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Professor Sinclair works with the Indira Gandhi National Open University, India. Her interests include algebra, mathematics education, open and distance learning systems and school education. She headed the National Council of Educational Research and Training (NCERT) for two-and-a-half years. In 2005, she worked with NCERT on creating the National Curriculum Framework based on a version of the constructivist approach to learning, with focus on the syllabi and materials related to the National Curriculum Framework. Together with her team, she developed the Certificate programme in Teaching of Primary School Mathematics – a 16-credit programme run by the Indira Gandhi National Open University.
1. What’s your earliest memory of doing mathematics?
Many of my early memories include what other people have said. For me, maths is about the special form of reasoning – which is really basic – the essence of mathematics. The kind of reasoning where you move step-by-step to a conclusion. When I was a kid, my parents told me to move logically, study from the beginning. When talking about school maths, I always did self-study, right from Grade 2. I remember enjoying abstraction and playing with abstraction more than I did with numbers.
2. How has mathematics education changed in the time you have been involved in it?
Hmm, what hasn’t changed, right? In India, people in maths education seem to continue to teach maths really formally from early school on. This is what has continued to create a fear of maths in the learners. I got into maths education because I wanted to do something about this, and from 1980 onwards I started thinking more about the issues concerned and the math teaching-learning scenarios. In the National Policy on Education (1986), the focus was on how to improve the high school level of understanding of mathematics. Teachers and teacher education continued in the same (formal) way, not even trying to get into what maths is. Then the MLL (minimum levels of learning) movement came in the 90s, which was another major problem. Now, in the last year (2020) India declared a new National Education Policy. There isn’t much change in the school-related bit in this policy. What did change over the years was that a lot of NGOs got into school education. I worked with several of them and tried to do something about learning starting from early on, as we are trying to form a basis of understanding for the later years and for this you need to start early. In 2005, I was part of the NCERT group, for formulating the new National Curriculum Framework (NCF). And, can you imagine that was the first time an NCF was designed based on the level and way a child thinks and grows? For the first time in all these years, the curriculum was from the bottom up, in a sense, rather than it being top down. However, it hasn’t been easy to implement. India is a huge country in numbers, spread and diversity, and just orienting teachers to this sea change of mindset required a lot of effort, much more than was actually put in.
The 2005 National Curriculum Framework was based on the constructivist way of learning. Some states in the country accepted this, but it has been a challenge. So, there’s been some change in the way maths is taught, there are a few voices. But the states do have their own hidden curricula, and the different subject areas are treated differently. You can’t have maths being taught differently from say social science or science, or the local language. One wants to bring a supportive learning approach. We want to bring a problem-based approach, an experience-based approach across the board. And then, of course, most teachers don’t like being questioned by the learners. So, there are these kinds of issues that haven’t really changed over the years, and we are still grappling with them. So, there are some limited results of our work. One has to try to improve the education of teachers, and also, help them share the understanding and philosophy on which the NCF is developed. In a lot of rural areas, it can be very difficult, as teachers want to follow the textbook and go by that. Teacher educators need to rethink their ideas of learning too. There is a battle among maths teacher educators, and quite some resistance to trying, for example, to introduce discussions like what maths is about to high school children.
3. Tell me about a time in your career when something totally flabbergasted you.
Up to the time I joined the Indira Gandhi National Open University, my focus was on hardcore algebra. While doing research in algebra, the “aha!” moments are out of this world! While helping others to learn about maths and working with young children, I have been often pleasantly surprised. It is wonderful when you see kids working on something and think “It worked! It came together!” – this is a beautiful moment.
I have been outraged also several times by several policy makers who have not worked with children, or in education, but make outrageous statements about these areas, impacting the whole schooling system. Unfortunately, every adult thinks they know how maths should be taught, but few of them bother to actually consider the children and how they learn.
4. Do you practise mathematics differently in company?
When I do algebra, there is a portion I do with myself and some I need to discuss with other people. There is a certain number of people who work in this area and we communicate. If I am working in maths education, I have ideas that I have learnt from others, e.g. theoretical models, and I need to discuss such things with other people. It is about working it out, sharing it and getting influenced by what other people are telling me. When working with a child, I will work at a level so that we can both communicate, and so that what the child says influences what I say and do. When working with an adult learning something, I change the conversation to suit their way of thinking.
5. Do you think a brilliant maths teacher is born or made?
Not really sure about the word “brilliant,” but a good teacher would have empathy. Does it (empathy) make a good teacher? Someone who really empathises with a learner? I think that empathy will really help in communicating with, and understanding, the level of the learner.
Teachers must also know and understand mathematics beyond the level they are teaching, and its different aspects to be able to teach them. They should also appreciate the beauty in the kinds of surprises that happen in learning. That comes with experience, I think.
6. What’s the most fun a mathematician can have?
I don’t think that “fun” is any different for me – a professional in any field would have fun working with students in general. You can have fun in different ways – reading good books (maths or other), fun with being with people you enjoy spending time with, like anybody else. I don’t really know if maths has anything to do with this.
7. Do you have a favourite maths joke?
I kept thinking about this question and I don’t have a joke, but I do enjoy good cartoons. I try to put some cartoons and jokes into my materials and people say they enjoy the materials with cartoons. I guess it depends on people’s sense of humour, though.
The work of Tom Lehrer, an American mathematician, also comes to mind. His song called “New Math” is very enjoyable.
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