Annotated Bibliography Entry Prepared By

Annotated Bibliography entry prepared by

Jeanette E. Horng

Arcavi, A. (2003). The role of visual representations in the learning of mathematics, Educational studies in Mathematics, 215-241.

This article describes the importance visual representations are in the teaching of mathematics. It highlights visualization: what it means and what it entails, as well as its benefits for students and teachers. On the other hand, this article also brings light to the detriments of using visual aids and other technologies geared to help represent certain topics.

First, Arcavi explains the benefits of visualization in teaching. In the times where things were too small and far to see, the use of technologies helped enlarge and enable students to be able to see certain things on the board. Instead of relying on our imaginations, the students can actually see whether or not their personal vision of the representation is accurate to what the teacher is trying to teach. After all, according to Arcavi, “seeing the thing itself, with the aid of technology which overcomes the limitation of our sight, provides not only a fulfillment of our desire to ‘see’ and the subsequent enjoyment, but it may also sharpen our understanding, or serve as a springboard for questions which we were not able to formulate before.” As a tool for more discussion and for ease of understanding, technology seems to be a beneficial tool used in educational practices.

Arcavi explains in great detail the importance of visualization in mathematics through specific examples and lessons used in mathematics. Basically, he explains that the subtopics in this subject seem to rely heavily on simply understanding the picture and the task at hand. Without the understanding of deeply understanding certain equations and its representation in the real world, students may not have the motivation to learn them.

Problem solving is another aspect in which visualization is key; in certain situations, it may “play a central role to inspire a whole solution, beyond the merely procedural.” Once again, use of technology in visualizing things may spur other ideas and further discussion. This ultimately engages the students in active, non-rote learning.

On the other side, though mathematics relies heavily on representations, the theory and practice behind mathematics is what is most difficult to grasp; however, visuals cannot aid students in understanding this side of math. As proofs come into play, merely seeing the ideas through graphs and diagrams does not prove a mathematical equation or theorem.

I find this article is very important for future math teachers like me. I realize the importance and heavy reliance on visual aids, especially technology. After having taken a course that helped me understand more programs and more fun, active ways to show certain lessons, I would love to use them in my classrooms, so long as I have access to them. However, I must be careful that my students understand the thought behind the projects: the ultimate goal.

As a student who has taken a few theory courses, I have learned “the hard way.” I learned that proofs are not formed simply using graphs and diagrams; there are better, more concrete ways of proving theorems. However, this importance needs to be implemented earlier on in a student’s educational lifespan – it is crucial for students to constantly know what they are doing and why, and how it works.