Wednesday, August 24, 2011

Accelerating within grade level with new new new Math: more strikes against math-inclined students

First, the "new new new Math." Pearson, the publisher of TERC Investigations, has collaborated with the power brokers at the highly-reputed, top-scoring Montgomery County School District (MCSD) to create a new "integrated" math program, eventually to be marketed around the country with help from MCSD's academic cachet. It's hard to track down specific details about this curriculum, which debuts this coming school year in Montgomery County, but, judging from its fifth and sixth grade objectives it looks suspiciously like Investigations. These objectives make no mention of standard algorithms like long division, instead emphasizing data, "representations," probability, statistics, and measurement. Nor do we see terms like "calculations," "automaticity,"  and "mastery"; rather, we find repeated instances of "explore", "examine," and "extend understanding." All good things, in theory; bastardized over the years under Reform Math, they also raise red flags.

Also suspiciously Reform-like are (1) the elimination of the "math pathways" model of grade acceleration wherein capable Montgomery County students could attend above-grade level math classes, and (2) a letter to parents sent out by the principal of Laytonsville Elementary School explaining why grade acceleration has been eliminated for "nearly all" students:

The new standards require students to develop deeper level of understanding in mathematics. Memorizing and repeating formulas will always be part of learning mathematics, but will not be sufficient in order to demonstrate deep understanding. Students will be expected to show understanding, computation, application, reasoning and engagement in a mathematical concept to be ready to move on to a new topic... In addition, the new standards are more challenging at each grade level. For example, many of the standards now in Grade 1 were previously in Grade 2 or higher or were not taught in the prior Montgomery Public Schools Curriculum. Therefore, the practice of grade skipping acceleration in mathematics will not be necessary for most students. Almost all of our students will be working at the challenging grade level standards this year and not in the next grade up.

To ensure that the needs of students who require more challenge are met, MCPS has developed enrichment and acceleration within the grade level curriculum that goes beyond the requirements of new standards. Students who have consistently demonstrated proficiency of a mathematics concept will be able to enrich their understanding of a grade-level topic or accelerate to a higher-level topic.
Ah, yes, deep understanding, application, engagement: why are these always associated with the most dumbed-down of math curricula? Even more oxymoronic is the concept of "acceleration within the grade level curriculum"--right up there with "differentiated instruction in heterogeneous groups."

One MCSD parent, whose daughter, then a 3rd grader, was deemed two years ahead in math in last year and placed in a 5th grade math class, suspects that her daughter would be "bored to tears" if kept at grade level under the new curriculum.

But eliminating ability-based grouping reflects one of the key findings of the Montgomery County Mathematics Working Group. Citing a study published in the Journal for Research in Mathematics Education, they note:
Mixed-ability grouping results in higher achievement for average and lower ability students and does not significantly affect achievement levels for higher ability students.
Montgomery County, of course, is part of a larger drive to eliminate ability-based grouping around the country. Montgomery County's new superintendent, Joshua Starr, succeeded in eliminating it in Stamford, Connecticut; where will he go next after he finishes up in Maryland? Perhaps he could come to Philadelphia, where we're currently looking for a new superintendent, and eliminate our magnet high schools.

Good studies on the effects of mixed-ability vs. ability-based grouping on math-inclined students are hard to find.  But one study suggests that gifted kids in particular benefit when grouped with like-minded kids and given material tailored to their abilities. And what is perhaps the one truly controlled study ever conducted anywhere in the world suggests that ability-based grouping is good for everyone.

There's at least some evidence that ability-based grouping has worked out well for Montgomery County in particular. Perhaps the lingering effects of that success will help Pearson sell its integrated Montgomery Math curriculum to the rest of the country.


Deirdre Mundy said...

When I was in 5th grade in Montgomery county, they discouraged acceleration-- you could take all the ISMs you wanted, but you had to teach yourself the stuff on them, and your math remained the same boring stuff.

When my mom complained, they tried to make me 'go deeper.' Which meant I got to spend math class playing math enrichment games on the Apple 2e. Well, except the school only had a couple of math games and they were easy, so my enrichment ended up being "Becoming an expert at Oregon Trail."

While I still love Oregon Trail, I think it was probably a very poor use of my math time.

Anonymous said...

The new Common Core State Standards are not particularly challenging. If that is what he is referring to, they must have really been behind before. The new standards are still behind the Primary Mathematics in some areas, and certainly a couple of years behind by 8th grade. So much for "world class". Half of them are poorly worded, even.

Deirdre Mundy said...

The other thing is that while "going deeper" might be entertaining for geomerty or precal or calc when the kids get older and can have fun with proofs and whatnot, there's not much place to go with elementary math.

If the class is calculating areas and volumes, well, sure, you can give the brighter kids irregular shapes and have them try to figure out the areas---but once they've mastered the technique for that, where do they go?

If the class is working on multi-digit addition, and the kid's mastered it, what are you going to do? Just tack on more digits? In many cases, going "deeper" instead of accelerating just means soul-crushing busy work and more practice with the same algorithms the kids have already mastered.

On the other hand, it's easier for a teacher to just give MORE work than it is for her to give harder work, especially if she's not particularly math-inclined herself.

Katharine Beals said...


From what I've seen, grade-level, Reform Math "going deeper" means helping out your less capable classmates and doing
"math projects" that apply grade-level concepts in ways that require lots of busy work.

Deirdre Mundy said...

The funny thing is, at least when I was in school, the teachers claimed that making us help the slow kids helped teach us 'compassion.'

As a fifth grader, I didn't have the maturity to learn 'compassion' from that. I just resented them for their slowness and ended up doing the work FOR them so that I could get back to reading whatever decent book I'd hidden in my desk.

All that it taught me was snobbery. We would have been better off with a lecture on how different people are better at different things, and that sure, I could do school well, but Suzy Slowpoke could embroider and I couldn't even sew a button without impaling myself. And then the teachers could have HELPED SS THEMSELVES instead of having another little kid do it! (who admittedly, was sort of socially retarded, so maybe if I'd been a normal 10 year old I would have been better, but looking back, I was more like a 6 or 7 year old on the whole 'dealing with others' thing)

Anyway, the other problem is that for a lot of the smarter kids, they CAN'T help the slower kids, because they literally can't understand how someone could fail to grasp something so intuitive. I mean, how many pictures do you have to draw to get someone to realize that 1/2=2/4=3/6=7/14 etc. etc. As a ten year old, all you want to do is scream and impale your head on a spike so the stupidity of it all will stop making your brain hurt.

As an adult, dealing with the same sort of things, I realized that some people just take a LOT more time and repetition to grasp things than others do... but as a kid, you really do assume that everyone's brain works like yours and that if they can't remember something it's because they're deliberately forgetting it.

Maybe instead of "going deeper," they should just make all the advanced kids work on motor skills.... it would probably be more helpful in the long run.....

(I'm a little hyper today-- sorry!)