If we do pre-algebra every day it's going to get boring. I refuse to do either decimals or long division or math facts or anything between kindergarten math (totally engrossing) and pre-algebra (marginally useful) because it's all boring and useless.
I need a fall back plan. He's been playing IQ Twist lately (highly recommend this game even though I don't get paid for any of my recommendations) and that got me thinking. There is this great math book called Mathematics 1001 that has 1000 math topics in addition to 2 pages on trig that allowed us to cheat our way through it. One of the topics in this book called 'Net's looked like the shapes in twist, and a little reading later uncovered this idea.
Here are two Nets for a triangular pyramid. If you cut out either Net, you can fold it into the triangular pyramid.
There are 11 nets for a cube. Draw them.
I watched two sets of skills in action. First, there was geometric visualization, including rotating, flipping, and 3 dimensional manipulation of shapes which trumps the two dimensional manipulation on a cognitive skills test. If we were facing a test this year, I would have only shown the diagram on the left above and asked for 2 more nets for the triangular prism (even through there is only one because cognitive skills tests test your ability to come to terms with incorrect questions).
Secondly, there were budding permutation skills at work, which is an extremely important math skill. Since no kid is going to get to 11, this gives me the opportunity to suggest permutations. "What's a permutation?" Well, take the letters a, b and c. I can write them as abc, acb, bac, bab, cab, and cac. There are 6 permutations of the letters a, b and c. Please give me the permutations of 1,2 and 3. This should be pretty simple. Then look at the basic T shaped Net for a cube, and start permuting the squares, one square at a time.
We got to 7, which is pretty good for my 25 minute time limit. I need to stop at 25 minutes to save room for follow up questions, like telling me the rules for building a Net while staring at the 11.
Real Math
I expect this child to go far in math. He's not going to go anywhere without some intervention. Here is my intervention.
I showed him a web diagram of the 11 nets for a cube. I stated that some guy (Albrecht Durer) asked how many ways you can create a folding diagram for a cube, and he came up with 11.
Then I showed my kid the pre-algebra worksheet of about 20 equations.
I asked this question. If there is a mathematics professor and researcher at some university asking questions and writing papers and going to conferences and helping his colleges in the Physics and Information departments apply abstract math to their work, which math is this professor doing right now? (And by way of association, which math are the physicists and computer sciences clamoring for?) Does it look like this (pointing to pre-algebra) or does it look like this (point to the 11 nets for a cube.)
The Answer
The answer is the net stuff. And why is it that your school curriculum looks like pre-algebra, the type of math that mathematicians don't do?
Here is my (mostly inaccurate but totally) true history of math curriculum in the United States. In 1930, a vice president at Ford Motor company created a list of skills needed by factory workers and accountants and dealers to create and sell cars. This skill set was widely applicable to industrial work of all types. A curriculum was created to teach it and used throughout the United States. Lots of cars were produced and everyone was happy. This curriculum is still used in 2017 in the midst of the Information Age.
Of the 96 maths out there, school is going to consist of the 5 that would help you build cars by hand or build a bridge, which you are never going to do. The maths that you actually need to get through your life - starting now - are not taught at all.
What I find most interesting is that the 5 maths taught in US curriculum are almost devoid of skills compared to the maths that could be taught.
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