in College Students’ Understanding of Mathematical Notation

Developing understanding of fractions involves connections between non-symbolic visual representations and symbolic representations. Initially, teachers introduce fraction concepts with visual representations before moving to symbolic representations. Once the focus is shifted to symbolic representations, the connections between visual representations and symbolic notation are considered to be less useful, and students are rarely asked to connect symbolic notation back to visual representations. In two experiments, we ask whether visual representations affect understanding of symbolic notation for adults who understand symbolic notation. In a conceptual fraction comparison task (e.g., Which is larger, 5 a or 8 a ?), participants were given comparisons paired with accurate, helpful visual representations, misleading visual representations, or no visual representations. The results show that even college students perform significantly better when accurate visuals are provided over misleading or no visuals. Further, eye-tracking data suggest that these visual representations may affect performance even when only briefly looked at. Implications for theories of fraction understanding and education are discussed.

Early on, students are introduced to many mathematical concepts using visual representations. Such visual representations are typically non-symbolic representations that do not contain literal numbers and are thought to be more intuitive for students ( Opfer & Siegler, 2012 ). For example, the very beginnings of fraction “concepts” are introduced to students as young as kindergarten age informally through visual representations (e.g., “pie” or “circle” representation; Common Core State Standards Initiative, 2014 ; Scott-Foresman & Addison-Wesley, 2011 ). By introducing mathematical concepts with these visual representations, students can avoid the confusion that often comes when learning the conventions of the symbolic number system (e.g., learning the words that map to the numbers). Thus, using visual representations and other non-symbolic systems can facilitate and provide bootstrapping for the later-developing symbolic number system (e.g., Condry & Spelke, 2008; LeCorre & Carey, 2007; Opfer & Siegler, 2012 ).

With the use of visual representations, students are able to display basic understandings of division and partitioning from an early age. Preschoolers are able to evenly divide or partition a set of items among two or three people by using distributive counting ( Frydman & Bryant, 1988 ). Additionally, when given the chance to visually compare scenarios where the same number of items are shared between a larger or smaller number of people, early elementary school students understand that sharing between a greater number of people (higher denominator) would result in a smaller share for each person ( Sophian, Garyantes, & Change, 1997 ). Thus, non-symbolic representations such as sharing processes and visual cues allow young students to demonstrate conceptual understanding of fractions and the relation between numerators and denominators ( Empson, 1999 ; Sophian et al., 1997 ). Additionally, visual representations even allow students to show understanding of basic fraction arithmetic ( Mix, Levine, & Huttenlocher, 1999 ). Visual representations may thus play an important role in students’ conceptual understanding of fractions.

Fractions present both a symbolic and a conceptual challenge for students. Fractions are symbolically notated with a bipartite structure with a separate numerator and denominator—rather than a unitary symbol—and fractions are the only number type that simultaneously represents a magnitude and a division relationship between the numerator and denominator. Indeed, a large body of research has pointed to misconceptions and errors that children and adults make with symbolic fraction notation, despite a seemingly well-developed intuitive understanding of fractions when using visual representations (e.g., Ni & Zhou, 2005; Stafylidou & Vosniadou, 2004 ; Stigler, Givvin, & Thompson, 2010 ; Vamvakoussi & Vosniadou, 2010 ). However, studies have also shown that young students are able to successfully divide a certain number of items among people only when provided with visual cues and fail to do so when the same problem is presented only with symbolic notation and no visual cues ( Squire & Bryant, 2002 ; 2003 ). Therefore, though students have difficulty transferring their understanding of division and fraction concepts from the intuitive visual representations to the literal symbols of fraction notation, being provided with visual representations can facilitate the transfer of division and fraction concepts to the literal symbolic fraction notation.

Despite the seeming usefulness of visual representations, once students do learn the symbolic notation system of fractions, teachers rarely go back to the visual representations, assuming that such representations have outlived their usefulness. Instead, more complex fraction concepts and algorithms, as well as extensions into algebra, are typically developed using the more precise system of mathematical notation alone, without reference to visual representations ( Borko, Eisenhart, Brown, Underhill, Jones, & Agard, 1992 ; Chao, Stigler, & Woodward, 2000 ; Kieran, 1992 ; Uttal, O’Doherty, Newland, Hand, & DeLoache, 2009 ). It is unclear, however, whether the connections between visual representations and symbolic notation are no longer helping students after they learn the symbolic notation of fractions.

There is some evidence that even among college educated adults, visual representations of fractions may facilitate representations of symbolically notated magnitudes. For example, students have difficulty representing magnitudes of fractions when presented symbolically and without visual cues ( DeWolf, Grounds, Bassok, & Holyoak, 2014 ). However, though adult students may have difficulty interpreting magnitudes of fractions, the bipartite symbolic notation of fractions have been found to be useful for more relationally rich tasks that require students to interpret visually represented ratios, especially when represented with discrete visual representations ( DeWolf, Bassok, & Holyoak, 2015a ; Rapp, Bassok, DeWolf, & Holyoak, 2015 ). Therefore, students may find a visually represented context for fractions to be helpful in interpreting what fractions are meant to represent.

It is also possible that when students move beyond a basic understanding of fractions as representations of magnitude, extensions of the concepts could still benefit from connections to visual representations. Stigler et al. (2010) asked community college developmental mathematics students to judge which of two fractions is larger, assuming that a is a positive whole number: a 5 or a 8 . Students performed at chance on the task, indicating an inability to extend their basic understanding of fractions as magnitudes to a more conceptual situation. However, students who were able explain their answers by referencing a non-symbolic representation (e.g., referring to some quantity, a , being divided into different numbers of pieces), were always led to the correct answer. Thus, although connections to visual representations might be ignored as students progress through the mathematics curriculum, such connections may still be activated when students are asked to make more conceptual judgments and to explain such judgments.

Indeed, asking students to generate explanations for their thinking has proven to be an important tool in better understanding how students think differently about fractions depending on the context ( Fazio, DeWolf & Siegler, 2016 ; Stigler et al., 2010 ). For example, Fazio et al. (2016) found that adults spontaneously use a variety of different types of visual representations or cues to help think about the magnitudes of fractions (e.g., a ¼ measuring cup is smaller than a ⅓ measuring cup). Similarly, Vosniadou and colleagues ( Stafylidou & Vosniadou, 2004 ; Vamvakoussi & Vosniadou, 2004 ) have looked at middle school and high school student explanations of fractions. These analyses revealed important misconceptions about fractions and important insights about how these change over time. Such explanations help to identify the types of strategies people use for thinking about fraction magnitudes abstractly and conceptually.

