Friday, July 22, 2011

8th Grade Algebra

In this country we seem to get in a tizzy whenever Algebra 1 in 8th grade is discussed. My favorite is when people trot out "cognitive theorists" who say that most 8th graders are not capable of Algebra 1; my usual response is to question why they're capable of it in so many other countries but not ours. A friend, who chooses to remain anonymous, gave me permission to post the following:
Perhaps I should use this opportunity to clarify my take on this whole Algebra-in-8 issue.

I consider the 'developmental' and 'cognitive readiness' arguments against algebra in grade 8 completely baseless. And when they come wrapped in 'brain scans' and 'PET images' they are either charlatanism or pretentious ignorance... I often use the example of 1990 Japan, as described in Kodaira's preface to his math curriculum translation into English, as a convincing evidence that a whole cohort, with its full bell-curve ability distribution, can reasonably master both algebra 1 and geometry by grade 9.

That being said, it does not mean that in the average case students *need* to study algebra in grade 8 to succeed. Just that they can. In the ideal situation, only those students that are prepared and interested would study algebra in grade 8. After all, I don't see a big difference whether it will be studied in grade 8 or 9. And I don't think that every student needs 4 years of HS math *beyond* Algebra 1.

But we are not in an ideal situation. For years elementary and middle school teachers could dilute math education, and not prepare students for algebra even in grade 9, as there was no 'capstone' course like Algebra 1 at the end of K-8 span. All their ill-prepared charges were thrown over the wall to high school, and it became a high school's problem, instead of elementary and middle problem, to cope with the results of ES and MS neglect.

And that's why I believe having Algebra 1 in grade 8 is so important. As opposed to '7th grade math,' or '8th grade math,' Algebra 1 still has a much better defined content across the land, and placing it as a capstone for K-8 forces ES and MS to face the results of their own preparation, rather than evade responsibility and later place the blame on HS, that often anyway belongs to another school district.

So, no. I don't believe Algebra 1 in grade 8 is critical to child's future, although it should be a breeze for any reasonably prepared child, even with an IQ a full standard deviation below average. But it is critical to the improvement of our non-academically focused school system with its under-prepared ES and MS teachers.
I disagree with none of this.


Anonymous said...

Another argument in favor of 8th grage algebra for those who are ready (which CAN be more than 50% of the students) is that it can be used to free up class time later for other subjects. Why waste the kids' time teaching something in 9 years that can be taught in 8? If time doesn't matter, why not wait until 12th grade to teach algebra? Or college? One good answer is that this would waste everyone's time ... which is bad.

-Mark Roulo

Happy Elf Mom said...

Hey. Ok, not a standard question, but I find this is where my kid is falling flat on his face. He had always done ALL his math in his head and with algebra, you must write the process down.

It's very slow going. Is this true for all children or just mine? And do you know of any software or other helps for kids who can't write well? Emperor is 9 and he knows the math but has trouble with slowing down and doing each step in order. Don't see any suggestions on homeschooling boards. Thanks for listening. :)

PS. I'm still not sure where I will ever use the algebra, but I still remember most of it 100 years later. Yayy.

Darren said...

It's pretty much the same for every kid--*no* kid on the planet wants to write *anything* down!

I don't know of any software that would enforce writing something down.

Wow, I'm great help, aren't I? :-)

Happy Elf Mom said...

LOL Well, at least you are honest!! And see, I don't have 150 other children to compare the kid to, so there is no way for me to know these things, really. :)

Darren said...

Contractually I can have any number of kids they can give me for the first 20 days of school, after that I'm limited to 165 (and no more than 36 in any particular class).

150? Would *love* that! :-)

And yes, kids are lazy. They don't want to write *anything*. It amazes me. I was probably the same way, though, back in the day....

Anonymous said...

I homeschool (a boy) and he knows that Dad uses math at work. What I have told him is that it isn't enough to get the correct answer ... in the real world other people aren't going to be able to check in the back of the book, so you have to show the other people how you got the answer that you came up with. Because they are going to want to check it themselves and checking is much faster than solving from scratch ( again).

He gets this.

Might be worth a try.

One other thing I do if he's skipping too many steps is to give harder numbers. Bigger often works, as does switching from whole numbers to mixed numbers.

-Mark Roulo

Cal said...

" I don't believe Algebra 1 in grade 8 is critical to child's future, although it should be a breeze for any reasonably prepared child, even with an IQ a full standard deviation below average. "

I very much doubt this; I suspect that an IQ of 100 is needed to truly comprehend first year algebra and apply it to subsequent math study. But even if this assertion were true, remember that the average black IQ is slightly lower than 1 standard deviation below the national average, and the average Hispanic IQ is just slightly higher than 1 standard deviation below the national average.

In other words, using your own statistic, over half of blacks and slightly less than half of Hispanics do not qualify cognitively for it "being a breeze". (Yeah, right.)

Japan's not a good measure, as the country's IQ baseline is slightly higher, and its standard deviation is slightly smaller.

Incidentally, the obvious means of resolving this debate would be to turn to the research. Except, alas, there is no research on this recently. No one wants to look and see if there might be any link between cognitive ability and algebra success. We used to do it, back in the 70s. But we don't do it any more. Anyone want to guess why?

By the way, whatever the rationale for teaching algebra in 8th grade, it's absurd to pretend that there's an advantage to introducing it early for the reasons this guy gives. I'm a high school algebra teacher, and, in our district, 80% of our algebra students are repeating it--most of them from the 8th grade. So high schools are still held responsible for algebra--it's a major PI area for schools held to be failing. The kids just feel like losers for having to repeat it.

It's also pretty silly to assert that elementary and middle school teachers are just kind of randomly teaching math. Most of them are working hard to teach the skills needed. But the kids who do have the cognitive ability are usually taught too slowly, and the kids who don't have the ability are out of their depth.