Last time in this quick-look-at-improving-assessment series (which began here) I shared my attempt at improving the questions related to distribution on an Algebra 1 assessment. As always, you can check out the topic list here (or here, if you want “I can…” statements as well).
Algebra 1 • Topic 2 Assessment, Before
This time we’ll take a look at a series of questions related to operations on numbers. Here’s the rubbish version (from the original Form A):
I was trying to get a read on whether students understood what additive and multiplicative properties are. For reasons similar to those shared in the first post in the series, this question type wasn’t particularly effective. Also, there’s the issue of “What am I actually trying to accomplish with these questions?” I don’t think I had that settled in my mind when I wrote the original assessment, and that led to the lackluster questions shown above.
Algebra 1 • Topic 2 Assessment, After
If this assessment was going to improve at all, I first needed to nail down what I wanted to accomplish. Then I needed to work on better ways to ask questions (even just spicing up the originals with “explain your reasoning” or “defend your answer” would have been a nice start.
At any rate, I decided on three goals, so I wrote three mini-sections of the assessment. Here they are:
Goal 1: Students will know the colloquial nicknames for additive inverse (opposite) and multiplicative inverse (reciprocal)
And here’s how I attempt to measure that on the new-and-hopefully-improved assessment:
Simple, but to the point. On to the next one…
Goal 2: Students will be able to use the idea of additive and multiplicative inverse (possibly without even knowing their names) in order to “make one” and “make zero”
Here’s how I tried to assess that skill:
I decided that this was actually the main reason we were exploring additive and multiplicative inverses in the first place, so a rather direct assessment question seemed appropriate. On to the third goal related to inverses…
Goal 3: Students will justify their reasoning with verbal and numerical support
The content isn’t profound or complex, so I thought it might provide a nice opportunity for students to create their first “mathematical” argument, one with complete sentences and mathematical “evidence.” With these two questions, I’m really trying to pave the way for more complex arguments students will make in Geometry, Algebra 2, Precalculus, and Calculus.
Now that I’ve written three of these posts, I’m wondering if I should add student work. I don’t have anything for the original versions, but for some of the revamped assessments I took pictures of strong and weak responses in order to facilitate in-class discussions the following day. If I can dig those images up, would they be worth posting? Share your thoughts (on this last question, or in general) below.