Point of Inflection

I made some rookie mistakes with my Algebra 2 skills checklist in semester one this year.  I have invented a word to describe each problem.

Hyperseparation

In my enthusiasm for separating skills, I gave determinants of 2×2 matrices and determinants of 3×3 matrices each their own spot on the list.  They should have been combined.  I also separated multiplication of polynomials from their division and even, astonishing in the euphoric clarity of hindsight, addition of matrices from their subtraction.  This overzealous separation led to inflated grades (students got a 5/5 on matrix addition, matrix subtraction, both kinds of matrix multiplication, AND twice for finding determinants) and tests that felt kind of… stupid.

Unrampability

A more subtle mistake: some skills on the checklist did not have discernible differences between intro-level problems and master-level problems.  For instance, an intro simplification test might look like “3x+2p-x+2x,” and a master might look like “3x+2p-x+2x-p+2p+r,” but for some students it felt silly to bother giving the intro level test first.  If a student can calculate “3+2+8+9,” do you really need to check to make sure they can calculate “3+2+8+9+1?”  In contrast, my favorite skills had some fundamental difference between the intro level and master level tests.  For example, the “dividing polynomials” intro test asked for a division that would have no remainder, and the master test involved remainders.  This was nice because a student could pass the class with a basic understanding of the concept, but would need a more advanced understanding before getting the 100%.

Bad Planning

I did not have an effective way to deliver master-level tests to the students who wanted them.  Early in the year I promised that students would be able to attempt a master-level test on any skill once per day, and early in the year this worked great.  Late in the year, when two thirds of my students wanted six tests a day, it was harder.  I need a better system.  Luckily, this won’t be a problem again until the end of this semester, so I’ll start thinking about it then.  ;)

So, now the task is to create the lists for next semester (my school doesn’t start until January 10!), hoping to avoid these problems and keep the amazing benefits I got from the system last semester.  Stay tuned!