How a Focus On Visuals Supports Math Success

• Enhancing Math Performance: Using a variety of visual representations in math education significantly improves students' math performance, concept acquisition, and problem-solving abilities.
• Visuals in Word Problems: Adding pictures to mathematical texts improves student accuracy and confidence in problem-solving, particularly benefiting those with learning difficulties or non-native language speakers.
• Visuals Boost Learning and Memory: Incorporating visuals into educational materials enhances learning and memory, as visual information is tightly integrated with memory processing in the brain, leading to improved understanding and long-term recall.

Are Numbers Real?

Perhaps you have never thought much about it, but there are various philosophical views on the ontology—the reality—of numbers. Are numbers actual things or are they simply ways people talk about things? Some popular views include:

• Platonism: This view holds that numbers are real, abstract objects that exist independently of human minds. Platonists argue that mathematical truths are discovered, not invented.
• Nominalism: Nominalists argue that numbers do not exist in any real sense outside of human language and concepts. According to this view, numbers are merely labels or names we give to patterns of objects.
• Formalism: Formalists see mathematics as a game played according to certain rules. Numbers and mathematical theorems do not convey any intrinsic truth but are merely the result of playing the game with symbols according to agreed-upon rules.

Regardless of your viewpoint—if you even have one . . . do you even need one?!—we necessarily encounter numbers as abstract ideas. In turn, to help us make sense of ideas that we essentially cannot see, we represent those ideas visually.

So, for example, whenever we engage with the idea of “three,” the representation of that idea as a word “three,” as a number “3,” or as some other form such as “III,” we are engaging with visual representations of an otherwise abstract idea.

Using the Concrete to Make Sense of the Abstract

In our article about multiple representations, we explore how using visual representations to make the abstract concrete in mathematics education improves math performance [1], concept acquisition [2], and problem-solving skills [3].

As we note in our discussion about the challenges of using representations, to effectively understand and interpret representations in mathematics, students need to comprehend both the broader context and specific details of each representation [4], including its form, function, language [5], and key features, patterns, and relationships [6].

We summarize the challenge this way: representations help students make sense of concepts only if students can make sense of the representations!

The Word Problem

While this challenge is true for all visual representations, it is particularly true when words are used to represent mathematical concepts.

Word problems in mathematics are complex because they require the integration of both language and numerical information [7]. Success with word problems requires students to have not only sufficient proficiency in the language of instruction generally [8], but also comprehension of and the cognitive abilities to make sense of math vocabulary more specifically [9]. These complications become even more pronounced for students experiencing math difficulties [7] [10] [11], students with learning disabilities [12], and non-native speakers [8].

A Picture’s Worth

A meta-analysis of 39 studies conducted between 1985 and 2018 involving a diverse range of learners showed that adding graphics to reading materials has a significant positive effect on reading comprehension across all grade levels [13].

In mathematics, a comprehensive meta-analysis involving 51 studies with 38,987 participants found that adding pictures to mathematical problem texts has significant positive effects on student accuracy, confidence, and meta-cognitive aspects of problem solving [14].

Visuals in mathematics have been shown to increase engagement and creativity [15], reduce cognitive load and facilitate problem-solving skills [7], improve spatial reasoning resulting in improved performance [16], and enhance inclusion and accessibility [10].

Everyone’s a Visual Learner

Because of the number and variety of associated benefits, we utilize and rely on intentionally designed [13] [17] visuals to enhance the instructions, problem texts, and the overall user experience in our app.

While there has been significant debate around [18] and a lack of common understanding about the reality and relevance of learning styles [19], the latest research into the neuroscience of learning shows that, in some sense we are all visual learners [20].

Visual information plays a much bigger role in how we process and remember information than was previously thought. This is because the brain does not strictly separate visual processing and memory—instead, these functions are tightly integrated. This means that when we see something, our memory system is actively engaged in processing this visual information.

In other words, when we see something, we actually begin to remember it!

Visualizing Students Success

Because they so powerfully support learning, we utilize visuals as an integral part of our overall learning experience and learning interaction design strategies. In our commitment to supporting the success of each individual learner and each learner as an individual, we leverage the power of visuals to increase short-term understanding, long-term recall and transfer, and improve overall student success.

References

[1] Sokolowski, A. (2018). The effects of using representations in elementary mathematics: Meta-Analysis of Research. IAFOR Journal of Education, 6(3), 129-152. http://iafor.org

[2] Çetin, H., & AYDIN, S. (2020). The effect of multiple representation based instruction on mathematical achievement: A Meta-Analysis. International Journal of Educational Research Review, 5(1), 26-36. https://doi.org/10.24331/ijere.647531

[3] Liang, C. P., & She, H. C. (2023). Investigate the effectiveness of single and multiple representational scaffolds on mathematics problem solving: Evidence from eye movements. Interactive Learning Environments, 31(6), 3882-3897. https://doi.org/10.1080/10494820.2021.1943692

[4] Van Meteris, P., List, A., Lombardi, D., & Kendeou, P. (2020). Handbook of learning from multiple representations and perspectives. Routledge.

