Mathematics Education – Examining our approach…
(This is the second blog post in a series of three blog posts examining where we are with respect to Mathematics education and what we can do additionally. In this blog post, I present my views on our current approach towards Mathematics education.)
In my previous blog post, I presented the current advancements in the field of Mathematics education, specifically the proliferation of resources for aiding Mathematics education and the associated challenges. I ended the blog post by presenting a need to create a fundamental shift in our approach towards Mathematics education, by asking the question – “What needs to change fundamentally in our approach towards teaching/learning Mathematics?”.
In this blog post, I would like to start exploring this question by making a probably obvious observation:
Mathematics is still a struggle for many!
I have noticed that in spite of the availability of so many learning resources, students still struggle with Mathematics. To give an example, over the last few years I have interacted with students (by virtue of the workshops/classes/one-on-one sessions that I have conducted) who struggle with things like whether to add or multiply, or whether to use LCM or HCF when dealing with a problem; when their classmates have already mastered these concepts and are applying them with relative ease. We are talking about elementary Mathematics here. One can very well imagine how things will be for them when they go to higher grades.
Is something missing in our current approach?
The reasons for this struggle could be many and I am by no means an expert in identifying all the reasons. However from the (limited) perspective that I have gained on this topic, I feel that partly the reason is because our approach towards learning Mathematics has remained the same in spite of all the technology advancements that we have made. I feel that our approach is not fundamentally tuned towards students being exposed to different perspectives of Mathematics and needs to change. But, before we look at how our approach needs to change, we need to first take a look at our current approach first.
What is our current approach?
The way the curriculum of most schools is designed (and I am speaking from my personal experience interacting with students of various schools and also from my experience studying textbooks that some schools follow) makes us move from one concept to another using a standard process.
Teachers (who use these textbooks as an aid) define a concept, probably spend sometime exploring the need for the concept, relate it briefly to concepts presented earlier, solve lots of problems in the classroom, assign more problems to students as practice problems (and of course, test them on their ability to solve problems in timed settings). One look at a typical text book and the schooling calendar of a typical school will easily reveal this process and the emphasis that we place on problem solving as a way of learning Mathematics.
Issues with this approach
I am not saying that the current approach is flawed. Probably, there is a need to solve problems and be tested as well on the ability to solve problems. After all, it builds analytical ability that will stand the students in good steed. But it may be probably worthwhile examining where this approach is leading us. For that, let us look at how students learn Mathematics currently.
Some students have a natural flair for logical thinking and solving problems (I don’t want to go into the reasons for this flair). When concepts are presented to them, they somehow understand them faster and better. They are also able to follow the solutions to problems better. They are then able to use the insights that they gain and the patterns that they glean to start solving problems on their own. When they are successful at solving problems by themselves, they get a kick and want to solve more problems. When they get good at solving ordinary problems, some of them want to solve more complex problems. (I have a separate take on what else can foster the desire to solve complex problems but that is the topic of another blog post, I guess. More on this at a later date.) These really good students of Mathematics start seeing insights and patterns that were never presented to them by their teachers. Some of them realize that Mathematics is their true calling and could go on to become Mathematicians. But as you can guess, these cases are far and few between.
Then there are the students who don’t have a natural flair for logical thinking and solving problems. Mathematics is simply not their forte. They are good at other things – maybe sports, maybe art, maybe something else. But the way the schooling system is designed, they can’t get away from learning some amount of Mathematics. And anyway some amount of Mathematics is required for handling day-to-day life (although it is debatable how much Mathematics is actually required for handling day-to-day life). These students are not able to ingrain the same insights and patterns that are so easy for their classmates to grasp. Some of them are good at solving problems using basic concepts. But as the concepts start becoming more abstract, Mathematics starts looking like a tough subject to them. They lose interest and needless to say, the beauty of Mathematics is lost on them. They start relating to Mathematics as a set of rules/processes that one has to remember and apply. But the problem is even if you somehow manage to remember the process for computing the LCM & HCF of two numbers, what do you do with this knowledge if you don’t know whether you have to compute the LCM or HCF in the context of a problem. Similarly, what is the use if someone who knows that he/she needs to compute the LCM in the context of a problem doesn’t know how to do the computation (just because he/she learnt it in a lower grade and has now forgotten the procedure).
Parents of such students, on their part, feel that if their children go through the drill (solve lots of problems), they will eventually become good at Mathematics. They either sit with them after school or arrange for private tutoring to take care of this. No doubt, the drill approach may work, at least in some cases. But it doesn’t make the process of learning more enjoyable for someone who doesn’t have a natural flair for Mathematics. A drill makes things more mechanical and pattern based in some sense and if the student doesn’t like the process, it can lead to a dislike for the subject.
What can be done differently?
It is clear that not everyone needs to become a Mathematician (The world would probably be a scary place if that happens anyway:-)). However, we need to ensure that all students become proficient in at least a basic level of Mathematics. So, we definitely can’t shy away from the need to impart Mathematics education. The question then is, how do we improve the process of teaching/learning in such way that students enjoy learning Mathematics and at the same time, become proficient in the subject to some extent.
For that, we need to ask ourselves the questions:
- How much does practice contribute to internalising a concept?
- Are there other things which we can place emphasis on (other than practice) for internalising a concept?
My personal view is that although practice does play a part in internalising a concept, practice without understanding a concept fully can actually make Mathematics look like a chore for some students. And nobody enjoys chores, after sometime.
It is clear that we need to answer the second question to be able to improve our approach to learning Mathematics. We need to complement practice with something else – something which can help students gain a better understanding of Mathematics and help them find purpose in practice as well. The question is – “What can we add to our current approach to enhance Mathematics learning?”
In my next blog post (which is the last post in this three post series), I examine this question and propose the addition of an element of enquiry to make students understand Mathematics better and enjoy the learning process at the same time.
