Algebra 1 Growth in Geometry and Algebra II

Last September, I wrote about my classes and the pre-algebra/Algebra 1 assessment results.

My school covers a year of instruction in a semester, so we just finished the first “year” of courses. I start with new students and four preps on Monday. Last week, I gave them the same assessment to see if they’d improved.

Unfortunately, the hard drive on my school computer got wiped in a re-imaging. This shouldn’t have been a problem, because I shouldn’t have had any data on the hard drive, except I never got put on the network. Happily, I use Dropbox for all my curriculum development, so an entire year’s worth of intellectual property wasn’t obliterated. I only lost the original assessment results, which I had accidentally stored on the school hard drive. I should have entered the scores in the school grading system (with a 0 weight, since they don’t count towards the grade) but only did that for geometry, the only class I can directly compare results with.

My algebra II class, though, was incredibly stable. I only lost three students, one of whom got a perfect score—which the only new addition to the class also got, so balance maintained. The other two students who left got around 10-15 wrong, so were squarely in the average at the time. I feel pretty comfortable that the original scores didn’t change substantially. My geometry class did have some major additions and removals, but since I had their scores I could recalculate.

Mean Median Mode Range
Original just above 10 9.5 7 22
Recalculated just below 10 (9.8) 8 7 22

I didn’t have the Math Support scores, and enough students didn’t take the second test that comparisons would be pointless.

One confession: Two Algebra II students, the weakest two in the class, who did no work, scored 23 and 24 wrong, which was 11 more than the next lowest score. Their scores added an entire point to the average wrong, increased the range by 14 points, and you know, I just said bye and stopped them from distorting the results the other 32 kids. (I don’t remember exactly, but the original A2 tests had five or six 20+ wrong scores.)

So here’s the original September graph and the new graph of January:


The geometry class was bimodal: 0 and 10. Excel refused to acknowledge this and I wasn’t sure how to force it. The 10s, as a group, were pretty consistent—only one of them improved by more than a point. The perfect scores ranged from 8 wrong to 2 wrong on the first test.


In short, they learned a lot of first year algebra, and that’s because I spent quite a bit of time teaching them first year algebra. In Algebra II, I did it with data modeling, which was a much more sophisticated approach than what they’d had before, but it was still first year algebra. In geometry, I minimize certain standards (proofs, circles, solid shapes) in favor of applied geometry problems with lots of algebra.

And for all that improvement, a still distressing number of students answered x2 + 12 when asked what the product of (x+3) and (x+4) was, including two students who got an A in the class. I beat this into their heads, and STILL some of them forget that.

Some folks are going to draw exactly the wrong impression. “See?” these misguided souls will say, nodding wisely. “Our kids just aren’t being taught properly in early grades. Better standards, better teachers, this problems’s fixed! Until then, this poor teacher has to make up the slack.” In short, these poor fools still believe in the myth that they’ve never been taught.

When in fact, they were taught. Including by me—and I don’t mean the “hey, by the way, don’t forget the middle term in binomial multiplication”, but “you are clubbing orphan seals and making baby Jesus cry when you forget the middle term” while banging myself on the head with a whiteboard. And some of them just forgot anyway.

I don’t know how my kids will do on their state tests, but it’s safe to say that the geometry and second year algebra I exposed them to was considerably less than it would have been had their assessment scores at the beginning of class been the ones they got at the end of class. And because no one wants to acknowledge the huge deficit half or more of each class has in advanced high school math, high schools won’t be able to teach the kids the skills they need in the classes they need—namely, prealgebra for a year, “first year” algebra for two years, and then maybe some geometry and second year algebra. If they do okay on the earlier stuff.

Instead, high schools are forced to pretend that transcripts reflect reality, that all kids in geometry classes are capable of passing a pre-algebra test, much less an algebra one test. Meanwhile, reformers won’t know that I improved my kids’ basic algebra skills whilst still teaching them a lot of geometry/algebra II, because the tests they’ll insist on judging me with will assume a) that the kids had that earlier material mastered or b) that I could just catch them up quickly because after all, the only problem was the kids’ earlier teachers had never taught them.


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11 responses to “Algebra 1 Growth in Geometry and Algebra II

  • Roger Sweeny

    I’m a little confused about the last paragraph, particularly as it relates to the two students who got an A but thought that the product of (x + 3) and (x + 4) was x2 + 12. Doesn’t the A announce “that the kids had that earlier material mastered”? They didn’t–but I can’t blame an outsider for getting that impression.

    And isn’t there a deeper problem here? Most everyone in and out of the ed business acts as if grades represent what students learned, where “learn” means “understand and will not forget.” However, in reality, grades represent what students were able to do during and immediately after a class. That “knowledge” will begin to “decay” as soon as they stop using it. For many, it will decay to almost zero in a remarkably short period of time.

    • educationrealist

      In one case, it was a geometry student, and I can’t grade them on their algebra skills. In the other, the student was just, as you say, forgetting.

      And yes, that’s what grades represent. They do forget. However, my tests are always comprehensive to that point. If my students just learned logs, their test of 25 questions might have 5 log questions, and then everything else they’d learned.

      That’s one of the reasons I go deep and not terribly broad, so the students might remember more of the essentials.

  • Don

    Excel histograms are horrid. No problems with histograms in R.

    hist(data, xlim = range(dest$x), xlab = “x”, ylab = “test score”

  • Matthew Levey

    so i’m really ‘special’ ’cause I can remember FOIL all these many years later?

    • educationrealist

      I suspect, but can’t be sure, that we’re teaching methods too early and so kids are forgetting everything. Or maybe kids back in the day studied more because fewer of them were taking advanced math.

    • Roger Sweeny

      Yes, you are really special if you can remember FOIL several years after your last math course. I would be willing to bet a very large amount of money that less than 20% actually do. For those who don’t take a course past Algebra 2, the percentage would be in the single digits.

      My sister-in-law has said on a number of occasions, “You and your brother are so unusual. You remember what you learned in high school.”

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