The current study thus examines the extent to which visual representations of fractions influence college students who already have an understanding of the symbolic notation of fractions. When offered the chance to view visual representations, do such students use them at all, or focus only on the more precise symbolic notation of fractions? Many previous studies have tested fraction understanding with traditional magnitude comparison tasks (Schneider & Siegler, 2010; Bonato, Fabbri & Umilta, 2007; DeWolf, et al., 2014 ). A primary goal of the current study was to test whether a conceptual understanding of fractions relates to their role in a division relationship. Therefore, in two experiments, students were given fraction comparisons in the form of algebraic expressions. Students were asked to compare abstract fraction expressions (e.g., “Which fraction is larger, 5 a or 8 a ?”) when paired with accurate, helpful visual representations that matched the expression or misleading, unhelpful visual representations that did not match the expression. Importantly, in this task, students must have a conceptual understanding of the relative sizes of fraction components (numerators and denominators), division, and variables. Though a simple strategy like “plugging in” a number for a is certainly possible, students must still conceptualize the division relationship between the numerator and denominator. The hypothesis is that students will perform better when accurate visual representations are provided than when misleading visual representations are provided. We also make use of eye tracking technology to assess the extent to which students’ visual attention to the visual representations during the decision-making process may influence their performance on the fraction comparison problems. Additionally, though the main focus of the current study was on college level students’ performance on a fraction comparison task, we also gave participants a traditional magnitude comparison task to test whether students’ understanding of magnitudes—when expressed solely with symbolic fraction notation—is related to their performance on the fraction comparison task.

## Experiment 1

The primary goal of Experiment 1 was to examine whether accurate visual representations of fractions may help students’ performance on a fraction comparison task. If visual representations—and visual attention to visual representations—indeed affect students’ performance on fraction comparison problems, students should have higher accuracy on problems that are presented with accurate, helpful visual representations and have lower accuracy on problems that are presented with misleading, unhelpful visual representations. Additionally, a secondary goal was to characterize students’ strategies in solving fraction comparison problems and examine whether students could discriminate between accurate visual representations and misleading visual representations.

## Participants

Thirty-six undergraduate students participated (n female =18). Participants were between the ages of 18.46 and 28.04 years ( M =21.08, SD =2.03) and were students enrolled at a selective American university. Four participants’ data were excluded from analyses for the following reasons: poor eye-tracking calibration (n=1), reaction times that were more than two standard deviations from the mean (n=1), lack of responses during one entire task (n=1), and experimenter error (n=1). The final sample included 32 participants (n female =16). None of the participants were majoring or minoring in mathematics or a math-related field.

Stimuli were presented on a ViewSonic VX2268wm monitor with a 47.4 cm by 29.6 cm display (resolution: 1680×1050 pixels). Participants were seated approximately 60 cm from the display. Eye movement data were collected via an SR Eyelink 1000 eye tracker, and eye movements were recorded at 500 Hz with spatial accuracy of approximately 0.5-1°. Using Experiment Builder software, each participant’s point of gaze was calibrated with a series of dynamic circular stimuli shown at five points on the screen (top middle, bottom middle, left center, right center, center).

## Materials and Procedure

Four tasks were used in this experiment, in the following order: (1) Traditional Magnitude Comparisons, (2) Fraction Comparisons, (3) Fraction Comparison Explanations, and (4) Visual Representation Comparisons. Each task was introduced by an instruction slide that detailed what the participant was to do in that particular task. All study stimuli were created using Adobe Photoshop.

## Traditional Magnitude Comparisons

Participants’ understanding of magnitudes when expressed solely with symbolic fraction notation was tested using a Traditional Magnitude Comparison task. Participants saw a series of 10 different fractions (e.g., 35 54 , 20 97 , 5 9 ) and were asked to compare each fraction to ⅗ ( DeWolf et al., 2014 ). The 10 magnitude comparison problems were displayed in the middle of the screen, and the order in which participants were presented with the 10 fractions was randomized for each participant. Participants were given up to 120 seconds to respond to each problem and responded via mouse click: a left mouse click to indicate that the fraction was less than ⅗, and a right mouse click to indicate that the fraction was greater than ⅗. Participants’ performance on these traditional magnitude comparison problems were used to evaluate whether understanding of magnitudes expressed with symbolic fraction notation was related to performance on the more conceptual Fraction Comparisons task (below).

## Fraction Comparisons with Visual Representations

Participants were presented with a series of 40 fraction comparison problems, paired with visual representations of the fractions in the problem ( Figure 1 ). Each fraction comparison problem contained two fractions with an unknown variable ( a, b, c, x, or y ); for each problem, participants were asked to identify which fraction was larger (e.g., “Which is larger, a 5 or a 8 ?”). For every trial, a visual representation was provided for each of the fractions in the comparison. Half of the visual representations accurately represented the fractions (“accurate visual representations;” Figures 1a and 1b ) and half of the visual representations represented the fractions in a misleading way (“misleading visual representations;” Figure 1c and 1d ).

Example stimuli of different trial types in the Fraction Comparison task. Accurate (a, b) and misleading (c, d) visual representations were provided with common numerator (a, c) and common denominator (b, d) problems.

Each visual representation consisted of a simple bar representation composed of discrete parts. Each bar representation had the same number of discrete parts as the number in the fraction. Bar representations with discrete parts were used because adults show a preference for discrete visual representations for fractions over continuous representations such as circle graphs or pie charts ( Rapp et al., 2015 ). For example, the problem “Which is larger, a 5 or a 8 ?” would be shown with one bar representation composed of five discrete parts (corresponding to a 5 ) and another bar representation composed of eight discrete parts (corresponding to a 8 ). When this fraction comparison problem was paired with two bar representations of different lengths (i.e., a misleading representation for a common denominator problem), each of the discrete parts in both bar representations were 100×100 pixels and had 6 pixel borders. When this fraction comparison problem was paired with two bar representations of the same length (i.e., an accurate representation for a common denominator problem), the bar representation with more discrete parts (i.e., a 8 in this example problem) had 100×100 pixel discrete parts and 6 pixel borders; the bar representation with fewer discrete parts (i.e., a 5 in this example problem) had discrete parts that were stretched evenly to make the entire bar representation match the length of the bar representation with more discrete parts, but each discrete part still had 6 pixel borders around it. On an instruction slide, participants were told, “You will be presented with math questions that will ask you to compare two fractions. Please answer these fraction comparison problems. In all problems, the letters ( x, y, a, b, c ) represent positive, whole numbers (e.g., 1, 2, 3, 4, 5,…). You will also see visual representations of these fractions. Please look at each visual representation before you answer the fraction comparison problem.” Participants were given up to 120 seconds to respond to each fraction comparison problem and responded to each problem via mouse click, clicking the left button to select the first fraction (e.g., a 5 ) or the right button to select the second fraction (e.g., a 8 ).

There were four conditions in this task, and all participants were presented with 10 trials of each condition. Two different fraction types (common numerator fractions: a 5 , a 8 ; common denominator fractions: 5 a , 8 a ) and two different visual representation types (accurate visual representation, misleading visual representation) were combined to create the four different conditions: (1) common numerator fractions with accurate visual representations, (2) common numerator fractions with misleading visual representations, (3) common denominator fractions with accurate visual representations, and (4) common denominator fractions with misleading visual representations. Trials were randomized for each participant such that no two participants were presented with the same order of problems.

