kitchen table math, the sequel: Surprise! Lack of Mastery of Earlier Math Makes Mastering Algebra Difficult

Wednesday, February 10, 2010

Surprise! Lack of Mastery of Earlier Math Makes Mastering Algebra Difficult

From Today's EdWeek

'Algebra-for-All' Push Found to Yield Poor Results

Spurred by a succession of reports pointing to the importance of algebra as a gateway to college, educators and policymakers embraced “algebra for all” policies in the 1990s and began working to ensure that students take the subject by 9th grade or earlier.

A trickle of studies suggests that in practice, though, getting all students past the algebra hump has proved difficult and has failed, some of the time, to yield the kinds of payoffs educators seek.


[snip]

“There’s no question that taking advanced courses boosts student achievement,” said Adam Gamoran, a professor of education policy studies and sociology at the University of Wisconsin-Madison. His 2000 study on algebra and tracking helped catalyze the interest in expanding access for all students to algebra courses.

“Where the area of disagreement comes,” Mr. Gamoran added, “is what should we do with students who performed poorly previously. In my judgment, the reason studies like mine show that students even with low levels of achievement do better in advanced classes is because the low-level classes are practically worthless.”

“And there’s no simple solution to this problem,” he added, “because we also know that when tracking is eliminated, students at high levels don’t gain as much as they do in high-level or [Advanced Placement] classes.”

[snip]

Tom Loveless, the author of the report from the Washington-based Brookings Institution on “misplaced” math students in algebra, said the issue is even more complex.

“No one has figured out how to teach algebra to kids who are seven or eight years behind before they get to algebra, and teach it all in one year,” said Mr. Loveless, who favors interventions for struggling students at even earlier ages.

Nationwide, research findings may diverge because testing content varies—the TIMSS test has more algebra content than many state exams taken by 8th graders—and because course content varies from classroom to classroom.

“If you take what’s called algebra class, and you look at the actual distribution of allocated time, you find that many of those teachers spend a very large portion of that year on basic arithmetic,” said Mr. Schmidt, who is a distinguished university professor of education at Michigan State’s East Lansing campus. His research on U.S. classrooms has found, in fact, that nearly a third of students studying algebra are using arithmetic books in their classes.

19 comments:

Independent George said...

Trust the spiral!

Ben Calvin said...

Guess we need to start with "Fractions for All!"

Then when that doesn't work we can go to "Long Division for All!"

Then.....

lgm said...

Full inclusion is alive and well. The statement 'course content varies' and 'very large portion of the year on basic arithmetic' is the PC way to phrase it.

The US DoEd is taking ideas at
http://openeducation.ideascale.com/a/panel.do?id=7030

farmwifetwo said...

Surprise... surprise...

Just hand them a calculator... what do they need to learn math for... Why do we take so much pride in saying "Math was difficult for me"...

I'll keep afterschooling math...

SteveH said...

It reminds me of the definition of insanity. They're big on thinking outside of the box, but they can't get out of their own ed school box.

The problem in our town is that to change things, the schools would have to admit that their fundamental assumptions are wrong and that they have been ruining kids for years. Damn the evidence, full inclusion ahead.

SteveH said...

It's also time once again in our town for the glorification of relative over absolute. Our state testing numbers are in. Math scores have gone up. They never explain that the raw percent score you need (on a simple test) for proficiency is something like a 60% - 65%. I just love how they translate the lousy raw score into a good looking percentage number in the 80's and 90's. That's what goes in the paper. Our schools exclaim how good the education is.

Hainish said...

Sorry, OT, but I discovered this blog and have to recommend it:

Reading and Word Recognition Research

Does anyone have a link to the Brookings report on misplaced math students?

Anonymous said...

The Brookings report can be found at
http://www.brookings.edu/~/media/Files/rc/reports/2008/0922_education_loveless/0922_education_loveless.pdf

Allison said...

--Full inclusion is alive and well. The statement 'course content varies' and 'very large portion of the year on basic arithmetic' is the PC way to phrase it.

It's something else, too. It's a way to say without saying that the states are gaming the requirements to teach Algebra I to everyone by year X.

So sometimes the full inclusion model is what happens when states dictate in top down fashion how schools will "teach" without changing any of the underlying structure leading to that teaching.

In our state, MN, that year is now 8th. It would be great except that the standards in place don't define what 8th grade algebra is; they only define what mastery of the two year algebra sequence (alg 2 is now a grad requirement of high school) is. So schools can cheat and rename their prior pre algebra course as algebra 1, and parents are not understanding this is so.

Not only did they change the 8th grade requirement without enforcing standards, they didn't change any of the lower grade standards--those will change in later years (yes, that's right, they have more years to change the lower grades, instead of changing the standards in the lower grades and then increasing by year over time.)

and they didn't change the teacher certification requirements either.

kcab said...

"...It would be great except that the standards in place don't define what 8th grade algebra is; they only define what mastery of the two year algebra sequence (alg 2 is now a grad requirement of high school) is. So schools can cheat and rename their prior pre algebra course as algebra 1, and parents are not understanding this is so."

This is extremely interesting, I will have to see if that is what is going on here in CT too. I have commented several times to my daughter that her (supposed) Algebra I class seems like a repeat of pre-algebra.

Allison said...

I will try to get a post up this weekend about authentic algebra, and how a parent could determine if their child was taking authentic algebra or not.

Bostonian said...

Here are some taboo facts.

There is an IQ threshold below which one cannot learn algebra, no matter how good the curriculum and teaching. I'm not sure what the level is (I'd guess at least 100), but it exists. Many children will never learn algebra or get a college-prep high school education (of which algebra is part). Those children come from all races, but apparently not in equal proportions.

