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@ Isai Ambalam School

Towards integrated mathematics education at Isai Amlabam – Sanjeev Ranganathan

We moved to the Isai Ambalam school in Auroville in May 2013 and I have been working on Mathematics (and Science) education since. This page consolidates the work here.

We took a step towards integrated approach to mathematics at Isai Ambalam school for the children in grades 5th to 7th. The NCF 2005 document places the purpose of mathematics education primarily as Mathematization i.e. on developing the ability of children to think and reason mathematically, to be able to handle abstraction. It includes a way of doing things, and the ability and attitude to formulate and solve problems. This idea ties in with the idea of a more integral mathematics where is not a disjoint set of skills to be acquired, but to cultivate a patient problem solving approach to life.

To handle abstractions the children needed to be able to see the application of mathematics in real life. The very basics of addition and subtraction of natural numbers was understood in real quantities, but children lacked the same a feel for fractions, decimals, percentages and even measurements. We looked to address this with a real life problem of estimating the volume of water that is stored in the school tank. Children took measurements of a cylindrical tank and then tried to relate it to its volume. How does the perimeter that could be measured related to its volume? How does the perimeter of a circular object relate to the radius? They took measurements of various circular objects and tried to relate it to its diameter/radius. On a computer they saw how these all converged, but how they were unable to handle these manually or make reasonable guesses. We learnt as much from what we could not do (and aspire towards) as from what we could do (rigor).

We also made measurements in experiments e.g. the period of the pendulum and how these measurements can be made more accurately if we can deal with dividing decimal numbers. We also looked at relating it to the mass of the bob, amplitude of oscillation and length of the pendulum. We realized that not all quantities in life vary linearly and the need to learn more became stronger. With these as context we re-learnt the basics well including fractions and decimals. We used TLM like Densiel blocks, pizza party to do the same.

We continued doing some science experiments throughout the year (speed, momentum, sound, volume, density, electronics) providing context for mathematics and to see how the progress in mathematics helps us understand and learn about life accurately.

The masterstroke this year was a multi-grade classroom in the second and third term. The number of children in the 6-7 grade was small and it was possible to enlarge the classroom with the elder children already enrolled into the idea of learning by doing. As the 7th graders approached algebra we realized that understanding of even basic concepts of multiplication and its corresponding (two) division stories was weak. The same is true for addition and its two subtraction stories possible, but we focussed on multiplication as these relate to many physical phenomenon (speed-distance-time, speed-momentum-mass, density-mass-volume, current-voltage-resistance, etc). In a multi grade classroom for children in lower grades would tell stories of baskets with mangoes, while elder children told the same with speed of a car. In a little time 5th graders got a hang of speed and distance (which they decided to demonstrate with a play for the school Annual day). The 7th graders in turn got a hang of abstractions needed for algebra. We moved to puzzles that needed to be abstracted into algebraic equations and they were not only able to create the equations, but also solve them. They were also able to pick up the connection between algebra and geometry and developed their intuition further with the use of Geogebra.

The girls in 7th grade also built a wind-chime that required them to saw and use a drilling machine. The exercise helped in getting the idea of approximations (holes need to be drilled at 22% of pipes with varying lengths), but also gave them a lot of confidence through the use of power tools.

When the children made their final examination papers to demonstrate what they had learnt – word problems and algebra figured prominently in their tests. These two areas are good indicators of the progress of children in abstraction.

Blogposts corresponding to the work at Isai Ambalam School can be found here.

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