Wednesday, April 15, 2015

Summer Math Program of Awesomeness

I've got both parts of my Summer Math program - the SAT test prep book and the "Math Leads for Mathletes" book.   I'm replicating my age 4-5 test prep regimen, only this time for ages 10-12.  As I have been suggesting all year, my goals include an exciting At Home Schooling math program full of problem solving, and reluctantly, the beginning of test prep for the 7th grade testing hell in Chicago.

The Mathletes book is exactly what I want - real math.  It says in the introduction that the book targets advanced 4th and 5th graders, or even really bright 3rd graders.  It looks more like graduate level work to me.  I am not kidding.

You may recall that we tried Patterns in Mathematics by Paul Swan the summer before third grade.  It is similar material with a similar approach to Mathletes, only easier and more accessible, but like early Algebra, we had limited success.   For material of this nature, learning takes place either when it's a tool to the end, or the child has the maturity and math experience to see its value in applications or appreciate it's beauty.

The SAT test prep is much easier, at least the official test questions from the College Board which are available online.   I noticed right away that the test questions require the same basic cognitive skills that the K and 1st grade cognitive skills tests (aka OLSAT and COGAT).  The questions present regular concepts in a novel way and require at least 2 steps to solve.  I feel like there are no new tricks once you get pass testing 5 year olds.

This curriculum will probably last through the summer after sixth grade, unless we go faster than I expect (which usually happens 9-12 months into it as the kids pick up skills and mature) or unless I come up with the next fad of my choosing.

Like the 4-5 year old program, the new program requires an different approach on the part of the parent. With normal homework and workbooks, the child might be given 30 routine problems of the same topic, and be expected to complete them in 30 to 60 minutes.   When using SAT or Mathletes material, a single problem might require 30 minutes, or a week.  The book might have to be shelved while background or introductory material is found on the net and then given a second or third chance.  Some of the material may have to be skipped and then revisited 6 months later.  This is all about patience.

Here are some examples.

SAT Example
This is question #2 on the College Board's free online test.


The table above shows the temperatures, in degrees Fahrenheit, in a city in Hawaii over a one-week period. If m represents the median temperature, f represents the temperature that occurs most often, and a represents the average (arithmetic mean) of the seven temperatures, which of the following is the correct order of m, f, and a?  (Answer choices not show, but it's variants of the answer below.)

The answer is a < m < f

This material is covered in Every Day Math at least for 4th and 5th grade.  Notice that it's not about solving the for mean, mode and median, but ordering the results to derive the answer.  Most of the work is in figuring out what the problem is asking and analyzing the data.   It requires a whole bunch of skills from my Math Problem Solving Skills list, starting with "OK, I have no idea what I'm doing here.  What do I recognize?  Median...Mode...Average...I need to reread the question a few times...".   I am confident that this will break 4th grade habits ingrained in children by boring arithmetic sheets.

It's not enough to solve this problem an get it right.  If it takes the child a long time to calculate the average, challenge them to do better.   Instead of adding all of these big numbers, how about adding 70 minus the number and adding back 70, ie -4 + 8 + 5 + -1 + 8 +7 + 0 to calculate the average.

Also, unlike homework, it's not at all about getting it correct the first time.  It took me 3 tries, and I was more than happy plodding patiently along to find my mistake.   That is the approach to math the kids need to get to higher levels - spending time figure out what to do with a math problem (instead of memorizing math facts) and overcoming incorrect answers.

Mathletes Example
In graduate school, I took a two semester course that had a single 60 page book.  30 pages the first semester, and 30 pages the second.  At times we spent 6 classes on a single line from the book.  It was a math book, but had no numbers.   Mathletes is a little like that.

As I scroll through the book, there are things like this:

Even more generally, we find that the formula for m-gonal numbers is 
Nn(m) = n + (m -2)n(n-1)/2

Even though the content leads up to this line, and explains things as it goes, this line might take a few weeks for the child to sort through.  On the other hand, this material is great for young children - lots of new concepts and vocabulary and ideas and history that a child can handle, and lots of very slow thinking week by week to figure out what the math is.  If you did articles from a few years ago, this was how I taught math to a 4 year old.  The difference is that with younger kids, there is more vocab and concepts than thinking, and with younger kids lots more thinking.  (This is the Classical Education at work.)

In high school, I remember working through trigonometry proofs on at a time, probably 20 minutes each, with more memorization than actual understanding.  The material in this book will assist greatly with the sign function, and I've never seen this material covered in depth in a context where the student actually gets as much time to think through it and digest it as the original mathematician took to come up with it.   Is it fair that a high school student gets 20 minutes on a proof that took a mathematician 2 years to derive?  This book is great early prep work for trig.  There is some algebra and geometry needed, but very little, and only used as a tool for other material.  (This is how Jo Boaler once described how math should be taught.)  I'm going back to the SAT prep for algebra and geometry.

I'm probably not going to get a mathematician despite my efforts, but I am going to get a thinker and a problem solver.

1 comment:

  1. I know I loved your post about daily schedule. Any chance you have something like that you are planning for summer? My kids will be home most of the summer (although doing camp here and there) and I am seriously scared to death primarily because I don't trust myself, in about a week or two into summer I might be tired of having them at home with me all day and every day and I might slack off my part time homeschooling and sooner or later they might spend more time playing with their electronics than during regular school months. Unless I have some kind of daily schedule, I know I will fail and regret in August that the kids are not ready for school or reasonably ahead.