Saturday, April 8, 2017

Teaching Algebra to 4 Year Olds

It is possible for a new freshman in high school to walk into Algebra II having nothing but a lame average US grade school math experience and get it immediately and dispense with algebra in a week before moving on to Trig.  It's totally possible, but highly unlikely. It's also possible for this kid never to read the book except before tests and get A's even though he never turns in homework.  Possible but even more unlikely.

What I've been wondering ever since having kids was this:  If it's possible to have such an easy time as described above, would it be possible for a 6th or7th grade child to master algebra in the hopes that he doesn't spend high school getting in trouble like I did and then waste college and decide what he wants to do after 7 years of grad school?

If you read through my how to teach math articles, we're leading up to high school.   This is hard to imagine for the parent of a 4 year old, but if you're child is a smashing success in high school, you win, and if not, all the GAT education in grade school didn't matter.  In fact, there are quite a few really bright kids in college and grad school who never had any GAT at all, so let's stay focused here on what's really important, which is my child being so over skilled that none of this matters.  Then in high school I can focus on will, values, morals, etc and not grades or skill.

Occasionally I write about writing skills.  I applied the exact same approach to math with the core skills to writing and it works.  If I can parlay that sentence into a book, I will, or you can just send me $12.95 for saving you 18 hours of reading.

Anyway, I see 4 year old math just leading up to algebra 2 and the formula works really well until we're actually ready to study algebra.  I think my best innovation is the insanely hard questions in Section 2 of TPM that teaches abstract thinking. I'm totally crushed when other kids get to the point where they can identify F as '+ 8'.  I formally retract all of my articles that my child is the smartest child in the world just because he did all of my over the top books first.  Apparently, the word is out and other kids are going to catch up.

Now I've got to worry about competition at Stanford.  What I would like is for the Test Prep Kid to have a major with about 9 hyphens, and then stop by the math department to get an easy A in some advanced class (skipping prerequisites of course) and not have to open the book except for the test. I also want to do this efficiently as possible and compete with harding working, highly educated, well raised children.  I thought about statement this all day.  I don't think compete is the correct word.  It's more like 2 brothers on the same wrestling team.  Also, the biggest pool of highly educated and hard working comes from immigrants almost by definition.  My younger son and I counted over 50% first generation immigrants in his class.  The bar is raised.

Unfortunately, my diabolical plan behind Section 2 got pretty close but wasn't the magic bullet I expected.  After TPM, I've decided the best course of action is to go straight into 8th grade math.  I'll explain how to do this later, but it's a lot of bread baking.  Your take a loaf, like powers, add yeast, and set it in the rising box for a long time, and then you can bake it with some work sheets.  It's the bread approach to math.  It's totally effortless, takes no time at all, and isn't hard, provided your child already has the core skills.

I started my child on the y  = mx + b exercise I outlined in a prior article.  At some point, I'll detail the whole bread baking factory of which this is a key part.  Anyway, how could y or x be an issue if we've already mastered F and G, and even worse, not F and not G, where are way harder than simple x and y?  Here's how the discussion went.

TPK:  What's y?

Me:  It's a number.

TPK:  Which number?

Me:  Any number?

TPK:  Which one?

Me:  Any number.  Ok, let's say it's an integer,

TPK:  Which one?

Me:   You tell me,

TPK:  You tell me.

Me:  I'm not doing your work You tell me.

TPK:  It's 2.

Me:  What else could it be?

TPK:  I just said it was 2.

This went on and on.  He managed to graph all of the 'intereting' values of m (b = 0) and we're moving along, but he still doesn't see x is an integer.  I don't think this is a matter of abstract thinking. This a matter of system thinking, which is a skill very few of us even know exists.  Kids who have this skill win international math competitions and don't open books. I'm going to find this skill, figure out how to teach it, and then write the book.

By the way, I figured out how that ChemE major pulled off easy A's in college so many years ago. His dad was an engineer, and gave his son the books during the summer to study ahead of time.  A child may not get it at all on his own the first time, but yeast works its magic.  Look for a recent article with Bucketing in the title and you'll see my earlier thoughts that led to me solving the mystery 30 years later.

We started bucketing in K, and it's magic.

Sometimes with Bucketing, we bucket topic A, then  topics B and C magically appear.  Not with algebra.

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