In my own experience, I have found that encouraging intuitive understanding in mathematics tends to overwhelm many students. They show little interest, often asking if they can just memorize it or learn a trick. While memorization presents an easy way to get a good score on a test or complete homework, it can create a foundational gap that becomes evident when students encounter higher levels of math.
One of the most apparent hurdles is the move from high school to college level math and science. Highly ranked colleges and universities will have a more theoretical approach to mathematics, and students will be forced to draw on intuitive understanding as opposed to rote memorization. Oftentimes, advanced high school classes leave students ill-prepared, and students struggle a great deal during their freshman year. First year college students often complain that tests are different than homework, but what they don’t realize is that an in-depth understanding of the topic reveals the similarities between homework and exam problems. Knowing how to do a problem is simply not good enough; you must know why you are solving it this way.
While this lack of interest can be frustrating, it makes sense. Where is the motivation to learn the theory if they will be assessed based on the formulaic way they were taught? Moreover, how do you encourage this type of learning for students before they enter college? One alternative is to change the way the students are assessed. I know of one undergraduate professor who asks for their students to design homework problems for the class. Others deliberately avoid exams and opt for students to complete take-home projects instead. The objective is to design levels of assessment that require the student to go beyond formulas and equations to demonstrate their understanding of the topic.
Perhaps the most simple and obvious way is to assign more word problems. As many of you know, word problems can be like kryptonite to even the most advanced students. They are required to use a difficult combination of reading comprehension, quantitative skills and writing, which are not often pulled together in high school math and science.
Baruch College Campus High School has faced this challenge head-on and was recently rewarded for its innovative approach to math and science. The school has made it their priority to encourage engaging ways to teach math. For example, projects are designed by the students themselves. Popular topics have spanned the mathematics spectrum, ranging from physics equations in video games to statistical analysis of baseball averages.
Obviously, this does not call for the removal of written exams. I am merely encouraging a creative approach to teaching mathematics. Math and science teachers are by nature problem-solvers. If we begin to consider ways to make mathematics come alive for our students, perhaps we can change the way they feel about math and science. After all, each of us had a moment when we fell in love with our subject. I argue that with a bit of creative thinking, maybe we can provide that moment for our students as well.
By Ima Abia, Private Tutor