Page 43 - Ramanujan Yatra

Ramanujan
YATRA
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The Position paper identifies “mathematization of the child’s thought processes” as the primary goal of mathematics education. It recommends that mathematics teaching at all levels be made more “activity oriented” and student centered, so that the students understand the basic structure of mathematics, learn to think mathematically and relate mathematics to life experiences. The document suggests a “shift from content to processes” and recommends that a pedagogy be evolved which emphasises the processes of learning mathematics such as visualisation, estimation, approximation, use of heuristics, reasoning, proof and problem solving. It also recommends the use of technology in the form of computer software and calculators to enable students in visualising and exploring mathematical concepts.
This article will highlight the role of technology-driven explorations in enabling the process of mathematisation and in developing students’ mathematical thinking. As an example, we shall describe how secondary school students explored Fibonacci numbers using a spreadsheet and in the process learnt new mathematical concepts.
Fibonacci Numbers and the Golden Ratio
The Fibonacci puzzle was posed by Leonardo of Pisa who was also known as Fibonacci. The puzzle describes the growth of an idealised rabbit population. A newly born pair of rabbits comprising a male and a female rabbit is put in the field and is able to mate at the age of one month. At the end of the second month the female rabbit produces a pair of rabbits (again a male and a female). Rabbits never die and every mating pair always produces a new pair every month from the second month on. How many pairs will there be in one year?
Introduction to the Fibonacci Puzzle
The puzzle was posed to 30, grade IX students who were required to work on a series of investigatory tasks to explore the problem. The first task given to them was to find out the number of pairs of rabbits at the end of every month starting from the first month. To begin with there is one pair which mates at the end of the first month. By the end of the second month the female produces a new pair and thus there are two pairs. At the end of the third month, the female of the original pair produces a second pair, making 3 pairs altogether. It is important to note that the second pair, which was born at the end of the second month, is only able to mate at the end of the third month. At the end of the fourth month, the female of the original pair has produced yet another new pair and the female born at the end of the second month produces her first pair, making 5 pairs in all. Students were encouraged to represent this process diagrammatically. The