Software programs aid conceptualization

Editor’s Note: For many middle school and high school students, math is something to be tolerated, at best, and dreaded, at worst.

Many students complain that they don’t see its relevance in their lives once they graduate from high school unless they plan to go on to study higher-level math in college or to take up a profession in engineering or the sciences. When students were asked what can be done to make math more interesting, their most common suggestions were to make it relevant to their daily lives and to make it more fun.

We posed the same question to math educators. Shalom Labkovski’s responses follows:

Mathematics provides elegant ways of explaining and representing naturally occurring phenomena. However, many students are not able to see past the symbols and algorithms (rules) that often seem arbitrary or nonsensical.

Admittedly, I often felt the same way as a child, but eventually came around to understanding. I recognize that many of my students find it more difficult to make sense of math concepts than it was for me. Therefore, I deliberately approach the teaching of concepts through concrete representations before moving on to abstract algorithms.

Far different from my school experience, the advancement in technology has made it much easier for me to represent mathematical concepts. For example, I used to have my students participate in a tedious process for discovering the meaning of Pi (≈ 3.14…).

I would have them cut and measure string to determine the distance around a variety of circular objects and divide the result by the distance across those same objects. So much time was spent on the minutia of the activity that students had difficulty putting meaning to how each step related to the final goal of discovering Pi. Not to mention that small inaccuracies in student measurements were hard to avoid and led to confusion.

Today, I do the same lesson using a software package titled Geometer’s Sketchpad. It allows the students to quickly create circles of various sizes, determines the precise circumference and diameter, and proves that when the two values are divided, the result is always the same (3.14…) — regardless of the size of the circle.

This is but one example of how I leverage not only the technology that is available, but also the fact that my students are accustomed to using technology. In my class, my students no longer need to spend a painful amount of time drawing x and y-axes on grid paper. Instead they can use a digital display of grid paper to more efficiently plot points and lines. They can also quickly see the result of shifting the graph. These displays are also much more visually appealing than gray pencil on light blue grid paper.

However, my favorite technological advancement is the ever-improving, and forever-free, Khan Academy website. I serve as coach to all my students and I am able to view data about their levels of proficiency. The website has built in many video-game style dynamics that motivate students to practice skills. From the tones they hear when answering questions, to the energy points and badges they earn for accomplishing goals, to the avatars they can acquire; Khan Academy helps me motivate my students to work on rigorous mathematics tasks.

It is difficult to make math interesting — all of the time. Some would also argue that with increased technology, something is lost in not having the students hand-draw graphs or transform images on grid paper etc. However, if thoughtfully planned out, even far more is gained through the use of technological tools; student engagement being the most significant of these gains.

Shalom Labkovski is a seventh-grade math teacher at Ocean Intermediate School.