# Category Archives: Teaching

## If there is some good inflammable stuff it will catch fire

Do not try to satisfy your vanity by teaching them great many things. Awake their curiosity. It is enough to open the minds, do not overload them. Put there just a spark. If there is some good inflammable stuff it … Continue reading

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## Logical order

The most efficient logical order for a subject is usually different from the best psychological order in which to learn it William Thurston from his book Three dimensional geometry and topology.

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## 3.14.15 and Einstein

14 March 2015, was supposed to be the Pi day of the century — for obvious reasons. 14 March is also Einstein’s birthday, and 2015 interestingly marked 100 years of the theory of relativity. I liked this article written by … Continue reading

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## “Gods” make Comeback at Toyota

is the headline of this bloomberg piece that reports the strange phenomena that human beings are replacing robots in the manufacturing lines. The point is that by automating some of these production process, much of the skill learnt by the … Continue reading

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## Come Together

is not the beatles song but the title of episode 16 of a tv program called discover science. I happened to catch it on local tv and the combination of quirky Japanese humour and the clever introduction to mathematics and … Continue reading

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## Of word problems and place values

If you google “Abbott & Costello 7 x 13 = 28″, you can get a funny sketch of how to show 7 x 13 = 28 by dividing, multiplying and adding. There are a couple of versions, and in one … Continue reading

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## Mathematical Induction

Apparently the French terminology for mathematical induction is “raisonnement par recurrence” or reasoning by recurrence. That makes so much more sense. According to David Reid and Christine Knipping* “Mathematical induction” is based on deductive reasoning, not inductive reasoning. The confusing … Continue reading

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## I have trouble finding the mathematics

Two unrelated incidents. First, I attended a talk by Sergiy Klymchuk who talked about misconceptions in mathematics, especially in calculus. He also pointed out an example of a disastrous error in a paper published in a highly rated mathematics education … Continue reading

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## According to Socrates

… it is no true wisdom that you offer your disciples, but only its semblance, for by telling them of many things without teaching them you will make them seem to know much, while for the most part they know … Continue reading

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## Mathematical Sense Making

I like the following problem. It was shown by Alan Schoenfeld in his talk yesterday in Singapore. Among the many things he touched upon, he introduced the Mathematics Assessment Project which has a package of lessons for grades 6 till … Continue reading

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## Fake curves

Interesting post on how a supposed trig function is actually not trig. I have to admit I used to do things like this and use the arc tool (on powerpoint) to create curves that only look vaguely like the actual … Continue reading

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## Is 0 even?

I first saw this from BBC news. The aftermath of hurricane Sandy resulted in a shortage of fuel and New York City had to implement an odd-even system. The following is taken from their press release: 1) Vehicles with license … Continue reading

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## Paraphrasing Russell

William Mueller in his 2001 article in the American Mathematical Monthly suggested that we could take Bertrand Russell’s quote* on philosophy and substitute it with pedagogy. So here goes Pedagogy is to be studied, not for the sake of any … Continue reading

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## Why are Finland’s Schools Successful?

is an insightful article by LynNell Hancock published in the Smithsonian magazine in Sept 2011. It was recently republished in a local newspaper (strangely without reference to the original publication) and circulated by a colleague. I particularly love this para: … Continue reading

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## What is real world mathematics?

According to Tim Gowers, real world mathematics is not really about disguising equations into apples and pears.

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## Thurston on education

I was introducing mathoverflow to a student and wanted to show him that world class mathematicians hang out there. In the list of top contributors I saw Thurston’s name and pointed it out to the student. Of course the name … Continue reading

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## Magic formula

Was grading some student work and noticed that when they are supposed to solve for $\left(\frac{5y}{4}-\frac{1}{2}\right)^2 +\frac{1}{16} = 1$, 10 out of 16 students expanded the above into a quadratic equation and then used the quadratic formula to get … Continue reading

Posted in Algebra, Teaching | 2 Comments

## MOOC

stands for Massive Online Open Course. Not exactly a very recent concept since some universities have already been making their courses online for years. The “novel” bit perhaps lie in universities or institutions going out to woo international audiences, even … Continue reading

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## Of Dice and Math

With apologies to steinbeck. An article by Posamentier on how he taught arithmetic of fractions through applications to dice games. There is often talk of making mathematics relevant to students. This is important, but only when it relates to the … Continue reading

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## My infallible calculator

A student came to me today and asked if there was something wrong with my notes because I claimed that $\sin x \ge 0$ for $x \in [2k\pi, (2k+1)\pi]$. The reason that I was wrong was that … Continue reading

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