[5] Griffin, S. (2004). Building number sense with Number Worlds: A mathematics program for young children. Early childhood research quarterly, 19(1), 173-180. https://doi.org/10.1016/j.ecresq.2004.01.012

[6] Brezovszky, B., McMullen, J., Veermans, K., Hannula-Sormunen, M. M., Rodríguez-Aflecht, G., Pongsakdi, N., ... & Lehtinen, E. (2019). Effects of a mathematics game-based learning environment on primary school students' adaptive number knowledge. Computers & Education, 128, 63-74. https://doi.org/10.1016/j.compedu.2018.09.011

[7] Powell, S. R., Berry, K. A., & Benz, S. A. (2020). Analyzing the word-problem performance and strategies of students experiencing mathematics difficulty. The Journal of Mathematical Behavior, 58, 100759. https://doi.org/10.1016/j.jmathb.2020.100759

[8] Outhwaite, L. A., Gulliford, A., & Pitchford, N. J. (2020). Language counts when learning mathematics with interactive apps. British Journal of Educational Technology, 51(6), 2326-2339. doi:10.1111/bjet.12912

[9] Lin, X., Peng, P., & Zeng, J. (2021). Understanding the relation between mathematics vocabulary and mathematics performance: A meta-analysis. The Elementary School Journal, 121(3), 504-540. https://www.journals.uchicago.edu/doi/abs/10.1086/712504

[10] Root, J. R., Cox, S. K., Saunders, A., & Gilley, D. (2020). Applying the universal design for learning framework to mathematics instruction for learners with extensive support needs. Remedial and Special Education, 41(4), 194-206. https://doi.org/10.1177/07419325198872

[11] Ran, H., Kasli, M., & Secada, W. G. (2021). A meta-analysis on computer technology intervention effects on mathematics achievement for low-performing students in K-12 classrooms. Journal of Educational Computing Research, 59(1), 119-153. https://doi.org/10.1177/0735633120952063

[12] Peltier, C., Sinclair, T. E., Pulos, J. M., & Suk, A. (2020). Effects of schema-based instruction on immediate, generalized, and combined structured word problems. The Journal of Special Education, 54(2), 101-112.

[13] Guo, D., Zhang, S., Wright, K. L., & McTigue, E. M. (2020). Do you get the picture? A meta-analysis of the effect of graphics on reading comprehension. AERA Open, 6(1). https://doi.org/10.1177/2332858420901696

[14] Hu, L., Chen, G., Li, P., & Huang, J. (2021). Multimedia effect in problem solving: A meta-analysis. Educational Psychology Review, 1-31. https://doi.org/10.1007/s10648-021-09610-z

[15] Schoevers, E. M., Leseman, P. P., & Kroesbergen, E. H. (2020). Enriching mathematics education with visual arts: Effects on elementary school students’ ability in geometry and visual arts. International Journal of Science and Mathematics Education, 18, 1613-1634. https://doi.org/10.1007/s10763-019-10018-z

[16] Benavides-Varela, S., Callegher, C. Z., Fagiolini, B., Leo, I., Altoè, G., & Lucangeli, D. (2020). Effectiveness of digital-based interventions for children with mathematical learning difficulties: A meta-analysis. Computers & Education, 157, 103953. https://doi.org/10.1016/j.compedu.2020.103953

[17] Clinton, V. & Cooper, J.L. (2015). Teacher viewpoints of instructional design principles for visuals in a middle school math curriculum. Paper presented at the Annual Meeting of the American Educational Research Association Annual Meeting, Chicago, IL. https://eric.ed.gov/?id=ED574965

[18] Dantas, L. A., & Cunha, A. (2020). An integrative debate on learning styles and the learning process. Social Sciences & Humanities Open, 2(1), 100017. https://doi.org/10.1016/j.ssaho.2020.100017

[19] Papadatou-Pastou, M., Touloumakos, A. K., Koutouveli, C., & Barrable, A. (2021). The learning styles neuromyth: when the same term means different things to different teachers. European Journal of Psychology of Education, 36, 511-531. https://doi.org/10.1007/s10212-020-00485-2

[20] Steel, A., Silson, E. H., Garcia, B. D., & Robertson, C. E. (2024). A retinotopic code structures the interaction between perception and memory systems. Nature Neuroscience, 1-9. https://www.nature.com/articles/s41593-023-01512-3