News from the trenches

My son, who begins third grade in the fall, just finished Connecting Math Concepts level C (CMC C). CMC C is billed as a 2nd or 3rd grade curriculum.

We went through the 120 lesson sequence sporadically on weekday nights after school and weekends. It took about nine months. Had we been more diligent, we would have gotten through it in five months.

In his day job, i.e., second grade, he covered most of the 2nd grade Everyday Math (EM) curriculum. Generally, we were ahead of what his school was teaching in EM, so EM mostly served as additional practice for what he was learning in CMC. Both curricula covered roughly the same skills, if anything CMC covered more topics than EM.

CMC provided significantly more distributed practice than EM which should not be surprising. The benefit of all this distributed practice was that at the end of the sequence he was able to take and pass a cumulative test of all the material covered in the sequence. In other words, he had retained material that had been covered up to nine months ago. We will jump right into level D because the more we do this summer, the less we will have to do during the school year, what with regular homework, piano lssons, various sports, and the like. I'm confident that he could go the entire summer without forgetting what he was taught, at least nothing that couldn't be refreshed with a few lessons of review. CMC Level D provides that review, but we'll skip those parts.

In CMC, lessons are easy to teach because they are scripted for an entire classroom. The difficult part is shortening and modifying the script to suit teaching a single student. I will present the script until he has learned what was intended and learn, which usually takes one example. Then I monitor his working of the remaining examples. Two thirds of each lesson is usually independent work practicing skills he's already learned. He does those exercises on his own, though I often let him skip parts of exercises if he balks or seems bored by the problems. Surprisingly, he will often work problems he already knows how to solve well without complaint.

We usually get through a lesson in about half an hour, fifteen minutes of which is independent work. I suspect presenting to an entire classroom would take longer. I also suspect that I'd have to do more teaching for average and lower performing students.

EM is known for its steep spiral. Topics come and go quickly. Nothing is taught to mastery. And, quite frankly, I don't see any of the supposed conceptual learning advantages I see touted. CMC does not teaching using a spiral and everything is taught to mastery. Needless to say I was surprised that CMC stayed ahead of the EM spiral the entire school year. To put it simply, CMC teaches much more efficiently than EM.

Perhaps too efficiently. My son has little tolerance for the hokey manipulative exercises that clutter EM, such as make a grid of dots to conceptualize multiplication. He knows how to do most addition, subtraction, multiplication, and some division problems mentally, so that is how he wants to solve problems -- mentally. I suspect there will be a clash next year when he writes down his "magic" solutions to problems. We shall see.

He knows the math part of math well. That's a good thing. he doesn't know some other important parts of math so well, however. he doesn't know the importance of neatness yet. he doesn't consistently provide the units for word problem answers. He doesn't consistently indicate the answers by, say, boxing them.

These problems are all my fault. I should have held him to a stricter standard, but I didn't for various reasons, mostly time considerations and to minimize crankiness when we did this extra work before bedtime. These problems are easy to remedy. Remedying deficient math knowledge not so much.

Next year he'll run through the EM spiral again reviewing, and for many students relearning, all the partially taught topics from second grade. In the meantime, he'll continue to overlearn the topics material covered in CMC D. This will lead to automaticity in elementary math skills which will be needed for learning algebra. That's the ultimate payoff -- learning algebra. If you don't know algebra, you're pretty much foreclosed from pursuing study in the hard sciences and engineering.