5 January 2016Wolfram:
Most of the improvement happens by the time you know your 7 times table. The odd bump at 10 is because the ability to approximate relies implicitly on knowing your 10 times table already (to be able to handle the trailing zeros).
But the improvement in error from 9% to 8% comes at a price. Knowing up to your 10 times table requires recollection of 100 facts (OK, 55, if you assume symmetry). But knowing up to your 12 times table is 144 facts. Improving the error from 9.3% of the result to 8.1% is a relative improvement of 12% in the size of the error. But to achieve that you need to memorize 40% more information. That seems like a losing proposition.
Look, the point of the Wolfram blog is to promote the Wolfram platform. Naturally, this blog post incorporates Wolfram computations. It feels a little forced, but the subject matter was compelling so I stuck with it. Interesting data analysis exploring the cost-reward tradeoff of learning higher order times tables. This sounds way more hyperbolic than I mean, but questioning stuff that is done because that’s how it’s always been done is how humanity moves forward. That reasoning applies to math and education as much as it applies to technology or anything else.
What’s also interesting is the frictions that hold up change, particularly on a situational basis. Compare how fast schools change the basics of the curriculum against how fast school dinner menus change to the latest healthy eating initiatives. If you want to tie this back into Apple, think about the headphone port controversy swirling around the iPhone 7. Digital has to be better than a 100-year old analogue standard, but the entrenchment of the 3.5 mm port is immense.