learning math is hard

Update: For more one error detection and correction, take a look at this video (quicktime) starting at about 5:30. He's talks about error correction with reference to reading instruction. It continues on into this clip up until about 7:00 and math gets discussed for the last 3 minutes or so.

That's my current position based on teaching my six year old son math for the past year and a half.

Actually, that observation isn't based on my son having difficulty learning math. So far he hasn't. It's based on the the material we've skipped. It is that differential that separates the higher preforming math students from the lower performing math students. That differential represents an enormous amount of practice.

Unlike most parents who use Saxon to teach math, I'm using Connecting Math Concepts. Both programs are scripted, both use a mastery learning "basic skills" approach, and both have lots of practice built into the program. Both are complete programs which don't require parents to know how to teach math; knowing elementary math is sufficient. For most kids there is not much difference between the two. Contrast this with Singapore Math which does require some teaching skill to present and requires practice to be supplemented. That's not meant to be a knock against Singapore Math, each program has its strengths and weaknesses. I actually think that the ideal K-6 elementary math curriculum would be some combination of all three programs, capitalizing on the strengths of each.

For the purposes of this post, however, I want to focus on the practice aspect of learning math. To master elementary math a student needs to practice what's been learned until it is automatic. Unfortunately, most math programs do not provide sufficient practice to safeguard against the ravages of forgetfulness.

Most parents do not take control of the educational process until there the need to remediate becomes evident. At this point, there is a tension between the need to devote time for practice and the need to reteach the child to get him back on track as quickly as possible. Practice tends to get the short end of the stick at this point. It shouldn't.

One aspect I like about CMC is that it's been field tested so you can be certain that if the student has the math skills to enter a level of the program, the program will teach clearly enough and provide enough practice for the student to reliably master all the material presented in this level within one school year, about 120 lessons.

The most important aspect of CMC, however, is that error diagnosing and correcting are built right into the program, unlike almost every other math program. Let's face it, if students didn't make any errors while learning math, a trained monkey could teach math using almost any commercially available math program. It is in the diagnosing and correcting of student errors where most math programs fail. When students derail, many teachers are unable to get them back on the track. Math, being brutally cumulative is not forgiving at all when students derail.

This is CMC's greatest strength.

CMC is designed to minimize students errors in the first place by providing clear instruction in small instructional steps. Students are then tested frequently (workbooks are checked after every lesson and tests are given every two weeks) to check student errors. based on the ten unit tests, student errors are evaluated and a built-in remedy is provided to the student based on the errors the student made. The student is then retested to see if the remedy worked before the student is permitted to advance. If the student were permitted to advance without mastering the material, then the diagnosing and correction of errors would be become much more difficult come the next ten unit test because now the teacher doesn't know where the student went astray. Was it one of the new skills taught in the past ten lessons of was it one of the previously taught skills? Now extrapolate out 80 more lessons and try to figure out where the problem is for a newly taught skill that the student can't do. Forget about it.

Contrary to popular belief, the greatest shortcoming of the "constructivist" math programs is not the less than clear presentation of new skills, though this is certainly a problem; it is that error detection becomes virtually impossible. This is not so much a problem in a class full of higher performers, but it is deadly in a class where students make errors.

I see this post is getting a bit longish and I still haven't touched on the main point -- practice. So, I'm going to break it up into two posts since there's already much to chew on in this post. More to come.

Part two here.