Tuesday, July 7, 2015

Update on Math Workbooks for Older Kids

I've been continuing my quest to find math workbooks that teach thinking skills. Ideally, there would be one that teaches the same cognitive skillset that is tested by cognitive skills tests like the COGAT, but I'll settle for one that teaches problem solving skills which are somewhat related to cognitive skills.

I have a big gap between first grade and 8th grade that I'm trying to fill.

Good news.  I have found that starting with the 4th grade, Singapore Math has Word Problem workbooks that have pretty hard, multi-step problems.  (The 3rd grade book does not.)  What I like about these books is that the each workbook begins with a few pages of problem solving techniques.  I think these techniques would be great for a parent as a reference when the child is stuck on a problem.  The parent can suggest a technique instead of doing the problem for the child and ruining the learning experience.

These books teach pre-algebraic thinking.  This is a skill to solve algebra problems without the benefit of algebraic modeling:  "Joe and Bill have the same number of marbles.  Joe gives 30 marbles to Bill, and now Bill has twice as many marbles as Joe."

The 7th grade way of solving this problem is to solve the equation 2*(X-30) = X+30.  The forth grade way of solving this problem is to start picking values for X and moving up and down the number line based on how far off the result is until X can be determined to meet both constraints.  Good for problem solving, good to reinforce arithmetic without boring worksheets.

There are a lot of kids who have to sit for the big test in the 6th grade.  These workbooks are not a bad way to prepare.   Much of the material in the SAT test prep book math section is very similar, although, as you can image, the SAT taps advanced topics in math like parabolic equations, so it's probably not suitable for most kids at this age.  Anyway, the questions in Singapore Math are very challenging if you pick an advanced grade.  When my oldest son passed the test, all the material I used fit under the heading of "Super Hard Material That Is Advanced And You Have Never Seen It Before But No One Told Me About Test Prep Books".  This is a pretty good way to prepare.

The downside of Pre-Algebra as found in Singapore Math is that the test questions on tests like the COGAT have a bunch of skills not covered in Singapore Math, like what to do in the presence of ambiguity and how to handle contrived failure.  Also, while pre-algebra is multi-step, the multi-step of the COGAT follows a different pattern, one of a) figure out what is changing, and b) apply the change to a different situation.   Working memory is reinforced with Singapore Math, but it is strongly built by hard core test prep.  (Another reason to do test prep even if you don't have a test).

When I closely reviewed the higher grade Singapore Math books, my first response was to buy them and begin assigning pages to my son.  My second response is to continue to work on my own material that I can make available and that won't result in me being sued by Riverside Publishing.  I'm pretty darn excited about this initiative.  I'm sitting on 1,000's of test prep questions that I made myself that I won't share.  Reason #1 is being sued.  Reason #2 is that when I got about 95% of the way through making and testing these, I realized that it was not about the child's ability to recognize and manipulate shapes, but about a big vocabulary, a big working memory, and cognitive skills.   My working title is "The Convoluted Ridiculously Hard Core Word Problem Book for Insane People Who Are Desperate To Pass The COGAT".


  1. Any quick update on how your summer is going with your boys? My days don't go without my kids crying or screaming about skipping their homework. :(

    1. See below. I always forget to hit the reply button.

  2. Ah, the joys of summer vacation. The heck with the kids. I've been working all summer about disciplining myself not to let them use the computer without doing math or practicing piano/trumpet. I've been making lots of progress. The parent is the key. Also, for the last 2 weeks, they've both been at Theater camp culminating in a performance last Friday. Theater camp is way more effective at turning my kids into geeks than I am. I feel a new article emerging.