## Fraction Comparison Explanations

Participants were presented with one trial of each condition from Fraction Comparisons (for a total of four trials in this task). In this task, participants were again presented with fraction comparison problems and asked to identify which of the two fractions was larger; participants solved each problem and responded with mouse clicks in the same way as in the Fraction Comparisons task. After solving the fraction comparison problem, however, participants were also asked to verbally explain why they believed their answer to be correct. Verbal explanations were audio-recorded using Experiment Builder software and later transcribed for analysis. The order of trials was fixed for all participants, and all participants were asked to solve the following problems in the following order: (1) a 7 versus a 4 with an accurate visual representation, (2) a 3 versus a 5 with a misleading visual representation, (3) 6 a versus 9 a with an accurate visual representation, and (4) 5 a versus 4 a with a misleading visual representation.

## Visual Representation Comparisons

Participants were presented with a fraction comparison problem and both the accurate and misleading visual representations ( Figure 2 ). Participants were asked to identify—using mouse clicks—the visual representation most helpful for solving the fraction comparison problem; left mouse clicks corresponded to the visual representations on the left side of the screen and right mouse clicks corresponded to the visual representations on the right side of the screen. Unlike previous tasks in this study, this task instructed participants to look at and compare the two visual representations and select the visual representation that they felt was more useful in solving the fraction comparison problem. Participants were then instructed to verbally explain why they thought the visual representation they selected was more useful for solving the fraction comparison problem. Verbal explanations were again audio-recorded using Experiment Builder software and later transcribed for analysis. The same two problems—a common numerator problem ( a 7 versus a 10 ), followed by a common denominator problem ( 3 a versus 2 a )—were presented in the same order to all participants. The side of the screen on which the accurate and misleading visual representations were presented was counterbalanced across participants.

Example stimulus from the Visual Representation Comparisons task. Fraction comparison problems were shown with both the accurate and misleading visual representations. Participants were asked to identify which visual representation was most helpful for solving the fraction comparison problem and explain why they felt that visual representation was most helpful.

## Results and Discussion

The primary goal of this experiment was to examine how visual representations of fractions might facilitate college students’ performance on a fraction comparison task. We first examined the distribution of students’ accuracy on the traditional magnitude comparison task and fraction comparison task. Students’ accuracy on the traditional magnitude comparison task was normally distributed, and students correctly answered an average of 59.7% of trials ( SD =1.18%, range=40-80%). On the fraction comparison task, students correctly answered an average of 86.40% of trials ( SD =18.4%, range=50-100%). However, a histogram of students’ accuracy on the fraction comparison task revealed a bimodal distribution: 7 students responded correctly on 50-60% of trials, and 25 students responded correctly on 80-100% of trials. Because most effects did not differ when only high-performing students’ data were examined, all analyses include all 32 participants.

To examine whether visual representations of fractions facilitated students’ accuracy on the fraction comparison task, a 2 (fraction type: common numerator vs. common denominator) × 2 (visual type: accurate vs. misleading visual) repeated-measures ANOVA was conducted. A significant main effect of visual type was found, such that students had higher accuracy when the fraction comparison problems were paired with accurate visuals ( M =92.65%, SD =1.32%) than with misleading visuals ( M =80.15%, SD =2.85%), F (1, 31)=8.23, p =.007, η 2 =.210. No other significant main effects or interactions were found. These results suggest that visual representations of fractions can influence students’ accuracy on fraction comparison problems, such that accurate visual representations can improve students’ accuracy.

Response times (RTs) on trials in which students responded correctly to the fraction comparison problem were examined as well. Log transformed RTs were entered into a 2 (fraction type: common numerator vs. common denominator) × 2 (visual type: accurate vs. misleading visual) repeated-measures ANOVA, which revealed no significant main effects or interactions (all p s>.05). These results suggest that the amount of time students took to respond to fraction comparison problems did not differ by the fraction type or visual type of the problem.

We measured students’ visual attention to further examine how visual representations of fractions might facilitate college students’ performance on fraction comparisons. We defined two areas of interest (AOIs) surrounding each of the two fractions and each of the corresponding visual representations on the screen. AOIs of fractions were 72×102 pixels, and AOIs of visual representations were the size of the entire visual representation with an extra 6 pixels around the entire visual representation (e.g., if a visual representation had three 100×100 pixel discrete parts with 6 pixel borders, then the entire visual representation was 324×100 pixels and the AOI was 330×106 pixels). A paired-samples t-test comparing students’ proportion of time spent looking to the visual representation versus fractions revealed students looked significantly longer at fractions ( M =.37, SD =.58) than visual representations ( M =.12, SD =.14), t (31)=2.27, p =.03. However, a 2 (fraction type: common numerator vs. common denominator) × 2 (visual type: accurate vs. misleading visual) repeated-measures ANOVA examining students’ proportion of time spent looking to visual representations on different trial types revealed no significant main effects or interactions (all p s>.05), suggesting that attention to the visual representations did not differ as a function of trial type. Additionally, analyses of the number of fixations students made to each AOI revealed similar results: students made significantly more fixations to fractions ( M =3.69, SD =2.25) than visual representations ( M =2.71, SD =2.65), t (31)=2.11, p =.04, and students’ fixations to visual representations did not differ as a function of trial type (all p s>.05). Altogether, these results—in combination with the results from students’ accuracy on fraction comparison problems—suggest that though students did not visually attend to the visual representation as much as they did to the fractions, students’ accuracy on the fraction comparison problems was still affected by the accuracy of the visual representations. These results are further considered in the discussion.

## Qualitative Analyses of Student Explanations

To further understand students’ conceptual understanding of fractions, we examined students’ verbal explanations on the Fraction Comparison Explanations and Visual Representation Comparisons tasks.

## Student explanations from the Fraction Comparison Explanations task

We examined students’ verbal explanations for why they felt their answers to each trial type of fraction comparison problem were correct. Table 1 shows the different types of explanations students provided and the percentages for each type. For all four trial types, students most often cited using substitution strategies to explain why they felt their answers were correct (40-43% of all explanations). The second most common type of explanation cited the relation between the numerator and denominator (29-35% of all explanations). Other types of explanations students provided were ones that cited division strategies, parts of a whole, and factual information about numbers. Overall, these results demonstrate that regardless of the type of fraction problem or visual representation shown, the majority of students explained their answers to fraction problems using substitution strategies.

Students’ explanations on the Fraction Comparison Explanations task

Percent of times students provided this explanation | |||||
---|---|---|---|---|---|

Common Numerator | Common Denominator | ||||

Example explanations | Accurate Visual | Misleading Visual | Accurate Visual | Misleading Visual | |

1. Substitution | . | 41% | 43% | 43% | 40% |

2. Numerator- Denominator relation | … . | 29% | 33% | 33% | 35% |

3. Division | . | 12% | 14% | 10% | 10% |

4. Parts of a whole | . | 12% | 5% | 10% | 5% |

5. Fact | . | 6% | 5% | 5% | 10% |

## Student explanations from the Visual Representation Comparisons task

We also examined (1) whether students could identify which visual representations were accurate or misleading for a common numerator and common denominator problem and (2) why they felt a visual representation was more useful than the other. Table 2 shows the different types of explanations students provided and the percentages for each type. For both the common numerator and common denominator problems, 62.5% of students correctly identified the accurate visual representation. When asked why one visual representation was more useful than the other, students most often cited the size of the discrete parts or length of the entire visual representation in their explanations (57-65% of all explanations). For the common numerator problem, the second most common explanation type (15%) was one that cited the relation between the numerator and denominator; for the common denominator problem, the second most common explanation type (14%) was one that simply described factual information about numbers or the visual representation. Other types of explanations cited division strategies, substitution strategies, and cross-multiplication. These results demonstrate that most students could indeed identify which visual representation was accurate for a given problem and did so by attending to the size of the discrete parts or whole length of the visual representation.

