Understanding The Beauty Of Math
First of all, I understand that not everybody likes math.
I am currently tutoring kids at a primary school nearby my college campus. Today, in the 4th grade class I work with, I was assigned students who were doing a practice exam, preparing for the 60-minute state-wide assessment tomorrow. My job was to help this group of students get through the whole set of problems in two hours. The practice exam featured problems about time and date, approximation, and spending. I thought to myself that I would have loved the class if I was given these kind of problems in 4th grade.
However, despite their real-life simulation, the problems did not interest the kids. Everything else seemed fine; my students did the exam anyway since the teacher was sitting at the next table. At first my excuse was that it is normal that math is not their favorite subject.
As my observation continued, however, I found that they were all using exactly the same approaches in solving these problems. It should not be surprising since everyone including me did that in 4th grade too. We were told how to solve the problems and we just kept using the method. Do my students know what mathematical concepts are behind it though? I asked them. It was surprising that “No” was the answer. For example, given the date of the first Monday, students were asked to find the date of the third Wednesday in that month. They knew that they had to add multiples of seven but they did not know why. This is indeed sad.
I was trying to think of what went wrong but my students were finishing all the problems in such short a time. Why do we prefer speed so much in a test? I have come to accept that a short exam time does indeed turn their “getting interested” button off. Although generalizing my observation is risky, this is the problem that we are facing in our education system.
To get the work done quickly, my 4th graders simply put everything into formulas they had already memorized. Such methods give them right answers and save some time; therefore doing so does not seem wrong, at least in their thinking.
I believe that grounded understanding is fundamental to early math learning. So it may be way too early for the state to assume mastery in both speed and preciseness in fourth grade. My observation suggests to me that an inadequate proportion of short exam time to a number of problems in the exam prompts teachers to teach their students only exam-taking strategies and neglect mathematical constructs.
Students, knowing that they have to finish all problems in time, cannot help ignoring the importance of formulas’ origins. Thus they respond to this exam format by merely memorizing all strategies needed. It entails that they skip mathematical foundations directly ahead to the formulas that are fruitful for them in an exam. Such a jump intensifies the problem that students lack basic backgrounds when they learn more complicated materials because the only time they learn the essentials of mathematics is when they are in primary schools and the problem propagates as a class moves on.
The elaborate demonstrations are becoming less important and undervalued. When the question asked them to show all work, my students just wrote down the answers and skipped the rest of it. If to increase speed means to have something like formulas in mind, something in our current math curriculum is not right.
However inevitable in learning, memorization should not serve as a main component. Knowing formulas alone does not demonstrate students’ comprehension of the subject as when everyone uses the same method to solve the same problem without knowing its mathematical concepts. The recipe they have used is not derived from their own experiences. Memorization therefore must only be a by-product of learning processes, i.e. everything will come to one’s mind immediately as soon as one thoroughly understands the concepts.
Instead of exciting students, learning math is now submissive with teachers only giving and students just taking — since all we want to achieve is high quantitative academic performance. The beauty of math that they could find after numerous attempts at a problem is lost and will never be found. Students do not get to know how enjoyable (or painful) solving a math problem can be if they are programmed to receive inputs to produce outputs through given methods only. Weakening also is mathematical creativity. While handing formulas to kids in order to ace the tests in time, their boundless creativity is bounded. Why do they need to think if tools are given so easily?
Why must we do math in such a rush and neglect its beauty along the way? Solving a math problem requires logical thoughts that in early math should be traced step by step in an explanation of the problem. Revision is crucial. Once students practice such repeatedly, not only does revision give opportunities for the student to verify their process with their mathematical knowledge but it also allows teachers to know their students’ progress.
Short exam times, in contrast, give rise to multiple choice questions which are easier to be graded but incentivize students to memorize. As I already explained, we know how memorization undermines the perception of the mathematical beauty.
One may argue that 4th graders may not be proficient enough to critically understand or to question mathematical concepts in depth. What I say here, however, is not to have everyone grow up to become innovative mathematicians; rather, as well as in other subjects during early learning period, I want fourth graders to have a strong math foundation before they even make a judgement about whether they like math. We, as educators, need to properly nurture their attitude before it is too late because speed can be increased as long as students are grounded.
Or maybe, I just want everyone to enjoy math.