Category Archives: Learning

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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Logic joke

Three logicians walk into a bar. The bartender says:”Do you all want a drink?” First logician says “I don’t know.” Second says “I don’t know.” Third says “Yes!”. Meta: Why is this a joke?

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Halmos on how to study

It’s been said before and often, but it cannot be overemphasized : study actively. Don’t just read it; fight it! Ask your own question, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse … Continue reading

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What you have been obliged to discover by yourself leaves a path in your mind which you can use again when the need arises. — G. C. Lichtenberg I am not familiar with Lichtenberg but he was apparently a German … Continue reading

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On practice

I’m sure I am interpreting this in a context different from Vygotsky who was quoting Lenin Man’s practice, repeated a billion times anchors the figure of logic in his consciousness.

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10 surprising things about our brains

an article from huffington. Worth the read.

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Multitasking with studying

Another report on how students don’t learn as well when they attempt to multi-task.

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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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Social interactions and the development of control strategies

Is a sub section in Schoenfeld’s Mathematical Problem Solving. The argument is that when two students work together, this interaction can spur cognitive development resulting in approaches to the problem being solved that are qualitatively different than those taken by … 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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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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Writing mathematics

The literal physical act of writing out mathematics, I believe, helps in our learning. Even if it was just plain old brainlessly copying down what the lecturer is writing helps to a certain extent. But teaching locally has regressed “evolved” … Continue reading

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