kitchen table math, the sequel: kids need spiraled practice, not spiraled instruction

Wednesday, March 7, 2012

kids need spiraled practice, not spiraled instruction

Hainish left a link to a terrific post by a math teacher:
11th grade here = 9th grade here. In fact, Algebra 2 was such a rehash of the district's Algebra 1 course that some teachers called it "Algebra T-o-o." And really, the same point could be made about math curriculum as a whole in the U.S., since most content for any given year is a review of content from previous years. (The Common Core State Standards may help change this, but I'll believe it when I see it.)

This approach, where we touch on lots of topics each year--rather than go deep with fewer topics--and then revisit them in subsequent years is often called spiraling. But what it is for many students is stifling. And this is as true for kids who've yet to master a skill as it is for those who nailed it right away. I first noticed this when I taught 9th grade Algebra classes where every student was performing at least two years below grade level.

"Meet them where they are," fellow math teachers advised me. Makes sense, I thought, since I couldn't imagine teaching Algebra to kids who didn't know basic arithmetic. But what I soon learned is that perception matters more to students than performance. For many kids, having seen something is akin to having learned something. "Man, we already know this," students said, as I presented lesson after lesson on fractions, decimals, and percents.

Other students, meanwhile, knew they didn't understand the material, but had given up hope of ever understanding it. The implication was therefore the same for all students: encore presentations on previous years' topics were pointless. And though I was able to engage a few students when I found new ways to present old topics, one group of students was always slighted: those who really did "already know this."


The problem, of course, goes back to the disconnect between kids seeing something and actually learning--and retaining--it. But if it didn't sink in for them the first, second, or third time a teacher presented it, why should we present it again?

We shouldn't. At some point the focus needs to be on students practicing math rather than teachers presenting it.


[W]e should provide students spiraled practice, not spiraled instruction. When I did this in 10th grade Geometry classes, students said they learned more Algebra than they had learned in their 9th grade Algebra course. And, as a result, they were ready for more advanced math--starting with Algebra T-w-o.
Spiraled Instruction, Stifled Learning
By David Ginsburg on March 5, 2012 8:35 PM


Catherine Johnson said...

David Ginsburg is a terrific writer.

Jim H said...

"At some point the focus needs to be on students practicing math rather than teachers presenting it."

Yes Yes Yes!

I totally agree.

Although John Saxon hated the term "spiraling," he fully believed in continuous review. I pulled my son out of his math class (where the teacher did a lot of talking and the kids only did about 10 problems per day) and had him complete Algebra 1 using Saxon.

He does at least 30 problems per day, 26 of which review previously learned concepts.

He is about 100 lessons into the book, has completed well over 3,500 Algebra problems (with tests and practice problems), and has MASTERED a large number of concepts.

I used to believe that it was the job of a teacher to "teach understanding," but the more I think about it, the more I realize that in my life, understanding has always come from practice. Every job I've ever done in my life, mastery came through an iterative process of trying something and then changing my approach after thinking about the mistakes I made.

I feel that Math Education experts are giving themselves way too much credit....learning, for the most part, just comes from practice.

Anne Dwyer said...

I totally agree with this.

I have been teaching the Basic Math class at my local community college for 5 years now. I have gone through many iterations of what I do.

Lately, I've been dropping the games and group work for practice, practice and more practice. If they practice in class, at least I know that they are doing it.

Here's an example: yesterday we were finishing up the chapter on decimals. I gave them a worksheet that required them to add decimals and fractions: if the denominator gives a repeating decimal, they have to convert the decimal to a fractions and add or subtract. You know what I found out? They had already forgotten how to add fractions!! Actually, that's not quite correct. They could not access the script in their heads that told them what to do with that particular problem. Once we reviewed it briefly, they were able to finish the problems. But it took everything they had to finish the problem set.

Catherine Johnson said...

I think I mentioned that my neighbor, the other day, said that "the villification of practice" is a HUGE problem in U.S. education in her view.

I've been thinking that for a long time.

Schools have shunned all responsibility for a) providing an effective practice regiment and b) overseeing kids as they follow an effective practice regimen.

kathyiggy said...

Last year, our district eliminated the HS Algebra class which spreads Algebra I over 2 years, stating that this would allow "all students to be college ready." So now, my ASD daughter is in Algebra I as a sophomore, and it's the first time she has been in a gen ed math class since 4th grade. Needless to say, there is very limited's on to a new section every day with no looking back, except for the final exam when they get a 200-problem packet a week before the exam. Second semester has been a stuggle. Looks like another ALEXS summer around here.

Hainish said...

Ralated (to Kathy's comment): Vermont is planning to require algebra and geometry to graduate.

lgm said...

Our district has changed to giving cumulative review packets for high school Regent's math. It's been great. My kid that thinks he is poor at math has been forced to learn the concepts he shorted the first time. He's become much faster too, realizing that he has to knuckle down and get the concept when it's presented. I beleive the change is coming because the teachers have access to a problem set data bank and they are working together -every section is getting the same packet.

We also have the opportunity to use the online data bank the school subscribes to for science. That has been a blessing; makes it a lot easier for me to see where the kid went wrong and remediate on the spot.

lgm said...

There are still no challenge problems, a la Dolciani 'C' problems.