Students’ explanations on the Visual Representation Comparisons task

Percent of times students provided this explanation | |||
---|---|---|---|

Example explanations | Common Numerator | Common Denominator | |

1. Size | . | 65% | 57% |

2. Numerator- Denominator Relation | . | 15% | 10% |

3. Fact | . . | 0% | 14% |

4. Substitution | … … | 10% | 10% |

5. Division | . | 10% | 5% |

6. Cross- multiplication | | 0% | 5% |

## Students’ Magnitude Understanding and Conceptual Understanding of Fractions

A secondary goal of the present study was to examine how students’ understanding of magnitudes when expressed solely with symbolic fraction notation is related to their more conceptual understanding of fractions. Bivariate correlations revealed significant relations between students’ accuracy on (1) the traditional magnitude comparison task and fraction comparison task ( r =.45, p =.006) and (2) the traditional magnitude comparison task and trials of the fraction comparison task that were paired with accurate visual representations ( r =.41, p =.01). Thus, students with a better understanding of symbolically-notated magnitudes performed better on the fraction comparison task. This suggests that understanding fraction magnitudes may be related to students’ conceptual understanding of fractions as well.

## Experiment 2

Experiment 1 demonstrated that students had higher accuracy on fraction comparison problems that were paired with accurate visual representations than on fraction comparison problems that were paired with misleading visual representations. To further examine the effects of visual representations on students’ performance on fraction comparison problems, we added a control condition—a fraction comparison task without visual representations—in Experiment 2. If helpful or accurate visual representations indeed improve students’ accuracy on fraction comparison problems, then students should be more accurate when problems are presented with accurate visual representations than when problems are presented with misleading visual representations or no visual representations. On the other hand, if helpful or accurate visual representations do not affect students’ accuracy on fraction comparison problems, then students’ accuracy on fraction comparison problems should not differ by the presence or absence of visual representations.

Thirty-four undergraduate students participated (n female =26). Participants were between the ages of 18.25 and 22.94 years ( M =20.58, SD =1.32) and were students enrolled at a selective American university. Two participants’ data were excluded from analyses for the following reasons: poor eye-tracking calibration (n=1) and experimenter error (n=1). The final sample included 32 participants (n female =24). None of the participants were majoring or minoring in mathematics or a math-related field.

The same apparatus as Experiment 1 were used.

Three tasks were used in this experiment: (1) Fraction Comparisons with Visual Representations, (2) Fraction Comparisons without Visual Representations, and (3) Visual Representation Comparisons. Presentation of the first two tasks—Fraction Comparisons with Visual Representations task and Fraction Comparisons without Visual Representations task—were counterbalanced across participants; the Visual Representation Comparisons task was presented after those first two tasks for all participants. Each task was introduced by an instruction slide that detailed what the participant was to do in that particular task. All study stimuli were created using Adobe Photoshop. Additionally, to assess participants’ general mathematical abilities, participants also completed a paper-and-pencil math assessment after completing the three eye-tracking tasks.

This task was identical to the Fraction Comparisons task used in Experiment 1.

## Fraction Comparisons without Visual Representations

This task was a combination of (1) Fraction Comparisons problems used in Experiment 1, except that no visual representations of the fractions were given with the fraction comparison problems—that is, participants only saw fraction comparison problems (e.g., “Which is larger, a 5 or a 8 ?”)—and (2) Traditional Magnitude Comparisons problems used in Experiment 1 (e.g., “Which is larger, ⅗ or 26 71 ?”). Twenty traditional magnitude comparison problems and 20 fraction comparison problems were randomly ordered within the task for each participant. The purpose of this task was to measure participants’ (1) performance purely on fraction comparison problems—without the aid of visual representations—and (2) understanding of magnitudes expressed with symbolic fraction notation.

This task was identical to the Visual Representation Comparisons task in Experiment 1, except that participants were not asked to verbally explain their answers.

## Algebra Assessment

Because previous work has found relational understanding of fractions to be related to algebra understanding ( DeWolf et al., 2015b ), a measure of algebra understanding was added in Experiment 2. A 27-question paper-and-pencil assessment provided a baseline measure of participants’ algebra understanding ( DeWolf, Son, Bassok, & Holyoak, 2015 ; adapted from DeWolf et al., 2015b ). This assessment included algebra problems that were either taken from the California State Standards for Grade 8 or adapted from Booth, Newton, and Twiss-Garrity (2014) .

The goal of this experiment was to examine whether accurate, helpful visual representations of fractions indeed improved college students’ performance on a fraction comparison task. We first examined the distribution of students’ accuracy on the algebra assessment, traditional magnitude comparison task, fraction comparison task without visual representations, and fraction comparison task with visual representations. On the algebra assessment, students correctly answered an average of 84.78% of questions ( SD =8.14%, range=60-96%). Students correctly answered an average of 53.73% of trials ( SD =12.06%, range=15-70%) on the traditional magnitude comparison task, whereas they correctly answered an average of 78.75% of trials ( SD =10.97%, range=45-95%) on the fraction comparison task without visual representations. Finally, on the fraction comparison task with visual representations, students correctly answered an average of 84.33% of trials ( SD =18.33%, range=40-100%). Unlike Experiment 1, histograms of students’ accuracy on all tasks revealed unimodal distributions; thus, all 32 participants’ data were included in all analyses.

To examine whether visual representations of fractions facilitated students’ accuracy on fraction comparison problems, a 2 (fraction type: common numerator vs. common denominator) × 3 (visual type: accurate vs. misleading vs. none) repeated-measures ANOVA was conducted. A significant main effect of visual type was found, such that students had higher accuracy when the fraction comparison problems were paired with accurate visuals ( M =90.27%, SD =13.41%) than with misleading visuals ( M =78.39%, SD =27.33%) or no visuals ( M =78.75%, SD =10.97%), F (2, 62)=8.11, p =.001, η 2 =.207. No other significant main effects or interactions were found. Consistent with our findings in Experiment 1, these results demonstrate that accurate, helpful visual representations of fractions improve students’ accuracy on fraction comparison problems. Moreover, these results suggest that accurate visual representations can boost students’ accuracy more than when misleading visual representations or no visual representations are provided.