Society needs to be realistic about how to educate the bottom half of the bell curve.

SteveH said...

"I'd guess at least 100"

That's the rub, isn't it. I think it's much lower. But this is not a hard cutoff line, is it? How do you make sure that all kids have a proper chance? How do you avoid using this as an escape clause for bad curricula and teaching?

Many at KTM are all about fixing the really, really horrible math curricula and teaching being foisted on millions of kids across the nation. Fix that first, and then I'll be happy to talk about minimum high school graduation requirements.

momof4 said...

I am totally in favor of improving both curriculum and instruction in arithmetic/math k-8, so that many more kids are prepared for algebra, but there will be a significant fraction that will not be ready until 9th grade or later. They will just need more time and some will be ready in 6th gradeor before. Some will never be ready, because algebra and higher math are about abstractions and abstraction requires an IQ level that some don't have.

However, ensuring that all non-cognitively-handicapped kids finish 8th grade with a solid working knowledge of the 4 basic operations, plus decimals, fractions and percentages would be a significant improvement over the current situation. Since the changes in curriculum and instruction (and improvement of teachers' math knowledge) are not congruent with the prevailing educational philosophy and worldview (and political reality), they won't happen with much less than a revolution. Small districts probably have the best chance.

concernedCTparent said...

I was recently in a math meeting in my district where the middle school math teachers were discussing the NMAP report (the chapter on conceptual knowledge in particular). I was hopeful that we might actually get somewhere and start asking the difficult questions.

The problem, you see, is that our middle school uses CMP2. CMP2 is definitely NOT what NMAP meant when they defined "authentic algebra".

Nevertheless, the middle school teachers read through the list of topics that constitute "authentic algebra" per NMAP and in the presence of one of the NMAP authors, declared that our district's middle school math program (CMP2) covered all of them. According to my district we are teaching "authentic algebra".

CMP2 is NOT authentic algebra, not even close. But they sure think it is. They LOVE CMP2. They love it, sing its praises, and would defend it to the death and then proceed to wonder why the students are struggling with Geometry in high school. Something couldn't possibly be wrong with CMP2, ergo it must be the kids. So there you have it. In my district, CMP2 "is" authentic algebra. NMAP's message corrupted and hijacked yet again.

The emperor's new clothes are splendid, aren't they?

Anonymous said...

Well, just to give you guys something to consider. I afterschooled my borderline IQ kid for two years in arithmetic, fractions, decimals, and percentages. I pounded it into him 4 to 5 nights a week using Saxon. Yes, he was much slower and less accurate than your average kid, but he was probably faster than your EM kid.

By the end of 8th grade he moved into basic easy algebra and he did understand it and could solve the problems.

No, he probably would never go beyond that and his accuracy would always be bad. But, the massive amount of practice on fluency and manipulating fractions (and hearing me say over and over again that the bar in a fraction was a division sign) made moving into basic pre algebra actually possible.

So, if my kid can get there, slow as he is, then there are many more with higher IQs who can too if they are just taught arithmetic properly and with adequate practice.

And just to help with perspective, this same child could not count using a number line until the 4th grade. I had all but given up that he would ever understand one to one correspondence when it just happened one day after years of trying.

SusanS

SteveH said...

It's too easy for schools to blame the kids. Bad teaching and curricula can make it seem like kids are below some unseen cutoff. It will happen in the earliest grades and it will be self-fulfilling. By middle school, kids will even blame themselves.


"...significant fraction that will not be ready until 9th grade or later"


Ninth grade is fine. What is the fraction after that? What is the fraction that currently gets there now? What's the purpose of raising the IQ flag? How do you tell the difference between not ready and bad teaching and curricula?

My nephew's school thought he was mentally challenged. My sister worked with him and now he is a programmer with a degree in computer science. He had a issue to get past, but his school gave up on him.


I don't even like the idea that some sort of algebra I or algebra II standards are being pushed as high school graduation requirements. The requirement should be algebra by 8th or 9th grade. The later target allows the schools to never figure out that many of the problems start in K-6. They just say that the kids were not ready yet and throw out some sort of vague IQ explanation.

Prove it.

Statistics might tell you something about the whole, but they're just so incredibly awful when they are applied to individuals by individuals.

SteveH said...

"They love it, sing its praises, and would defend it to the death and then proceed to wonder why the students are struggling with Geometry in high school."

I'm so sorry. We escaped that trap. I think the key point was that parents wanted the exact same algebra course the high school uses as a lead-in to their honors geometry course. Fortunately, they decided not to make two tracks and keep CMP. Now, the issue is the sorting that happens when kids get to 7th grade.

They offer 3 levels and what do I hear? I hear that the school tells parents that some kids are just not ready for the advanced material. No. They just have a lot of mastery skills that must be fixed. What do math teachers complain about? They don't complain that the kids are too slow for the material. They complain that they haven't learned the basics.

rocky said...

There is an IQ threshold below which one cannot learn algebra

abstraction requires an IQ level that some don't have

IQ is just pattern matching skills. It can be learned.

Consider how much abstraction is involved in driving a car: the steering wheel, the brake pedal, and (in manual cars) the gearshift ratio between rpm of motor and wheels. But even the most non-academic teenagers are willing to practice every day, and most of them become competent after a while.

Of course I'm thinking of basic algebra as the workmanlike substitution of letters for values and equation manipulations for converting one thing to another or just answering "how much of This do we need to make That". Is drawing a graph harder than reading a dipstick?

(Shh. Don't tell them it's hard. Tell them that little kids in Singapore do this for fun.)