Saturday, February 10, 2018

Visual Math Et Cetera

For years, I have been asked for a recommendation for 4th grade math.  I now have one, and one for 5th grade as well.  It's called Visual Math.  These are not expensive books.  The authors are from a ground breaking group of researchers that I've been following since the beginning of  Back in January, I wrote an article where I said that our current math curriculum needs to be flushed as an artifact of the Industrial Revolution.  There is equally challenging, more engaging, more pertinent math to the information age.  Visual Math.

Except that I'm stuck on fractions, polynomials, mononomials, exponents, algebra, trig and calculous because darn it, they show up everywhere in math and all fields whether you're doing machine learning, number theory, or Hollywood CGI.  I guess I'm always one rebellion ahead of the next trend.

I don't face the same broad classroom education challenges that the authors of Visual Math face.  I face the challenge of a single kid.  My idea of visual math starts with COGAT test prep, Building Thinking Skills, and the rest starting ASAP, like age 4.  See my curriculum page.   In a house enriched with crafts followed by Minecraft, visual skills are overdeveloped.

But the genius of Visual Math isn't just a much better more appropriate visual (and thus more timely) curriculum, it's the approach outlined by Jo Boaler years ago that is question heavy and solution light.  In other words, spending time understanding and defining the problem, whatever that may be, in the process really learning math, and as an after thought deriving a solution.  You've heard it before from me, and this is where I got it.  There is much more to the approach beyond this.

I'm a big fan of a single problem that is hard, multi-step (working memory intense) and requires a lot of time to solve, preferably something goofy or non-sensical, if that's what it takes to turn a predictable answer into an argument.  I don't want a child to come out of this having mastered 3 x 5, which is useless, but having mastered getting there from the unknown, or better yet, an unknown mess.

And that brings us to 1/2 and 2/3.  A few months ago, a reader asked what to do about struggling with fractions.   I offered to get on Skype, but since I'm insane, and can turn any 30 second problem into a 30 minute challenge, the reader declined.  Too bad.

There are 2 parts to a good fraction problem. 

The first part is 1/2 takes about 3 brain clicks to understand.  I think 98% of the problem with fractions is that kids expect 1 click, they don't get it on one click, and they are frustrated or worse.   I watch this with the brightest children trying to tackle fractions at a totally inappropriate age.  The second part is the fraction in a more complicated setting of a pre-algebra problem.  Too hard for younger kids, but doable at a pace 10 times slower than a 5th or 6th grader.  Solving a fraction problem is multi-step.  When I work with fractions and children, or algebra, or exponents, I expect a few weeks to get them to admit that they have to work the problem step by step.  They are determined to do one single step, because it's one problem after all, and if they have to do 3 steps, then it becomes three times the work.

Kids who are trained in math hit a wall with fractions.  Kids where are 99.9% wizzes hit a wall for the opposite reason.  Both groups underestimate the problem.

Lately I've been working on the next challenge.  How quickly can I get kids to be adept with pre-algebra, exponents/logs, functions, geometry proofs, algebra, trig and calculus?  By quickly, I mean a small number of problems and weeks per topic.  My group is 4th to 7th.

In each case, a few problems can be used to explore the basics.  During this time, there is wonder involved with the new syntax and the concepts that it articulates.  Like the first time a child stumbles on negative numbers or square roots.   A few problems get the job done.  To take the next step requires a special problem solving approach for each field.  We avoid the complicated applications that fill 90% of a decent text book and just stick with the basics. 

I've come up with a one session introduction to trig that addresses many of the questions (about 25%) on a good trig final.  One session for a 9 year old.  I remember struggling with this exact same material for about a month in high school, trying to remember formulas.   I'm really disappointed about how bad the course was and how unprepared I was (not having studied math between 1st grade and trig). But I'm mainly disappointed with the approach to math from the 1920's which I used in high school. 

The last thing I'm going to do is explore the other 75% or so of each of these topics.   I think this will be an 8th grade exercise.  Is it possible to send a child to high school prepared to be bored with A/B calculus or chemistry?  Can this be done with almost no work whatsoever?  I'm starting to think so. 

I enjoy getting articles from readers that include an age and a topic and a description of how much they are struggling.   I think, wow, we struggled much worse.  I can tell them that and actually solve a problem.  I can also state, if needed, 2 or 3 ways to get past it and how long it will take (longer than you think.)  In some ways, this is just like potty training.  Some parents wring their hands over every trip to the potty, and others let their kids poop all over the place until the problem takes care of itself.  The only thing I did differently was discuss plumbing while cleaning the poop off so that I'd have someone I could count on someday to clear clogs.

Someday is almost here in math.  In plumbing, my 13 year old routed the pipes right before his birthday.


  1. Have you investigated into the Montessori method and how it teaches math?

    1. I have investigate the Montessori method and Waldorf and about 19 different math curriculums (not interested in spell check) and a bunch of science curriculums. Our curriculum is cognitive (aka learning) skills based, and all of our other activities are project oriented. Best of both worlds. The one thing I like about Montessori is hands on - the kid learns and the parent doesn't teach - so this is fundamental to all we do.