July 1, 2008

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.


RMD said...

Thank you for providing a view from the trenches, so to speak.

I too am tutoring my son, even though he goes to a decent school full time during the school year. It's hard to get the lessons done because there are many distractions, and we're all tired.

I was wondering . . . what did you do to keep him motivated? Or is CMC pretty motivating because it allows students to show they can handle the concepts?

KDeRosa said...

Success is his motivation.

CMC presents its lessons very clearly and quickly, so he learns the material easily and is able to perform at a high level.

The work is easy, he is successful doing it, and he sees a tangible benefit.

He'd rather be watching Spongebob or playing Wii, but he will sit and do his math, usually without complaint.

Anonymous said...

Now that brings back memories. The only time I used CMC was when I was in the World's Worst Middle School (makes Corey's school look like Groton or Choate by comparison, I'm sure), teaching seventh grade. A couple of us decided to redistribute some of the classes for math -- nobody was anywhere near grade level, but with some grouping the thought was maybe we could teach some of them something.

I volunteered for the bottom group (I like a challenge). These were not "special ed" kids, by the way, though some might have been able to meet criteria if they were written up and tested.

I wasn't prepared for the reality. I had 17 or 18 students in the math group, none of whom could add or subtract with regrouping, count money to five dollars, or measure the perimeter of a square. Ouch! Of course we had no materials, either. A generous individual on the DI list sent me a set of CMC-C. Two kids did not pass the placement test, but I tried to nudge them along anyway. With no student materials, I used an old opaque projector (borrowed from another school) for the textbook, and put most of the work on the broken chalkboard (we had no overhead projectors or whiteboards). It took these seventh graders about two days to do a lesson, but at least they started learning some math -- maybe for the first time.

With lower performers, you have to use all the examples and non-examples, and you often have to circle back and "repeat until firm." Then farther along, you may find you need to go back and re-do parts of lessons because the group is not firm on those items. Frequently more practice than what was provided would be needed.

CMC is efficient because the students who do NOT need that amount of rehearsal and practice can sail ahead, but some students will progress very slowly. You're correct that in most cases little or no "forgetting" takes place over the summer -- when students are taught to mastery they retain all or nearly all they were taught -- in fact they may even gain over the summer (e.g. in reading) the way more advantaged students typically do.

Roger Sweeny said...

he doesn't consistently provide the units for word problem answers.

By the middle of the year, my eleventh grade physics students consistently provide the units for word problem answers.

KDeRosa said...

With lower performers, you have to use all the examples and non-examples, and you often have to circle back and "repeat until firm." Then farther along, you may find you need to go back and re-do parts of lessons because the group is not firm on those items. Frequently more practice than what was provided would be needed.

I had read something very similar in a recent DI NEWS article on CMC by Jerry Silbert, I believe. It is simply amazing the amount of extra instruction in math that lower performers need compared to higher performers. That amount of practice provided in CMC is about four times what you find in most other curricula and incrediblly some students need even more than that. When I teach my son, I routinely skip all the paired practice, all the math family practice, and often skip every other lesson if we are doing lessons consistently (4-5 a week). This year I've also been neglecting math, sometime for a month at a time. Then when we resume, he gets right back into it with little or know backtracking. Of course, my son falls into that 25% of kids who is going to learn math regardless how it's taught.

when students are taught to mastery they retain all or nearly all they were taught -- in fact they may even gain over the summer (e.g. in reading) the way more advantaged students typically do.

What's your take on the recent study taht suggested that low SES kids learn as much as high SES kids during the school year, and all the extra learning accomplished during the summer by the high SES kids. I find this difficult to swallow.

Anonymous said...

I homeschool my two sons ages 9 and 11. My now 9 year old began CMC C near the end of 2nd grade, completed it the middle of 3rd and is currently half way through D.

He's diagnosed with Tourettes Syndrome and ADHD inattentive variety, as well as expressive language delays. So, I guess he would be a "low performer" if he attended school.

In addition to other DI programs, CMC has been a life saver for us. He largely performs at grade level. We do every lesson, although not necessary every problem. I have had to back track lessons, due primarily to my failure to teach to mastery. Our largest issue during lessons is really keeping him focused and on task.

When I initially began the program I was too ridgid with the script and not sensitive enough in accessing his understanding. I've improved as a teacher as we've progressed. I have had to fight the urge to press on even when I know he wasn't completely "with me".

I've looked in detail at other programs and CMC covers more material with more depth than any other I've seen.

Just wanted to add my experience.

TurbineGuy said...

I have been meaning to do a field report, but still haven't worked up the energy.

The biggest news is my soon to be 3rd grader improved two grade levels in reading during the year thanks to an awesome teacher. The really good news is she has the same teacher next year (the teacher requested her). She still went to summer school, but she is finally performing on grade level.

My new 8th grader, the one who was failing math 2 years ago and spurred my education blogging kick, got straight A's the entire year...

The bad news... Anchorage School District formally adopted Everyday Math.

CrypticLife said...

We've been tutoring my older son with Kumon for several years -- my wife is Japanese and this lets her tutor in a way familiar and comfortable to her (do they make DI curriculum in Japanese? I could imagine a lot of the ideas being rather powerful). Anyway, the main point is that with sustained effort it's rather easy to outperform the inefficiencies of regular public schools, even good ones. My son's on fourth grade in Kumon (he'll be going into third in the fall in real life). He's also become good at mental math, and can add numbers into the thousands mentally, and is working on the last stretch of memorizing the multiplication tables to 12*12.

I agree that learning algebra is the payoff. And, that the school system's focus on manipulatives is a bit overdone. My son hated drawing the little dogs to add four dogs to five dogs, e.g., and started just scattering check marks or pencil dots to represent the dogs after doing the problem. Fortunately his teachers were relatively understanding about it (though, surprised he seemed bored).

I also tutor my preschooler (going into kindergarten this fall) with Engelmann's 100 Easy Lessons. My second son is not fluent in English, so this is a bit of a challenge (in fact, his spoken English is rather poor). Engelmann does warn about non-native speakers in the book, so I hold him blameless for any slow progress on our part. For what it's worth, though, we're making progress and have gotten through about thirty lessons (and it's helped with his English, as well). I could see us getting through another ten before kindergarten, and he'd be reading phonetically what teachers teach as "sight words". He may also be aided by going to a summer day camp for a month where most of the people won't speak Japanese (his first day was yesterday, and a disappointingly high number of the children speak Japanese, but at least none of the counselors do).

My third son is two, and has been taking an almost alarming interest in my lessons with my second son.