{"id":50863,"date":"2020-01-27T09:17:45","date_gmt":"2020-01-27T17:17:45","guid":{"rendered":"https:\/\/world.edu\/?p=50863"},"modified":"2020-01-27T09:17:45","modified_gmt":"2020-01-27T17:17:45","slug":"a-math-teachers-plea-lets-keep-pi-irrational","status":"publish","type":"post","link":"https:\/\/world.edu\/a-math-teachers-plea-lets-keep-pi-irrational\/","title":{"rendered":"A math teacher\u2019s plea: Let\u2019s keep pi irrational"},"content":{"rendered":"

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Computers have helped mathematical research accelerate in multiple directions and increased the presence of\u00a0mathematics in everyday life<\/a>.<\/p>\n

The role of technology in teaching and learning mathematics is increasingly on my mind as a math instructor who sees new students arrive at Simon Fraser University (SFU) every year. Both at SFU, and\u00a0when I visit<\/a>\u00a0Canadian math classrooms as a guest speaker<\/a>, I look out into rooms filled with vibrant young people surrounded by calculators, computers and smart phones.<\/p>\n

And that\u2019s OK. Like many mathematicians, I have not pushed back against the new technological winds ushered forward by modern times. But such technology should enhance and extend, rather than replace, the ability to think mathematically.<\/p>\n

Adieu geometry?<\/strong><\/h4>\n

Recently, I met with a young person who was interested in math and computing, but not certain which direction he would like to go in. I offered the following problem used by the University of Oxford to interview undergraduate mathematics candidates:<\/p>\n

\u201cImagine a ladder leaning against a vertical wall with its feet on the ground<\/a>. The middle rung of the ladder has been painted a different colour on the side, so that we can see it when we look at the ladder from the side on. What shape does that middle rung trace out as the ladder falls to the floor?\u201d<\/em><\/p><\/blockquote>\n

One way to approach the ladder puzzle is to use, in a relatively simple way, Euclidean geometry, to show that the answer is a quarter of a circle. See below:<\/p>\n

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Euclidean geometry can be used to solve the problem given to University of Oxford\u2019s undergraduate mathematics candidates. (Veselin), Author provided<\/p><\/div>\n

Rather than draw on geometrical properties, the young man used the\u00a0Python programming language<\/a>\u00a0to animate the problem and find the required shape. He had learned Python on his own earlier that summer. When I asked him about congruent triangles, the young man looked perplexed.<\/p>\n

Situations like this make me fear that if not used with due care in classrooms, technology may deprive students of fully developing their numeracy and spatial skills.<\/p>\n

Unreachable problems<\/strong><\/h4>\n

What mathematicians call \u201cthe computationally assisted approach\u201d has enabled researchers to explore and solve mathematical problems that would otherwise be unreachable. The computer-assisted proof of the celebrated Four Colour Theorem comes to mind.
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