RTs on trials in which students responded correctly to the fraction comparison problems were examined as well. However, problems without visual representations inherently had less stimuli to be looked at and processed. Therefore, we first examined whether RTs differed between problems with visual representations and problems without visual representations. Paired-samples t-tests of the Log transformed RTs for problems with and without visual representations showed that problems without visual representations ( M =3.44 seconds, SD =1.30 seconds) were solved significantly faster than problems with visual representations ( M =4.72 seconds, SD =2.44 seconds), t (31)=2.83, p =.008. As such, we next examined RTs for only the problems that were paired with visual representations. Log transformed RTs were entered into a 2 (fraction type: common numerator vs. common denominator) × 2 (visual type: accurate vs. misleading visual) repeated-measures ANOVA, which revealed a significant main effect of visual type, such that problems with accurate visual representations ( M =4.34 seconds, SD =2.04 seconds) were solved faster than those with misleading visual representations ( M =5.10 seconds, SD =3.03 seconds), F (1, 26)=5.02, p =.03, η 2 =.162. No other significant main effects or interactions were found. Thus, students solved fraction comparison problems without visual representations faster than those with visual representations, and—consistent with findings regarding students’ accuracy—students solved fraction comparison problems with accurate visual representations faster than they solved fraction comparison problems with misleading visual representations.

These RT findings do, however, contrast with those found in Experiment 1. In Experiment 1, the speed with which students solved fraction comparison problems did not differ by visual type. Thus, we examined RTs of only the students who completed the Fraction Comparisons with Visual Representations task—the task identical to that in Experiment 1—before completing the Fraction Comparisons without Visual Representations task (n=17). Log transformed RTs were entered into a 2 (fraction type: common numerator vs. common denominator) × 2 (visual type: accurate vs. misleading visual) repeated-measures ANOVA, which revealed no significant main effects or interactions (all p s>.05). In contrast, the same analyses with only the students who completed the tasks in the opposite order (n=15)—that is, the Fraction Comparisons without Visual Representations task before the Fraction Comparisons with Visual Representations task—revealed a significant main effect of visual type, such that students solved problems paired with accurate visuals faster than problems paired with misleading visuals, F (1,11)=6.35, p =.03, η 2 =.366. Together, these results suggest that the contrasting RT findings between Experiments 1 and 2 may be due to differences in methodology between the two experiments. In particular, solving fraction comparison problems without visual representations before being presented with problems that do have visual representations may bias participants into spending more time on problems that are paired with misleading visual representations.

Students’ visual attention on fraction comparison problems with visual representations were also examined. The same two AOIs as in Experiment 1—that is, AOIs surrounding each of the two fractions and each of the corresponding visual representations—were used in Experiment 2. A paired-samples t-test comparing proportion of time spent looking to the visual representation versus fractions revealed students looked significantly longer at fractions ( M =.15, SD =.11) than visual representations ( M =.07, SD =.07), t (31)=2.99, p =.005. However, a 2 (fraction type: common numerator vs. common denominator) × 2 (visual type: accurate vs. misleading visual) repeated-measures ANOVA examining students’ proportion of time spent looking to visual representations on different trial types revealed no significant main effects or interactions (all ps >.05), suggesting that attention to the visual representations did not differ as a function of trial type. Interestingly, analyses of the number of fixations students made to each AOI revealed students did not differ in the number of fixations made to fractions ( M =3.52, SD =2.35) and visual representations ( M =2.69, SD =2.66), t (31)=1.55, p =.13, but students made significantly more fixations to misleading visual representations ( M =2.96, SD =3.11) than to accurate visual representations ( M =2.40, SD =2.41), F (1, 31)=7.51, p =.01, η 2 =.195. However, students who looked longer at the fractions also made more fixations to the fraction ( r =.69, p <.001), and students who looked longer at the visuals also made more fixations to the visuals ( r =.66, p <.001). Altogether, these results suggest that students did not attend to the visual representations for very long or with many fixations and may have found looking to the fractions to be more useful than looking to the visual representations. Additionally, students’ increased fixations to misleading visuals over accurate visuals—combined with results from students’ RT on problems with misleading versus accurate visuals—suggest students required more time and visual attention to process misleading visuals.

## Visual Representation Comparisons task

We also examined whether students could identify which visual representations were accurate or misleading for a common numerator and common denominator problem. On average, only 64.7% students correctly identified the accurate visual representation for common numerator problems, whereas 76.5% of students correctly identified the accurate visual representation for common denominator problems. Nonparametric tests examining whether students who correctly versus incorrectly identified the accurate visual representations differed in their performance (in terms of accuracy, RT, proportion of looking time, and fixations) on the Fraction Comparison Task—with and without visual representations—revealed no significant differences between the two groups (all p s>.05). These results suggest that students’ ability to correctly discriminate between accurate and misleading visual representations did not affect their performance on the Fraction Comparison Task.

## Students’ Algebra Understanding, Magnitude Understanding, and Conceptual Understanding of Fractions

A bivariate correlation revealed no reliable relation between algebra understanding and accuracy on the traditional magnitude comparison task; additionally, there was no reliable association between accuracy on the traditional magnitude comparison task and accuracy on fraction comparison problems either (all p s>.05). However, there were significant correlations between (1) algebra understanding and accuracy on fraction comparison problems without visual representations ( r =.49, p =.005) and (2) algebra understanding and accuracy on trials of the fraction comparison task paired with accurate visual representations ( r =.57, p =.001). These results are consistent with previous work showing relational—but not literal magnitude—understanding of fractions to be related to algebra understanding ( DeWolf et al., 2015b ) and suggest that understanding of algebra—rather than symbolically-notated magnitudes—may be related to performance on the fraction comparison task.

## General Discussion

In this study we investigated the extent to which adults utilize visual representations during a fraction comparison task. The design of the fraction comparison task required participants to solve fraction comparison problems composed of abstract symbolic fractions, either with a common denominator (e.g., 5 a vs. 7 a ) or a common numerator (e.g., b 4 vs. b 9 ); in Experiments 1 and 2, each of these fraction comparison problems was also paired with a visual representation of the abstract symbolic fractions. The visual representations were set up so that they either had equal total lengths split into different size pieces (modeling common numerators) or equal size pieces that were different in total length (modeling common denominators). This study is unique in that we also made use of eye tracking technology to verify whether participants attended to the visual representations or only the symbolic representation.

College students performed more accurately when the visual representation was helpful or accurate than when it was misleading (Experiments 1 & 2) or when no visual representation was provided (Experiment 2). Students’ accuracy on fraction comparison problems were improved by accurate visual representations, but accuracy on problems with misleading visual representations was not different from problems without visual representations. Thus, though accurate visual representations improved students’ performance on fraction comparison problems, misleading visual representations did not impair students’ performance. Students may not have been impaired by misleading visual representations because students looked more at misleading visual representations than accurate ones (Experiment 2), and consequently, took longer to solve fraction comparison problems with misleading visual representations than those with accurate visual representations (Experiment 2). Therefore, it is possible that students may have actively examined and then disregarded the misleading visual representation when solving fraction comparison problems. Interestingly, however, our participants tended to view the visual representations only briefly, yet accurate visual representations still improved accuracy performance. Thus, minimal exposure to the accurate visual representation seems to have affected performance.

The participant explanations (Experiment 1) also provided useful insight into how students were incorporating the visual representations in their assessments of the symbolic fractions, as well as how they thought about the comparisons in general. Participants showed a strong tendency to use substitution strategies but also showed evidence of thinking more abstractly about the task by providing general rules about division and how the numerator and denominator correspond to each other. Additionally, most participants were able to discriminate between visual representations that were accurate and those that were misleading. This suggests that participants were able to incorporate their abstract understanding of how the symbolic and visual representations model the same or different types of division.

