Teaching Mathematics: Some Approaches

Discussing teaching-learning of any subject requires a basic understanding of how children learn. That should form the basis of our program particularly if each different component of the subject has a character that gives a specific tinge to its learning. The experience of these components for a particular child and the nature of the expectations from her can also be very different in comparison to the other children. For many years, Mathematics learning, like all other learning was considered to be linear and through repeated practice. Whatever was to be learnt had to be broken up into small components and given to children to practice bit by bit. The MLL (Minimum Learning Level) was a crucial example of this approach. In this the pedagogy was claimed to be competence directed. There is also an expectation from the text book and other materials that for each small element termed as 'competency', there would be one page or one section entirely devoted to it. It was expected that once the child has gone through this she would automatically and surely have developed that part of the competency and needs now to go on to learn the next part. The MLL document itself used the word competency in many different ways. It was used loosely to describe information recall, procedure following, applying formula and in some cases concepts and problem solving as well. As a result of this, it is not clear how the word competency in the MLL document should be unpacked. The on-ground discourse on competency has also not moved forward. In this case Mathematics given its so-called hierarchical nature, its learning seems to be still analyzed in the same framework and conceptualized as bit by bit and through practice of procedures and remembering facts.

Another element that pedagogy is crucially dependent on is the presentation of the teaching learning material

(workbook and textbook) and what it expects the child to do and how it suggests the class be organized and

assessment made. The material needs to be clear on whom it is addressed to and therefore what it should contain. If the material is for the child then it has to have appropriate spaces, font size, suitable illustrations designed for children and appropriate language. The textbooks and Mathematics classrooms before the advent of MLL and after the advent of MLL have remained essentially similar due to the fact that students are still being asked to practice algorithms and learn to numerate quickly. Articulation by the child, inclusion of the language of the child and allowing the child to explore and create new approaches to engage with mathematics situations are still not expected and not even accepted in materials. They follow the "consider the given solved example and do some more", approach to Mathematics learning. We may also point out that the mention of a specific competency to be acquired meant the earlier mixed exercises that at least exerted the mind of the child in someway, also got limited to practicing just one option. It was at this time recognition for design, need for illustrations and color in the books emerged so at least the books were different. The principles informing the illustrations, design and other aspects however did not include the need to create space for the child to actively engage her mind.

In the absence of clear articulation, word competency was focused on explanation and telling short-cuts and facts. The key words ‘learning by doing’ and ‘competency’, in the context of Mathematics were inadequately explored and insufficiently addressed. Addition was a mere operation and acquiring it was the capability of adding single digit, and more digit numbers with no carry over and then with carry over as column additions. In the quest to make Math a doing subject, competency based fractional numbers Mathematics will be learnt when the student will develop her own strategy, use the concepts and the algorithm in the way she wants. This clearly implies that children must have the opportunity to do lots of problems and solve them in many different ways. We must expose the learner to these different varieties and

develop not only the capacity to construct their own answer but also look and attempt to analyze and comprehend somebody else's answers. They need to be unafraid of making mistakes and confident of articulating their understanding. The implications in the classrooms are that children will work on their own, in groups make presentations on the solutions they have found and construct new problems as well as new generalizations. 

The classroom has to be such that the child is involved and engaged at each moment. There has been a lot of talk about constructivism and teaching-learning processes. There have been arguments suggesting that teaching-learning process should be constructivist. This is sometimes interpreted to mean that children should be allowed to follow their own paths and decide what they want to do. It must be emphasized here that like the use of materials in Mathematics the space for the child to articulate her own understanding and building upon it needs to be interpreted in the context of an organized sharing of knowledge with the child and the nature of the discipline. Once the basis of deciding the Mathematics curriculum is arrived at then the classroom and the school has to help the child develop capability in the areas considered important. The teacher cannot ask children what should be done. At best she can construct options that are in conformity with the goals and objectives set out in the program for them to choose from. The notion of constructivism itself and its relationship to Mathematics teaching-learning needs to be explored and analyzed more carefully.