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Genetics of math and reading

30 Sep

Yesterday, I blogged about the misuse of the word “proof” by science journalists. Wouldn’t you know it, later, I came across this blog post, which tells us:

“Now, a new study proves that people who are good at reading are also quite naturally talented at math.”

Actually, not really. The study, in and of itself, is quite interesting, but this blogger, apparently relying on an LA Times piece rather than the original paper, gets a number of the details wrong.

You can read the original paper here. The abstract reads:

“Dissecting how genetic and environmental influences impact on learning is helpful for maximizing numeracy and literacy. Here we show, using twin and genome-wide analysis, that there is a substantial genetic component to children’s ability in reading and mathematics, and estimate that around one half of the observed correlation in these traits is due to shared genetic effects (so-called Generalist Genes). Thus, our results highlight the potential role of the learning environment in contributing to differences in a child’s cognitive abilities at age twelve.”

One of the big confusions that accompanies a study like this is the misunderstanding of the concept of heritability. Heritability is not a measure of the percentage of a trait is caused by genes. It is not even an individual level measure of a trait, it is a measure of how much of the variance in a population is genetic.

One of the consequences of this is that heritablity is not fixed, it will be affected by the level of environmental variance. We can see this by a simple thought experiment. Imagine a society with total absolute equality between individuals. In that circumstance, since there would be no difference in environment, heritablity would be one hundred percent. This conclusion, strikes many as counterintuitive but if you contemplate it for a while you will see that this must be true.


How to memorize a formula

18 Sep

Yesterday, I blogged about a mnemonic for learning the quadratic equation. Here is an excellent video that teaches a general mnemonic technique for formula memorization:



Quadratic formula mnemonic

17 Sep


Going through some of my notes I rediscovered this mnemonic for the quadratic formula:

From square of b, take 4ac;
Square root extract, and b subtract;
Divide by 2a; you’ve x, hooray!

I am not sure of the origins of this mnemonic. The earliest version I could find was from J. S. Mackay in 1894, but he says the mnemonic was given to him by a member of the Edinburgh Mathematical Society.

Here’s another mnemonic for the quadratic formula:




And let’s not forget the Quadratic Formula Rap:


Tales from my library: Raymond Smullyan

2 May

The books of philosopher, mathematician, magician, musician, Raymond Smullyan are priceless. If you are not familiar with his work, his autobiography is good place to start.



I own many books by Smullyan. Including these:

images (1)

images (2)

I have also been working through his book  Set Theory and the Continuum Problem



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Arthur Benjamin on math education

2 Apr

The amazing Arthur Benjamin makes the argument that statistics, not calculus, should be the goal of mathematics education.

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