Wednesday, July 5, 2017

Whole Language Math


Let's start this article with Whole Language Everything and then I'll get back to Whole Language Math.

Whole Language Everything began for me when I noted that 75% of every test score is predicted by the level of vocabulary of the child.   Other researchers noted that the child's level of intelligence depends on how many words are used at home and how long the sentences are.

Suppose you have 2 fairly average children at home.  If you have a college degree, these kids are probably slightly above average.  You're looking at test in the fall for gifted and talented.  Take the COGAT for example.  It has 3 sections directly related to vocabulary,  3 sections that are quantitative, and 3 sections that are non-verbal shape related.

Here's the strategy that I came up with.  We were already doing daily math, so our daily math is going to look a lot like the COGAT instead of something you'd find in a school math text book.  This takes care of 6 of the COGAT sections.   For these 6 sections, I prescribe covering any vocabulary you can find up to 2 or 3 years beyond grade level.  A 4 year old is not going to have much luck with the concept of division or fractions, but this child will know the difference between a rectangular prism and a cube.  For age 4, I packaged all of this in Shape Size Color Count, and for age 5 and beyond, the vocabulary is all there in whatever material you use if you just take the time to see it and name it.

The other thing I did was Vocabulary Workshop and the Word Board.   We covered Test Prep Phonics, that oddity of phonics and vocabulary, and didn't bother to practice the 3 non-verbal vocabulary sections on the COGAT at all other than to learn the rules with a practice test.  My strategy was to crush the 6 sections that vocabulary provides a definite competitive advantage, and the other 3 will take care of themselves.

Our daily math continued way beyond test prep, and it was mainly 2 or 3 hard problems that we spent a lot of time talking through.  My kids never practice routine math problem outside of school.  Instead, we tackle a new problem that is nearly incomprehensible to start with and talk our way through it.   After a few weeks, some of it sticks, some of it doesn't, but it will eventually.  I need to start drawing more pictures to look at things visually, but mainly we do a lot of talking.

I recently revised the article "How To Create A Mathematical Genius", which you'll find in the links on the top right of this page.  I think this article is almost finished, but I don't cover Whole Language Math.  We are currently talking our way through algebra and calculus.   Daily math at the pace of 2 or 3 problems a day (which we only do on Saturday's during the school year) just keeps chugging along to a ridiculously advanced level.   Every problem involves a discussion of new concepts.

Yesterday for 4th of July Math, I asked my 12 year old to calculate the derivatives of sin(x) and cos(x).  I was hoping this would take 3 weeks, but it only took 30 minutes.  You'd think a kid who doesn't really understand sin(x) and doesn't understand infinite series and factorials would struggle, but apparently 'struggle' doesn't preclude 'solve'.  I never thought we'd end up here.

We spent a lot of time talking through this problem.   I have plenty of work to give these kids that they can do on their own that doesn't involve a discussion.   But I was struck by the fact our discussion was exactly like the discussions we had at age 4 doing 2 or 3 problems that involved shape transformations.  

Many parents define math as a child applying calculation methods to a doable problem and not making mistakes.   Under this definition, math requires teaching the child calculation methods so that they can do the next set of problems.  With this approach, the child can do a lot of problems correctly and perhaps get A's. I don't want a child who can do a lot of problems correctly and perhaps get A's. I want a child who can figure out next year's math on their own and perhaps go to Stanford or MIT.   I want a child who writes really good papers for AP English or AP History some day because they can think at a really high level and has really great verbal skills.  If one of my children comes to me in the future and announces 'I want to study Number Theory' then we're going to stop doing Whole Language Math, but until then, math is more talking and less calculating.

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