TEACHING MATHEMATICS

 

A teacher of Mathematics once told me that if I could add, subtract, divide and multiply, I could master Mathematics because these skills were the foundation of Mathematics. Well, I can add, subtract, divide and multiply, quite well, as a matter of fact. But I wouldn’t say I mastered Mathematics.

My memories of Math classes are not great, but they do not leave me depressed. One of my Math classes in third form stands out in my memory to this day. It is the only one that holds a position of prominence in my mind. The teacher was quite pleasant. I remember her sitting at her desk for most of the class, waiting for us to bring our work to her for correction after she had “taught” us the fundamentals of whatever topic was introduced. (Sitting is not a bad thing to do. I like the idea of having a chair at the ready in my classroom so I can rest my weary legs, if I choose to).

So, back to my third form Math class. I can still see a “stick man”, standing at the top of an incline. Our job as students was to say something about the man’s position at the top of the incline in relation to a point at the bottom of the incline, I can’t remember what. But, calculations were involved. The ‘fundamentals’ that the teacher presented to us went something like this: “Today we are going to be doing... “ [I cannot remember what we were supposed to be doing]. If we want to... we ...” [She must have presented a formula or some other instruction on the board]. She then wrote a ‘problem’ on the board which, following some steps, she “solved” . We watched as she provided the solution. After we had watched her at work on the problem, the teacher put a problem on the board and told us to solve it following her example.

I can still remember looking closely at the problem and not discerning where to start to make sense of it. It seemed to have been a foreign language which was yet unknown to me. So, I raised my arm and waited politely to be acknowledged. When I was finally acknowledged, I told the teacher that I did not understand the problem on the board. Her response, “What don’t you understand?” I did not understand anything but I couldn’t find a way to articulate that without offending her. I repeated my statement that I did not understand the problem on the board. She was pleasantly dismissive. She glossed over my not understanding - probably telling us that we needed to pay more attention or something to that effect. Then she turned back to the class and asked if everybody understood what they had to do and everybody, except me, replied in the affirmative. Having been assured that her teaching was as clear as crystal to everyone, she took her seat and studied her textbook while she waited for us to solve the problem and take it to her for her perusal. Some students eagerly set to the task, (these were the “bright” ones); some students conversed in small groups and some doodled. I buried myself in a novel that I had brought for occasions such as those – occasions when I was not gainfully employed in the classroom.

Mathematics does not have to as abstract as teachers tend to make it, at least that is my view. I believe that teachers of Math need to make the subject accessible to students. One way of doing that is to start from the beginning. What do I mean by starting from the beginning? The teacher is introducing his/her class to algebra for the first time, for example. It would be nice if the teacher would carefully explain to the students the concept of algebra. What is it? How is it applied? Why do we need to use it? Translate it into the language that the students speak. Using Mathematical language will not help. Relate the topic to real life scenarios so that the students can get excited about it and feel invested in learning it.

Some students have naturally logical brains, I don’t know if this is a scientific fact. They need no explanation except, “Today, we are going to do algebra. A+B=C. A, B and C can stand for any number. If A is 1, B is 2 then C is 3. And he/she presents more examples progressively more difficult. The students are then given some problems to solve.

The students whose brains are wired differently from the math geniuses prefer to, initially, have the teacher use many words (in non-mathematical language) to explain the mathematical concepts. When they understand these concepts, they will respond to them. Therefore, teachers of Math anticipate your students’ unanswered questions: How is this relevant to me, the student? Under what circumstances will this be useful? What are the real life implications of my learning these things? It is said that a picture is worth a thousand words. Probably. But, oftentimes, one can’t find enough words to make sense of the picture. 

Math teachers, if they want their students to learn mathematical concepts, to pass examinations, to enjoy Math, must take Math out of the realm of the exotic and esoteric. They must apply the concepts to real life situations. They must show how it is useful in the real world, beyond simple addition, subtraction, multiplication and division. They must be willing to address the concerns of the “slow” students who cannot immediately “wrap their heads” around the subject. Students are going to ask why. They want reasons. Math teachers must be prepared to give those reasons. When students understand why they are doing Math and its relevance in daily life, they can then use the basic skills of addition, subtraction, multiplication and division of fractions, decimals and whole numbers that they would have learnt by at least the end of primary school, to master the other elements of Mathematics. However, before teachers of Math can inspire their students to want to learn the subject, they must, first, have a deep understanding of the subject themselves and the ability to communicate what they know.