Eye-tracking Evaluation of Visual Abstractions for Math Formulae

Theoretical (Analytical):

Practical (Implementation):

Literature Work:


Math is used as an objective language to communicate facts in science as well as in daily-life activities.

A very well-known example is “The Monty Hall” probabilistic puzzle:  “Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?”  (http://statisticshowto.com/probability-and-statistics/monty-hall-problem/).

There are previous evidence that shows differences between the reasoning of people with a mathematical background (math-literates) and lay-users [1,2].

In this context, some interesting questions arise related to how visual abstractions of math formulae can help to understand:

  • How humans perceive, process, and understand math statements and expressions?
  • Is there any way to improve the communication of math by using visual interactive analysis instead of text?

Problem Statement

  • Are visual mathematical expression-trees (VMEXT, see example) a good medium for math understanding?
  • Does the VMEXT visualizations help humans to understand mathematical expressions? 
  • What other hierarchical visual abstractions can be used?




  • Summarize the literature on human understanding of math expressions and,
  • Derive hypothesis that are objectively testable in an experimental setting,
  • Carry out the user experiment,
  • Summarize the results.


  • Gambling
  • Programming
  • Statistics
  • Math


  • Bachelor/Master, 6 months, Immediately.


  • Dr. Alexandra Diehl (diehl@dbvis.inf.uni-konstanz.de), Dr. Moritz Schubotz (moritz@schubotz.de).


  1. Fu, Bo, Natalya F. Noy, and Margaret-Anne Storey. "Eye tracking the user experience-An evaluation of ontology visualization techniques." Semantic Web 8.1 (2017): 23-41.
  2. Kuno Kurzhals, Brian Fisher, Michael Burch, and Daniel Weiskopf. 2014. Evaluating visual analytics with eye tracking. In Proceedings of the Fifth Workshop on Beyond Time and Errors: Novel Evaluation Methods for Visualization (BELIV '14)
  3. Heidi Lam, Petra Isenberg, Tobias Isenberg, and Michael Sedlmair (Eds.). ACM, New York, NY, USA, 61-69. dx.doi.org/10.1145/2669557.2669560
  4. Kohlhase A., Kohlhase M., Fürsich M. (2017) Visual Structure in Mathematical Expressions. In: Geuvers H., England M., Hasan O., Rabe F., Teschke O. (eds) Intelligent Computer Mathematics. CICM 2017. Lecture Notes in Computer Science, vol 10383. Springer
  5. Moritz Schubotz, Norman Meuschke, Thomas Hepp, Howard S. Cohl, Bela Gipp: VMEXT: A Visualization Tool for Mathematical Expression Trees. CICM 2017: 340-355.