In a little over 15 years the mathematics classroom has undergone a vast transformation. We have come from a straight piece of chalk to a new array of gadgets to help use them to bring a subject like mathematics to life for children. It can be argued that mathematics has now more IT possibilities than any other subject, starting with MS Excel to a bewildering array of web resources like YouTube, Google Earth and a large number of java applications. Software like Physical illustrator, Xthink, Cabri-3D, Autograph, T1 N-Spire, Casio classpad may be fascinating tools. But the fact remains that most of the mathematics classrooms and teachers in India are yet to embrace the use of technology at all.
                                                                                                                                                                                              
Mathematics has one of the richest histories in the world and some of it can be seamlessly put into its teaching without it seeming like a lesson in history. For example, a Pythagoras lesson can be greatly enriched by a visit to the TSM resources site where you can find out about the tunnel of Samos, which was actually dug in the times of Pythagoras, which was started from both ends.

It is this aspect of mathematics teaching the Casio Global Meet on Mathematics Teaching has been exploring for the last few years. The Meet held annually looks at application of mathematics to life, societies, geographical and ethnic situations, and has developed a rich fund of material on teaching of this subject. The latest Casio sponsored Meet was held at Tokyo University in December 2007.

Technology in teaching

Nearly 75 teachers representing 12 countries participated. Mr Antony D’souza, Principal of the Primus Public School, Bangalore was the only representative from an Indian school.

The 2007 Meet had a special focus on the use of technology in teaching mathematics. It was a surprising revelation that Japan, the largest manufacturer of calculators (and other electronic gadgets) does not allow use of calculators in mathematics classrooms till 12th grade and the Meet this year became a launching pad for this experiment in Japanese schools. They perhaps took a cue from the German experiment narrated by Prof Norbert.
Norbert, in his presentation, said that German schools felt that technology like calculators, computers and web tools were a definite help. However, the Germans have a two-tier testing for mathematics, i.e., calculators are allowed to be used in the first set of papers while the second set of papers has to be solved without them. Students are trained accordingly.

Mr D’souza in his presentation debunked the myth that use of technological tools like calculators creates perpetual dependence and weakens computational faculty of the kids.

He emphasised that technology should not be taken as a demon. It is rather a liberator. Teachers tend to avoid techno-tools as they are slow and kids are smart in learning their use. So a kind of technophobia develops and teachers dare not use them in the classrooms, lest they are ‘taught’ by the children. D’souza says this should not be the case. Technology is a redeemer and teachers cannot be replaced by tools. Technology empowers the teachers and reinforces their personality.

Moreover, mathematics is not merely computation. D’souza says, the Primus Public School has opted for awarding marks if the student has followed the logical sequence and missed the right answer narrowly. In traditional mathematics teaching, there was heavy emphasis on computation. So the students lost everything if he did not produce the right answer, however, logically he might have proceeded in solving the problem.

The old method was effective in making them learn or replicate algorithms. But it was ineffective in developing mathematical thinking. But mathematics today combines elements like gathering information, finding relationships, and discovering new knowledge in the planned activity. This means it involves abstracting, discovering, proving and application. The question therefore that should be asked is: should the teachers ask the students to solve non-routine problems, find patterns and build models or mathematise.  D souza says much of the mathematics in India is taught in terms of abstract ideas. Take for instance, the value of pi i.e., 22/7. Every student could tell you the value of pi. But few teachers ever bother to explain pi in terms of the ratio between the measurement of circumference and diameter which is a constant. There is this need to explain it in the classroom by measuring the circumference and diameter of say, a tyre or a round lid and asking the kids to determine that constant value.

It is usually seen that a carpenter would exactly determine the volume of timber required for paneling a wall. But not a mathematics student. This speaks ill of the teaching methodology of mathematics which totally bypasses application. This only emphasises the significance of teaching mathematical application in life situations. In order to reach the students, a mathematics teacher must connect mathematics to his life and to the lives of the students.

It is also noticed that often children weak in mathematics are roundly condemned and made to leave the school. This tendency fosters math-phobia which is not healthy. No child can attain total perfection instantly. The Japanese follow this method known as ‘kaizen’ where benchmarks for success are elevated gradually, in components of achievable levels. For instance, in the workshop the graphic display calculator was given to eight Japanese teachers for use. On the first day, the success level was 30 per cent. Next day it improved to 50 per cent and on the third day it rose still higher to 66 per cent.  The benchmarks set for success were 5, 25 and 50 respectively on first, second and the third days. 

Need for change

A few other traits too need some correction. In India, our target is to embarrass the candidate during an interview by asking tough questions beyond his/her capacity while in Japan and other western countries, candidates are made to feel comfortable. Similarly, Japanese teachers take pride in sharing their knowledge. It is commonly observed that every individual student develops patterns of relationships between numbers while computing.

The teachers should encourage such exchange and sharing of pattern in the classroom.
Knowledge and skills are important, but more important is attitude. Globalisation has heralded a new attitudinal shift in the corporate sector where bosses are of the same age as senior employees and do not shy away from working together. Perhaps education too needs breaking of barriers between teachers and students. 
Until now the only technology aiding the teaching of mathematics that was assumed to be helpful, was entirely handheld. Even that is advancing tremendously. But bringing software into the classroom can give more exciting opportunities with computer hardware becoming more affordable and there is a golden opportunity to save the subject from oblivion.