The fraction comparison task required participants not only to integrate visual and symbolic representations but also to have an abstract conceptual understanding of different aspects of division. Even though some participants substituted numbers in place of the algebraic symbols, they still had to consider many substitute cases and how those cases corresponded to each other across the two fractions, and this in turn requires some level of understanding of how the symbolic and visual representations were modeling different aspects of division. The common numerator case modeled a slightly simpler definition of division in which equal sized “wholes” were divided into different sized pieces. This is similar to how many students are introduced to the idea of fractions and map division to fractions ( Empson, 1999 ; Wu, 2009 ). The common denominator case was slightly more complicated despite the high levels of performance on the common denominator problems. In this case, the visual representation was modeling the multiplicative definition (e.g., 5 a is equivalent to 5 “ 1 a “ parts or: 1 a + 1 a + 1 a + 1 a + 1 a ). In this sense, students needed to understand fractions as units and how that corresponds to their theoretical sizes when compared to a fraction also made of equal sized units. This type of understanding is less often taught but is another critical conceptual component of understanding fractions and their relation to division ( Kellman et al., 2008 ).

A secondary question was whether performance on our fraction comparison task—which utilized both visual representations and symbolic representations—is related to performance on a traditional fraction magnitude comparison task. Experiment 1 revealed performance on the fraction comparison task to be related to the traditional magnitude comparison task, suggesting that understanding of magnitudes may benefit conceptual understandings of fractions as well. However, Experiment 2 did not find a significant correlation between performance on the fraction comparison task and traditional magnitude comparison; instead, performance on the fraction comparison task was related to algebra understanding. In the fraction comparison task, the fractions were actually algebraic expressions (e.g., 5 a ); they did not represent an absolute magnitude, as the stimuli in the traditional magnitude comparison task did. The fraction comparison task required more abstract relational reasoning about the relative sizes of various expressions whereas the traditional magnitude comparison task is typically thought to measure the representations of actual magnitudes. Thus, as has been previously posited ( DeWolf et al., 2015b ), the relation between algebra performance and the fraction comparison task—but not the magnitude comparison task—in Experiment 2 suggests a possible dissociation between thinking more abstractly about the relation between the numerator and denominator and actually assessing the size of the fraction magnitude in the traditional task. Further studies might investigate the relation among conceptual fraction understanding, magnitude understanding, and algebra understanding.

In general, these findings suggest that even adult participants at a selective university are affected by the correspondence between visual and symbolic representations. These findings have important implications for educators in that visual representations of fractions must be considered carefully. Further, the shift from understanding visual representations to symbolic representations is not straightforward. That is, even when students have good working knowledge of symbolic representations, students still incorporate visual representations when they are provided. They do not seem to ignore unhelpful representations and go with the more precise symbolic representation to make their judgment. Thus these findings suggest that the symbolic understanding of fraction expressions is somewhat fragile and can be confused when conflicting cues, such as misleading visual representations, are provided.

Eye tracking data also point to another important implication for educators and designers of instructional materials. Even when students only process visual cues with a minimal number of fixations, accurate visual representations can benefit students. This indicates that educators should carefully consider how material is presented on a white board or other visual display. For example, if a problem is presented on a white board with potentially misleading information surrounding it, this information could lead to confusion in students—even if the student’s attention is not drawn to the problematic information; on the other hand, presenting problems on the white board with accurate information could benefit students. Future research could determine what exactly constitutes misleading information that can cause this confusion in students, and further, what level of exposure is necessary to cause detrimental effects.

## Acknowledgements

This material is based upon work supported by the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-07074240707424 to Natsuki Atagi and DGE-1144087 to Melissa DeWolf, as well as NIH grant R01-HD73535 to Scott P. Johnson. The authors would like to thank the UCLA Teaching and Learning Lab and the UCLA Baby Lab for their helpful feedback and comments.

