Below is a reflection prompt & response for my class, ETEC 533, technology in mathematics and science classrooms.
Why is visualization necessary (or not) for student understanding of math or science?
As pointed out by Edens and Potter, students who used “schematic” style drawings versus “pictorial” style drawings to assist in solving word problems, performed significantly better in their mathematics scores. As a review, a schematic drawing is one that may not included buch superficial details like the sun, houses, etc, that are irrelevant to the word problem, and instead includes figures and numbers that are pertinent to the problem at hand.
Below are examples of a schematic versus pictorial drawings. Imagine a word problem asking students to discover how much water is displaced by a boat in the water.
Often times, being able to draw out one’s thinking can assist in being able to solve the problem. This is where computer simulations can come in handy, as many concepts are difficult to draw out or visualize with paper or in a child’s mind.
Try out this game below on balancing two variables for mathematics.
Essentially, the game allows players to place 2 variable “blocks” onto either side of a scale, change the value of said variables at any time, in order to have students match the weight and discover that variables can be in constant flux (and are not constants).
Imagine trying to work this problem out on paper. One has 2 blocks (of unlimited quantity), they need to balance a scale, be able to change the value of a variable at will, and see the effects of the scale change in real time. Even if one had a scale, it would be impossible to change the value (weight) of a variable in real time; and this is where the beauty of a computer simulation can come in to play.
By using the above variable explorer, students can get a better understanding of what variables are, simply containers that can hold different values. They can get a better understanding of this through the ability to make changes in real time, and to see them change on the screen before them. Computer simulations are capable of taking complex problems like variables, and simplifying them down into easier to manage visualizations like the above example.
Clements, M. K. A. (2014). Fifty years of thinking about visualization and visualizing in mathematics education: A historical overview. In Mathematics & Mathematics Education: Searching for Common Ground (pp. 177-192). Springer Netherlands. Available from UBC. https://libphds1.weizmann.ac.il/Dissertations/Mathematics_and_Mathematics_Education.pdf#page=175
Edens, K., & Potter, E. (2008). How students “unpack” the structure of a word problem: Graphic representations and problem solving. School Science and Mathematics, 108(5), 184-196. Available in Course Readings.