The Math Programme started in October 2006, with an idea of implementing some of the activity-based ideas in schools and centers in Chennai. We wanted to work on the following topics:

• Measurement
• Geometry
• Algebra
• Arithmetic
• Visual representation

Of these, we first started with Measurement and Geometry.

I) Measurement

In measurement, we started with teaching area as a concept. We wanted to link the idea of multiplication and the concept of a rectangle’s area, to bring out the connection between two topics that children learn separately. We started with a survey of what students knew about this connection.

Survery and Observations:
The survey consisted of about 4-5 questions pertaining to area and forming rectangles, and was done with students of class 7 and 8. One of the questions we had asked was the area of a rectangle of length 5 and width 4. The results we found were shocking. In many schools, not even a single student (out of a class of 40 to 50 students) got the answer right! Overall, a miniscule percentage of children (less than 5%) got the correct answer. Worse, more than 95% of those who attempted the problem gave an answer that was not numeric! It was instead a formula: in about 25% cases it was the correct formula ‘lxb’, sometimes it was ‘½ lb’, ‘l+b’, and even ‘4a’! The children did not have any idea about which formula to apply in which situation and for what problem. More importantly, there is no understanding of what the different symbols in a formula mean, and how to correlate them with the numeric values given.

Measurement Intervention Module:
Given the results of this survey, we wanted to first focus on the topic of area. We have devised a module of about 10 classes for introducing and explaining the concept. The module consists of the following activities:

• Introducing the concept of area: Use two congruent right-angled triangles to form different possible shapes. This by itself is an interesting and challenging activity. The common “property” that all the shapes possess is that they have the same area.
• Rectangle area: Through small cubes. Ask to find how many rectangles are possible with a certain number of cubes. Again, common property is that area is the same. Relation between factors, multiplication and area in terms of small unit squares. Showing how the formula for area (LXB) is derived.
• Rectangle perimeter: Using above material
• Area of shapes obtained by combining different rectangles: Using geoboard, ask to form different possible shapes. Area as number of square units.
• Area of triangle and shapes that contain triangles: Again using geoboard. Also used to show how areas add and subtract, as well as the property that “Area remains unchanged if the shape is rotated”.
• Filling a shape with small pieces and finding its area: Give different shapes that can be formed by all 7 Tangram pieces. Then other shapes that use only 6 or 5 of the pieces.
• Area of irregular shapes: With small square pieces

We did a pre and post evaluation for children’s understanding of the area concept. About 75% of children were able to get correct answers in post-test. Detailed data on the questions used and the percentage of children who got it correct are available separately.

II) Geometry

A number of new ideas are introduced at the middle school level in geometry. The foundations for geometrical thinking in children begin with shape recognition. When small children are given a number of shapes to sort, they first look at colours, sizes etc. Only at the next level does the number of sides, property of the shape etc. come in. Again, to find out the level of the child we did a survey among students.

Survery and Observations:
In the survey, we had asked questions on identifying triangles, rectangles, quadrilaterals. One of the questions that more than 80% children got wrong is in identification of triangles. Most children think that only equilateral triangles (or ones which look like them) are really triangles. Most children did not pick scalene triangles into the category of triangles at all.

When it comes to recognizing other shapes, more than 50% children are not able to identify a rotated square or rectangle as one. It appears that the shape “changes” after rotation for them – Not just for figures depicted on a piece of paper, but with concrete material like cardboard shapes etc.

Intervention in Geometry:
In geometry, the main material we have used is different shapes made in cardboard. We try and classify students into four possible levels of learning:

• Level 1: Identifying, sorting and describing shapes. Distinguish between relevant features (Angles, Number of sides, relative lengths etc.) as opposed to features like color, absolute size or orientation.
• Level 2: Properties of shapes – Can recognize important properties of shapes. Ex: A rectangle has all 4 angles as 90 degrees.
• Level 3: Relationship between properties – Can deduce relationships between properties as they apply to different shapes. For example, “If a quadrilateral has 4 right angles, must it be a rectangle?” At this level, the student is not only able to look at pictures and describe them, but look at a description and be able to visualize and draw a picture.

A child who cannot even do the first level activity is at starting level (Level 0).

Ideally, children should attain Level 3 by class 8 and our curriculum expects them to do so. However, our preliminary surveys show that a majority of children are either in level 0. (Most are unable to recognize that changing of orientation does not change the basic characteristics of a shape). Accordingly, our first priority has been to get them to this level by showing different kinds of shapes.

To bring them up to level 2 and 3, we introduce activities with the shapes and also discuss properties of each. More activities are being developed for this module.