Criticality of Primary Math

Math is Different

Math is a different kind of subjects compared to other school subjects.

In the chapter "Nature of School Math" in Section 33, we present a detailed analysis of how math is different from other subjects taught in school.

Math is Full of Interlinked Concepts

It is heavily concept-laden right from the pre-school stages. Further the concepts are interlinked across topics in the same grade level as well as across the grades.

One way of visualizing the difference is in terms a house of cards built with playing cards. Let us call 2 cards kept in a triangle-like formation as a tent. Subjects other than math can be thought of as a series of tents kept next to each other. Even if one of the tents is weak and falls down, it does not affect the formation of other tents. For example, not understanding the properties of air does not affect our understanding of water very much.

But math is like a pyramid made of such tents. A series of tents is built on a lower level of similar tents. And the pyramid can rise to several levels. Here the weakness of any tent can affect the strength of the entire pyramid.

The tents in the lower level of the pyramid are the concepts & skills learnt in the pre-primary & primary school. They need to be strong to support the pyramid which will be built in each subsequent grade level.

A weakness in a concept or skill needed in class 9, may be the result of not having learnt the related concept well in the primary school. For example, a weakness in subtraction skills & concepts will also affect the learning of multiplication, division, fractions, algebra etc.

Hence the Primary Math curriculum should aim at mastery of basic skills & concepts rather than a lot of information, concepts & skills learnt partially.

Even Procedural & Factual Knowledge in Math is based on Concepts

By information, we mean a lot of definitions, labels & descriptions of procedures which occupy most of the class time, reducing time for deeper learning. In primary classes, students should learn a little less but spend a lot of time practicing, discussing & thinking about many of the concepts. Understanding of underlying concepts will also enable “remembering” procedures in a logical manner than “memorizing” them as a series of steps.

In addition, many skills & procedures themselves have an underpinning of some concept. For example, mastering multi-digit addition depends on an understanding of the place value system. Hence many of the skills cannot be practiced in a vacuum of non-understanding. They have to be practiced with understanding. Such practice needs to be done regularly in class with the facilitation of the teacher. A block of 2 periods is essential to such practice.

Understanding of both concepts & skills need to be supplemented with activities with materials individually in the classroom and in groups in the math activity centre.

Math is Difficult - Unless Effectively Taught

These aspects make math a difficult subject, both for teachers to teach and students to learn.

There are many teaching approaches which would help in implementing many of these ideas. We will deal with these in Book 2 of the Primary Math Project.

Some of these approaches have been touched upon in the section "What is Mathematics?"

A Pass Level of 40% Not Sufficient

By the end of 5th grade, ALL students must be proficient in understanding the place value system and in the four basic arithmetic operations. They should also be able to apply these skills to analyse simple familiar events. These are the foundations on which math in higher grades is built.

All children in at the K-5 level, should score at least 80 to 90% in these basic skills & concepts. A pass level of 40% will not do. It may mean, for example, that a child is very good in certain aspects but not good at all in other aspects. This is a sure recipe for math anxiety in the higher classes.

The next 2 chapters will deal with the important aspect of the magnitude of numbers which need to be taught in pre-primary & primary schools.

In the last chapter in this section, we present the primary math curriculum in a slightly restructured manner. In fact, the sequence in which the book has been divided into sections & subsequently into chapters, reflects this perspective.