Math in the Primary School - A Honest Look

In Indian schools, it is a reality that primary school is not considered very important. All the attention is focussed on the secondary school, particularly the classes preparing for the board examinations.

Possibly because of this, the primary curriculum, particularly the math curriculum, and pedagogy have not been critically examined &n evaluated by curriculum planners.

The objectives of the primary math curriculum are (a) get children interested in math (b) provide them necessary basic concepts, skills & vocabulary so that (c) they can master the middle school curriculum effectively with confidence.

The curriculum and pedagogy adopted currently in the primary schools do not do adequate justice to these objectives

In this article I want to highlight some of these issues.

The children in primary school are in the “concrete operations” stage as per Jean Piaget’s Developmental Psychology. Their strengths and weaknesses in cognitive abilities juxtaposed with the unique nature of mathematics as a discipline, can be summarised as below.

1.	Their capacity to understand abstract concepts Is not fully developed. But even the mathematics taught in pre-school and primary school has several abstract concepts.

2.	At the same time the concepts are easily relatable to events and processes that children encounter in daily life. Children in primary school need a lot of exposure to concepts mirrored through experiences familiar to them.

3.	Children in primary school do not “value” things in terms of their usefulness. They are basically motivated by fun, friendship, surprises and happiness. If taught the right way, math offers a lot of opportunities for happiness & surprises.

4.	This implies that the mathematics pedagogy in the primary school should involve a lot of activities with familiar daily-use materials, role plays & connections to their life experiences.

5.	It should also provide children with opportunities for explorations and discoveries. It should put “fun” and “relevance” at the centre of math.

6.	Such a pedagogy requires more time, space and materials.

7.	Instead, the pedagogy still focusses on “memorizing” rules and facts with very little focus on “understanding”

8.	For children in primary school, even the spoken language of teachers contain several abstract concepts made more difficult by varying pronunciations. Most children at this age cannot focus and understand continuous spoken lectures for more than 10 minutes at a stretch. They easily get bored and lose their focus.

9.	But the reality in most of our classrooms is that children passively sit in crowded classes in desks listening to the teacher and looking at the black board.

10.	Children at this age also learn through physical movement. In the absence of learning through activities and play, the only physical movement children get in in their breaks or PE classes.

11.	In mathematics, even procedural skills are built on conceptual understandings. Without an understanding of the basic concepts, procedures become just rules to be memorized and hence forgotten easily.

12.	Mathematics is also a discipline where concepts link to and build on one another like a pyramidal house of cards. So, non-understanding of a concept or a procedure, compounds as more concepts are built on it, ultimately leading to math anxiety, math avoidance & math phobia.

13.	As concepts evolve, the same procedure undergoes subtle changes and the rules “seem” to be changing constantly. This again results in forgetting or getting confused with, the memorized rules.

The assessment policy followed in primary schools also needs to be re-examined.

Primary School is meant for building a firm foundation of basic concepts & skills. Middle school is for applying these basic concepts and skills to real life situations. And for learning complex concepts built on earlier ones.

Hence primary school should ensure that all the children, except a few who may have special learning difficulties, master at least 90% of the concepts & skills. Being satisfied by a 50% performance can be dangerous.

To give an extreme example, 50% achievement may mean that the child has 100% competence in addition but only 10% competence in subtraction. Such a student will certainly face problems as he proceeds to higher classes. He has to master both addition & subtraction. By the same logic each and every basic concept & skill should be mastered by all students.

Achieving this would mean that the focus should be more on completing a task correctly and not on how fast the task has to be completed. Time-bound assessments only create stress for most children.

Textbooks are another area of concern. Children in primary school do not have the ability to read a mathematics textbook and understand it. Hence it is mainly used to assign homework and to enable memorization of definitions and procedures.

Learning problem-solving skills is one of the universal objectives of a math curriculum. Constructing word problems is an important aspect of building this skill.

Use of problems from the textbook has made both teachers and students incapable of constructing problems by themselves. Children do not really need a textbook. The teacher may have a copy of the textbook just for her reference.

The math curriculum in primary school goes up to very large numbers like crores & millions. Children in primary school have no idea of such huge numbers and do not experience any situation which requires the use of such large numbers.

To have a sound logical understanding of arithmetic operations, practice with 3-digit numbers is more than sufficient. Students in middle school can learn these large numbers as they use them in other subjects like geography & science.

Formal examinations in primary school reduces time available for teaching & learning. It is better to have only formative assessments in the classroom. Assessments should include oral, practical & project assessments in addition to paper & pencil ones.

Based on the above arguments, I would suggest the following modifications to the primary math curriculum.

1.	The curriculum should be limited to basic concepts, skills & vocabulary necessary to equip students to apply them in middle school.

2.	The whole number curriculum should be restricted to 4-digit numbers

3.	Non-critical topics like clock arithmetic, Roman numerals & India/ International Number Systems should be shifted to middle school

4.	Pedagogy should involve activities with manipulatives, individual/groups activities and role plays

5.	Discussions with the teacher and among students should be part of the learning process

6.	Puzzles & number explorations which will introduce students to the joy of learning mathematics.

7.	Students need to have only a workbook rather than a textbook

8.	They should also be encouraged to make their own problems including word problems. Blank pages may be provided in the workbook itself.

9.	Summative assessments should be replaced with formative class-level assessments.

10.	Timed-tests should be reduced to the minimum.

11.	Pedagogy should ensure that most of the students master at least 90% of the curriculum