- Booth JL, Newton KJ, Twiss-Garrity LK. The impact of fraction magnitude knowledge on algebra performance and learning. Journal of Experimental Child Psychology. 2014; 118 :110–118. doi: 10.1016/j.jecp.2013.09.001. [ PubMed ] [ CrossRef ] [ Google Scholar ]
- Borko H, Eisenhart M, Brown CA, Underhill RG, Jones D, Agard PC. Learning to teach hard mathematics: Do novice teachers and their instructors give up too easily? Journal for Research in Mathematics Education. 1992; 23 (3):194–222. doi: 10.2307/749118. [ CrossRef ] [ Google Scholar ]
- Chao SJ, Stigler JW, Woodward JA. The effects of physical materials on kindergartners’ learning of number concepts. Cognition and Instruction. 2000; 18 (3):285–316. doi: 10.1207/S1532690XCI1803_1. [ CrossRef ] [ Google Scholar ]
- Common Core State Standards Initiative Common Core State Standards for Mathematics. 2014 Retrieved from http://www.corestandards.org/Math .
- DeWolf M, Bassok M, Holyoak KJ. Conceptual structure and the procedural affordances of rational numbers: Relational reasoning with fractions and decimals. Journal of Experimental Psychology: General. 2015a; 144 :127–150. doi: 10.1037/xge0000034. [ PubMed ] [ CrossRef ] [ Google Scholar ]
- DeWolf M, Bassok M, Holyoak KJ. From rational numbers to algebra: Separable contributions of decimal magnitude and relational understanding of fractions. Journal of Experimental Child Psychology. 2015b; 133 :72–84. doi: 10.1016/j.jecp.2015.01.013. [ PubMed ] [ CrossRef ] [ Google Scholar ]
- DeWolf M, Grounds MA, Bassok M, Holyoak KJ. Magnitude comparison with different types of rational numbers. Journal of Experimental Psychology: Human Perception and Performance. 2014; 40 :71–82. doi: 10.1037/a0032916. [ PubMed ] [ CrossRef ] [ Google Scholar ]
- DeWolf M, Son JY, Bassok M, Holyoak KJ. Implicit understanding of arithmetic with rational numbers: The impact of expertise. In: Dale R, Jennings C, Maglio P, Matlock T, Noelle D, Warfaumont A, Yoshimi J, editors. Proceedings of the 37th Annual Conference of the Cognitive Science Society; Austin, TX. Cognitive Science Society.2015. [ Google Scholar ]
- Empson SB. Equal sharing and shared meaning: The development of fraction concepts in a first grade classroom. Cognition and Instruction. 1999; 17 :283–342. doi: 10.1207/S1532690XCI1703_3. [ CrossRef ] [ Google Scholar ]
- Fazio LK, DeWolf M, Siegler RS. Strategy use and strategy choice in fraction magnitude comparison. Journal of Experimental Psychology: Learning, Memory, and Cognition. 2016; 42 (1):1–16. doi: 10.1037/xlm0000153. [ PubMed ] [ CrossRef ] [ Google Scholar ]
- Frydman O, Bryant PE. Sharing and the understanding of number equivalence by young children. Cognitive Development. 1988; 3 :323–339. doi: 10.1016/0885-2014(88)90019-6. [ CrossRef ] [ Google Scholar ]
- Kellman PJ, Massey CM, Roth Z, Burke T, Zucker J, Saw A, et al. Perceptual learning and the technology of expertise: Studies in fraction learning and algebra. Learning Technologies and Cognition: Special Issue on Pragmatics and Cognition. 2008; 16 (2):356–405. doi: 10.1075/pc.16.2.07kel. [ CrossRef ] [ Google Scholar ]
- Kieran C. The learning and teaching of school algebra. In: Grouws D, editor. Handbook of Research in Mathematics Teaching and Learning. Macmillan; New York: 1992. pp. 390–419. [ Google Scholar ]
- Mix K, Levine S, Huttenlocher J. Early fraction calculation ability. Developmental Psychology. 1999; 35 (5):164–174. doi: 10.1037/0012-1649.35.1.164. [ PubMed ] [ CrossRef ] [ Google Scholar ]
- Opfer JE, Siegler RS. Development of quantitative thinking. In: Holyoak K, Morrison R, editors. Oxford handbook of thinking and reasoning. Cambridge. Oxford University Press; UK: 2012. pp. 585–605. [ Google Scholar ]
- Scott-Foresman & Addison-Wesley . enVisionMath. Pearson Instruction Materials; 2011. [ Google Scholar ]
- Sophian C, Garyantes D, Chang C. When three is less than two: Early developments in children’s understanding of fractional quantities. Developmental Psychology. 1997; 33 (5):731–744. doi: 10.1037//0012-1649.33.5.731. [ PubMed ] [ CrossRef ] [ Google Scholar ]
- Squire S, Bryant P. The influence of sharing on children’s initial concept of division. Journal of experimental child psychology. 2002; 81 (1):1–43. doi: 10.1006/jecp.2001.2640. [ PubMed ] [ CrossRef ] [ Google Scholar ]
- Squire S, Bryant P. Children’s understanding and misunderstanding of the inverse relation in division. British Journal of Developmental Psychology. 2003; 21 (4):507–526. doi: 10.1348/026151003322535192. [ CrossRef ] [ Google Scholar ]
- Stafylidou S, Vosniadou S. The development of students’ understanding of the numerical value of fractions. Learning and Instruction. 2004; 14 (5):503–518. doi: 10.1016/j.learninstruc.2004.06.015. [ CrossRef ] [ Google Scholar ]
- Stigler JW, Givvin KB, Thompson B. What community college developmental mathematics students understand about mathematics. The MathAMATYC Educator. 2010; 10 :4–16. [ Google Scholar ]
- Rapp M, Bassok M, DeWolf M, Holyoak KJ. Modeling discrete and continuous entities with fractions and decimals. Journal of Experimental Psychology: Applied. 2015 Advanced online publication. dx.doi.org/10.1037/xap0000036. [ PubMed ] [ Google Scholar ]
- Uttal DH, O’Doherty K, Newland R, Hand LL, DeLoache J. Dual Representation and the Linking of Concrete and Symbolic Representations. Child Development Perspectives. 2009; 3 (3):156–159. doi: 10.1111/j.1750-8606.2009.00097.x. [ CrossRef ] [ Google Scholar ]
- Vamvakoussi X, Vosniadou S. Understanding the structure of the set of rational numbers: a conceptual change approach. Learning and Instruction. 2004; 14 (5):453–467. doi: 10.1016/j.learninstruc.2004.06.013. [ CrossRef ] [ Google Scholar ]
- Vamvakoussi X, Vosniadou S. How many decimals are there between two fractions? Aspects of secondary school students’ understanding of rational numbers and their notation. Cognition and Instruction. 2010; 28 (2):181–209. doi: 10.1080/07370001003676603. [ CrossRef ] [ Google Scholar ]
- Wu H. What’s sophisticated about elementary mathematics? American Educator. 2009; 33 (3):4–14. [ Google Scholar ]

## ToK Essay #5 May 23: Visual Representations

- October 26, 2022
- Student Support , ToK Essay

The video guide to ToK Essay #5 May 23: Visual Representations has been posted on YouTube today (and is linked below). This essay was a real challenge for me to summarise in a short video. When I wrote the Essay Guide Notes (linked) I found it to be a very wide ranging subject, and the notes ran to over 6,300 words !

## Visual Representations.

The focus on visual representations seems fairly straightforward, they’re tangible things such as maps and graphs. However, the knowledge links are a little more obscure in this essay than in the others. The essay question specifies that we look at visual representation in terms of the communication of knowledge. This lends itself to the purpose, and maybe, context of knowledge. I also played around with ideas such as the simplification of knowledge (harking back to a PT a few years ago), but this seemed to be a potential diversion.

There’s such a wide range of visual representations that students can look at, in some ways it’s a possible diversionary danger. It’s important that students stay focussed on whether those representations are ‘helpful’ in communication. I have tried to think of ‘helpful’ in terms of the purpose and context of knowledge.

## The Knower & Knowledge.

The focus on visual representations in the communication of knowledge seems to link well with the core theme of The Knower & Knowledge, and that’s mainly where I ended up. It gives us good links to the ToK Concepts of Interpretation, Explanation and Evidence. The (re)introduction of The Knower into the ToK course gives students a lot more scope in their ToK Essays to go beyond the production of knowledge that they were largely constrained to in the last syllabus.

You can find the video guide for Essay #1 linked here .

You can find the video guide for Essay #2 linked here.

You can find the video guide for Essay #3 linked here.

If you want more detailed notes on the Knowledge Questions and arguments raised in the video then please check out the detailed notes available here.

If you want help with your ToK Essay or Exhibition then please check out the Student Support page linked here .

You can always contact me at [email protected],

stay Tok-tastic !, Daniel

## Leave a Reply Cancel reply

Discover more from toktoday.

Subscribe now to keep reading and get access to the full archive.

Type your email…

Continue reading

Grab your spot at the free arXiv Accessibility Forum

Help | Advanced Search

## Computer Science > Robotics

Title: pretrained visual representations in reinforcement learning.

Abstract: Visual reinforcement learning (RL) has made significant progress in recent years, but the choice of visual feature extractor remains a crucial design decision. This paper compares the performance of RL algorithms that train a convolutional neural network (CNN) from scratch with those that utilize pre-trained visual representations (PVRs). We evaluate the Dormant Ratio Minimization (DRM) algorithm, a state-of-the-art visual RL method, against three PVRs: ResNet18, DINOv2, and Visual Cortex (VC). We use the Metaworld Push-v2 and Drawer-Open-v2 tasks for our comparison. Our results show that the choice of training from scratch compared to using PVRs for maximising performance is task-dependent, but PVRs offer advantages in terms of reduced replay buffer size and faster training times. We also identify a strong correlation between the dormant ratio and model performance, highlighting the importance of exploration in visual RL. Our study provides insights into the trade-offs between training from scratch and using PVRs, informing the design of future visual RL algorithms.

Subjects: | Robotics (cs.RO); Machine Learning (cs.LG) |

Cite as: | [cs.RO] |

(or [cs.RO] for this version) |

## Submission history

Access paper:.

