In these classes, we investigate Mathematical concepts that are part of most school curricula. The aim is attaining conceptual clarity - understanding why and how things work the way they do in the world of Mathematics.
I offer this program for three age-groups: Grade 7-8 (approx. 12-13 year olds), Grades 9-10 (approx. 14-15 year olds) and Grades 11-12 (approx. 16-17 year olds).
For each age-group, I nudge children to discover concepts for themselves through curated weekly problem sets that are solved by the children and discussed as a group. I select the topics for investigation based on the level of the group. But I also encourage the kids to share with me the difficulties they are experiencing in Maths classes (in school) so that those topics can be investigated too, doubts clarified and related problems solved.
To do well in school Mathematics, children must develop conceptual clarity and strong foundations, which is the intent of this programme. However, this may not be enough. Kids will need to back this up with their own effort. If they take the initiative to solve similar problems from their textbooks, they are more likely to internalise these concepts and eventually develop, fluency and speed.
You can find some sample problem sets below. As you will see, the attempt is to get children to think and find answers to the questions: 'Why...?'
Age group: 12-18 years (3 levels)
Batch Size: 8-12
Mode: Online via Zoom
Duration: Ongoing, 90 min/session, 4 sessions/month
Timings (IST): Weekdays (contact for details)
Monthly Subscription: Rs. 2000 per month
While working with children on recreational explorations, I gained some insights into their abilities and thinking. Here are some observations and questions that came to my mind.
1. When moving from primary school to middle school, children are expected to make a 'mental leap'. The journey into the abstract must now be taken without concrete aids and manipulatives which were such an integral part of Mathematics education in the primary years. They must now systematically understand the language of Mathematics and its peculiar syntax, and gradually hone their powers of logic and deductive reasoning. Are children receiving the right sort of hand-holding through this transition?
2. At every level in school, children are expected to pick up Mathematical techniques, procedures and formulae, which serve as tools for problem solving. Some children pick these up quickly. Others struggle to develop fluency. But most children undertake the task by rote, without a proper understanding. They rarely develop a deep sense of the vocabulary used in their textbooks or why the stated procedures work. Wouldn't it be wonderful if they were given the chance to discover some of these truths for themselves?
3. Children, fatigued by repetitive school exercises attended to in an unquestioning manner, often pertinently ask: 'Why are we studying all this? Where is it all used?' As a mentor of mine once insightfully observed, 'The day they ask that question, we can be sure we have lost them!' For indeed, does it ever occur to the child to ask the same question while in the music room or the games field? Can Mathematics learning bring about the same kind of joy that music and sport do, making its application to our day to day lives irrelevant? Can we give children a taste of what it means to encode pleasing patterns in Mathematical language? But of course there are real world applications of Mathematics as well. Can these be showcased too?
To try and answer some of these questions and develop in children a deeper Mathematical understanding, I saw the need to extend the work of the Maths Club. Hence, the birth of 'Curricular Investigations' in 2021, which hopefully retains the same spirit of inquiry and discovery that is integral to the Maths Club.
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