Tuesday, May 08, 2012

The Use of Placement Tests

I think I have written about this before, but I can't find the post and I want to think about it again, so here goes a reconstruction of the idea.

Years ago, I was teaching algebra to 8th graders who were recommended by their previous math teacher for inclusion in the algebra class.  In general, the criteria she used for recommending students for the class were two-fold: they had to have good mathematical understanding (evidence: tests) and they had to have good work habits ("A"s in math, which, with her grading system meant that they turned in virtually all of their homework). 

Since I was the one who actually did the teaching of the algebra class, I thought it might be interesting to add to these criteria an algebra readiness test.  So we gave the algebra readiness test to quite a few more students than she anticipated were actually qualified to take algebra.  Interestingly, we now had a new problem.  There were the kids who had good grades and who scored high on the readiness test.  Clearly, they were ready for algebra.  There were kids who had good grades, but who scored fairly low on the readiness test.  Not quite as clear, but still relatively convincingly, they were not quite ready for algebra.  But the ones that really led to a disagreement between the two of us were the ones in a third group:  the ones who scored high on the readiness test, but who did not have especially good grades.  These students were often described as the unmotivated ones, the ones who were lazy, the ones who just weren't interested in math.  She felt these students should not be included, because they hadn't earned the right to be in the algebra class.

Not right away, but after thinking about it for a while, I began to wonder:  why do we give smart kids a pass on taking classes or learning material that they are clearly ready for?  For kids on the lower end of the ability spectrum, or kids with specific learning disabilities, do we let them opt out of addressing their weaknesses?  No.  We may give them extra support to help them handle their challenges, but we don't let them say, No, I am not interested in reading, so I am not going to do this hard reading, I am just going to read this lower level stuff that I know I can do just fine.

Why DO we let the smart kids opt out of challenging material? 

And then, to carry that a bit further, what if we re-framed gifted education in terms of not just letting kids advance to higher level material, but instead use a slightly different argument:  all students need to learn to work hard and to develop good study skills.  Therefore, we need to place all students in curricula that are in their zone of proximal development (ZPG).  Naturally, this will be an approximation.  Teachers with 25 or more students in their classes can't be expected to individualize the entire class for each student, but it should be at least a goal.  Kids who are reading 2 or 3 grade levels above their class level should be required to work just as hard at new reading goals as kids who are reading 2 or 3 grade levels below their class level.  Why shouldn't they?  Why do we let them coast?  Why couldn't we re-frame the curriculum offerings to REQUIRE the kids who have mastered the regular curriculum to address curriculum that they haven't yet mastered?

As an experiment, we agreed to accept one student into the algebra class, who scored quite high on the readiness test, but whose grades would not have allowed him to take the class.  He was the lazy one; the unmotivated one.  And, interestingly, he continued this same pattern in algebra.  He passed the tests, but often just barely; he could have done much better if he had actually done more of the work.  I am not sure what we learned from the experiment.  I think it would have to be repeated a number of times, before we could decide either way - and clearly, it also depends on the students involved.  Even with material better suited to his readiness, he didn't learn good work habits.  Was it too late?  Should we have tried this when he was younger?  Or are lazy students always lazy? 

I still think we should require the smart kids to work harder.  Perhaps this is because I never had to work hard in school myself, until I was well into college - and by then it caused a number of related imposter syndrome problems.  (An entirely different post).

One more thing about the boy who was required to take algebra, even though he refused to work hard.  I had a software program for my algebra students called Green Globs and Graphing Equations (from Sunburst, I think).  The idea is that the computer sprays some random green globs over an x-y grid and you are supposed to try to hit them with lines.  The more globs you hit at one time, the higher (exponentially) your score.  This gentleman got really interested in the program and didn't want to stop at just straight lines.  He asked for equations of different types of lines, so that he might try hitting more globs with one equation.  I gave him circles, parabolas, ellipses.  He wanted still more.  I gave him trig functions, exponentials, anything I could think of.  I showed him how to add parameters to the sine functions, so that he could make them more dense (that really racks up the points).  He may not have been motivated to do homework, but he certainly did find something that interested him.

I wonder what he does now.

1 comment:

  1. Great post, Laura. We face this at our home. Our 12 year old does NOT do math hw, and scores As on his tests and quizzes. That makes him a C student. It was worse last year, when teh teacher gave grades on how well they kept their notebooks.