- Other Formats

## References & Citations

- Google Scholar
- Semantic Scholar

## BibTeX formatted citation

## Bibliographic and Citation Tools

Code, data and media associated with this article, recommenders and search tools.

- Institution

## arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs .

## IEEE Account

- Change Username/Password
- Update Address

## Purchase Details

- Payment Options
- Order History
- View Purchased Documents

## Profile Information

- Communications Preferences
- Profession and Education
- Technical Interests
- US & Canada: +1 800 678 4333
- Worldwide: +1 732 981 0060
- Contact & Support
- About IEEE Xplore
- Accessibility
- Terms of Use
- Nondiscrimination Policy
- Privacy & Opting Out of Cookies

A not-for-profit organization, IEEE is the world's largest technical professional organization dedicated to advancing technology for the benefit of humanity. © Copyright 2024 IEEE - All rights reserved. Use of this web site signifies your agreement to the terms and conditions.

## IMAGES

## VIDEO

## COMMENTS

The use of visual representations (i.e., photographs, diagrams, models) has been part of science, and their use makes it possible for scientists to interact with and represent complex phenomena, not observable in other ways. Despite a wealth of research in science education on visual representations, the emphasis of such research has mainly been on the conceptual understanding when using ...

Chemists routinely use visual representations to investigate relationships and move between the observable, physical level and the invisible particulate level (Kozma, Chin, Russell, & Marx, 2002). Generating explanations in a visual format may be a particularly useful learning tool for this domain.

This type of chart is helpful in quickly identifying whether or not the data is symmetrical or skewed, as well as providing a visual summary of the data set that can be easily interpreted. 7. Waterfall Chart. A waterfall chart is a visual representation that illustrates how a value changes as it's influenced by different factors, such as time ...

Visual Representation refers to the principles by which markings on a surface are made and interpreted. Designers use representations like typography and illustrations to communicate information, emotions and concepts. Color, imagery, typography and layout are crucial in this communication. Alan Blackwell, cognition scientist and professor ...

Because our brains are adapted to easily process and comprehend visual information, visualization can be a powerful tool for influencing our thoughts, emotions, and behaviors. In fact, research ...

Learning by Drawing Visual Representations: Potential, Purposes, and Practical Implications. ... Do they help middle school chil... Go to citation Crossref Google Scholar. Effects of verbal and visual support on learning by tablet-based drawi... Go to citation Crossref Google Scholar.

Posted July 20, 2012. A large body of research indicates that visual cues help us to better retrieve and remember information. The research outcomes on visual learning make complete sense when you ...

Visu al information plays a fundamental role in our understanding, more than any other form of information (Colin, 2012). Colin (2012: 2) defines. visualisation as "a graphica l representation ...

Following the literature, the use of drawings as a visual representation has the following benefits: (a) Drawing allows us to represent science, reason in science, communicate and link ideas, and improve participation by molding students' ideas toward organizing their knowledge (Ainsworth et al., 2011 ). (b)

Despite the notable number of publications on the benefits of using visual representations in a variety of fields (Meyer, Höllerer, Jancsary, & Van Leeuwen, 2013), few studies have systematically investigated the possible pitfalls that exist when creating or interpreting visual representations.Some information visualization researchers, however, have raised the issue and called to action ...

Page 5: Visual Representations. Yet another evidence-based strategy to help students learn abstract mathematics concepts and solve problems is the use of visual representations. More than simply a picture or detailed illustration, a visual representation—often referred to as a schematic representation or schematic diagram— is an accurate ...

Information visualization is the process of representing data in a visual and meaningful way so that a user can better understand it. Dashboards and scatter plots are common examples of information visualization. Via its depicting an overview and showing relevant connections, information visualization allows users to draw insights from abstract ...

Thinking about many possible visual representations is the first step in creating a good one for students. The Progressions published in tandem with the Common Core State Standards for mathematics are one resource for finding specific visual models based on grade level and standard. In my fifth-grade example, what I constructed was a sequenced ...

On the nature and role of visual representations in knowledge production and science communication" In Science Communication edited by Annette Leßmöllmann, Marcelo Dascal and Thomas Gloning, 235-256. Berlin, Boston: De Gruyter Mouton, 2020.

As teachers, complete the mathematical tasks yourselves, a key component of Math for All, to explore and understand the various physical models, visual representations, and symbolic processes that can be developed in support of the mathematical content. Value the concrete models and pictures of the mathematical content in a similar way to how ...

Visual representations are a powerful way for students to access abstract mathematical ideas. To be college and career ready, students need to be able to draw a situation, graph lists of data, or place numbers on a number line. Developing this strategy early during the elementary grades gives students tools for engaging with—and ways of ...

More specifically, visual representations can be found for: (a) phenomena that are not observable with the eye (i.e., microscopic or macroscopic); (b) phenomena that do not exist as visual representations but can be trans-lated as such (i.e., sound); and (c) in experimental settings to provide visual data representations (i.e., graphs

2. Earlier Research: Learning About Price Through Visual Representations. Economics teaching frequently uses graphs to help students understand complex relationships (Cohn et al., Citation 2004; Reimann, Citation 2004; Wheat, Citation 2007a).This presumes that graphs facilitate learning about pricing by illustrating and simplifying complex processes and relations (Wheat, Citation 2007b).

Data visualization is the use of a visual representation of data which adds meaning to such data, supporting the transitioning of such data to information (Chen et al., ... Despite these and other criticisms the SDG's are an internationally recognized framework that help to focus international development efforts on many levels. The table ...

College students performed more accurately when the visual representation was helpful or accurate than when it was misleading (Experiments 1 & 2) or when no visual representation was provided (Experiment 2). Students' accuracy on fraction comparison problems were improved by accurate visual representations, but accuracy on problems with ...

A line is an economical representation of DNA. Like verbal jargon, however, this visual convention is a learned language. The two representations of DNA shown in this animation represent the extremes of a continuum. Unlike the shorthand shown on the left, the representation on the right makes most of the physical features of DNA readily apparent.

There's such a wide range of visual representations that students can look at, in some ways it's a possible diversionary danger. It's important that students stay focussed on whether those representations are 'helpful' in communication. I have tried to think of 'helpful' in terms of the purpose and context of knowledge.

Visual reinforcement learning (RL) has made significant progress in recent years, but the choice of visual feature extractor remains a crucial design decision. This paper compares the performance of RL algorithms that train a convolutional neural network (CNN) from scratch with those that utilize pre-trained visual representations (PVRs). We evaluate the Dormant Ratio Minimization (DRM ...

The student effectively communicates the chosen title "Are visual representations always helpful in the communication of knowledge? Discuss with reference to the human sciences and mathematics" at the beginning of the work, ensuring clarity for the TOK examiner. Throughout the essay, the focus remains on the helpfulness of visual ...

The spiking neural networks (SNNs) that efficiently encode temporal sequences have shown great potential in extracting audio-visual joint feature representations. However, coupling SNNs (binary spike sequences) with transformers (float-point sequences) to jointly explore the temporal-semantic information still facing challenges. In this paper, we introduce a novel Spiking Tucker Fusion ...