How to teach mathematics in schools

We teach so much geometry through the blackboard but fail to do a simple experiment like the one to determine the earth’s circumference
How to teach mathematics in schools

In the year 2012, the Organization for Economic Cooperation and Development (OECD) announced the results of the Programme for International Student Assessment (PISA) in which 73 nations participated. The PISA is a test devised by the OECD to gauge the quality and standards of mathematics, science and the English language of school students of the age of 15 years in different nations. It has been administered regularly since 2000. India dropped out of the PISA testing programme after 2012. This abstention was probably prompted by our dismal performance that year. In 2012, of the 73 nations that took part, India was outperformed by 71 nations. The only country below us was Kyrgyzstan. This was disappointing news indeed.

One would have thought that perhaps in the realm of testing of mathematics standards—as a standalone subject—we would have had a higher ranking. Unfortunately here too we were one slot above the bottom. Kyrgyzstan once more saved us from the ignominy of finishing last. This was an eye-opener. In that fateful year when we last took the PISA test, it was conducted in two of our better performing states in terms of education standards, Tamil Nadu and Himachal Pradesh. So this should also give us an inkling of where the rest of the country stood. The important thing is to look for the reasons behind such poor standards. In all fairness, there may have been some cultural and language biases and barriers, but I am not ready to believe that they counted for too much. After all, English is not the natural language in many other nations where the test was held. Thus, we need to introspect and seek to sort out the impediments that hamper the creation of good standards.

I am happy to note that India will now participate once again in the PISA testing programme in 2022. More importantly, we are working hard to prepare our students for it. What is not clear to me is whether the overall standards in these three vital areas of knowledge—across the rest of the nation—are improving much.

Perhaps we should first try and understand why we are not where we need to be in terms of general standards. In this context, perhaps the most important issue that arises is the lack of good teachers of maths. I have overwhelming anecdotal evidence in this regard. In fact, as recently as a few days ago, at a social gathering, I came across a lady who is a serving civil servant. She remarked to me that she has great trouble helping her son with his school homework. She traced this trouble of hers, with maths, to her early years in school when she found it difficult to keep up with what was being taught in the class. She also seemed to suggest that her son’s maths teacher at school was not discerning enough about his needs. This story gets repeated several times with me, on social occasions, as soon as people realise that I am a mathematician. They tend to recount what they term as their horror stories of learning maths at school. Of course I must add this phenomenon is not peculiar to India. I have come across similar stories in other parts of the world. Several years ago, I was at a private dinner with a British minister of education and she asked me if I could give some tips to help change her school-going son’s dislike of maths. However, the situation in India, in my experience, is perhaps more worrying.

On the basis of fairly extensive but anecdotal evidence, I feel that one of the reasons for such a situation in India is due to the poor quality of mathematics teaching. More often than not I also learn—at the above mentioned social interactions with individuals—that they were either in awe or in fear of their maths teachers. This must not be taken to mean that I am condemning all maths teachers. There are some extremely gifted teachers and I know several of them. Yet something is amiss. I say this for the simple reason that school principals seem to be forever on the lookout for a capable maths teacher.
There is another hard-to-ignore reason. The pedagogy has to improve hand in hand with the curriculum.

For instance I have not yet seen a single textbook or a schoolteacher explain the simple maths behind the Samrat Yantra at Jantar Mantar. So much geometry and trigonometry is taught in our schools, yet the Jantar Mantar remains out of bounds. Since I have experimented with school kids at the Delhi Jantar Mantar, I can vouch for the efficacy in terms of the pedagogy. Similarly, we teach so much geometry that deals with parallel lines through the blackboard but fail to undertake a simple experiment such as the one to determine the circumference of the earth or find the distance to the moon.

The point I am trying to make is that we need to take the learning of maths out of the classroom and into the real world more than what we do currently. We must not teach maths as if each and every thing has to be proved with complete rigour while the larger picture gets lost. In my experiments with school kids ranging from their primary years to the seniormost levels, my colleagues and I have had such rewarding moments. This happens when the kids make use of their hands and put maths into action through real-world applications. I recommend these thoughts in all humility for it seems to help make the teachers seem like storytellers and the subject too comes alive.

Dinesh Singh
Former Vice Chancellor, Delhi University, and Adjunct
Professor of Mathematics, University of Houston

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