# Welcome to the Makeover!

Here’s an idea: I’ll write a post. It will take me a few minutes, or more.

Next, you’ll read the post. It’ll only take you a minute. It’ll be about assessment. Specifically, me describing how I took a terrible assessment question and made it less terrible.

Ready? Here we go!

# Algebra 1 Assessment, Before

In my previous post I linked to the Algebra 1 SBG assessments I wrote in 2011-2012. Largely, they stink. Here’s an example of a terrible question from the Topic 1 assessment (full list-o-topics is here):

That was Form A, and I’ve created about a million forms (okay, more like 5-10 forms) for each assessment (in every class, though, so the total really is pretty close to a million). Here’s a similar question from Form B:

I was trying to write questions that assess whether my students understand the commutative, associative, and distributive properties. In particular, I wanted to see if they could name the properties based on an algebraic or numerical example. I was also hopeful that they knew which operations are commutative and associative (and which are not).

# Oh. My.

Well, what I ended up with in my first attempt were some miserable true/false questions that don’t really accomplish any of what I was hoping for. An especially unfortunate consequence of the way I wrote the questions was that students who might otherwise have explained their reasoning quickly learned that this problem demanded no such thing. A one-word answer for each part is all that was called for. Worse yet, because I failed to require any record of thinking on the page, the majority of my students resolved to do no thinking at all in their minds. It became a guessing game, and one that they’re not particularly skilled at.

# Algebra 1 Assessment, After

This year I’ve set about rewriting my Algebra 1 assessments. They’re not perfect, and I’ll probably want to run them through a revision cycle again next year (and the year after, and so on forever), but there are a few questions here and there that strike me as significant improvements over their original counterparts.

Here’s what the corresponding question looks like on the current Topic 1 assessment:

Just below #2 I ask whether multiplication is associative (#3) and whether division is associative (#4). It’s immediately more demanding, doesn’t let students off the hook, doesn’t tempt them to do less thinking than they might naturally do, and gives me a fairly clear sense of whether students know which property is which, and which operations are commutative/associative.

In writing this up, the only immediate change that I’d like to make to the question is to throw a third sentence in between the two already there. “Explain.” It’s implied, but it would be nice to state it explicitly. So then I would have something like, “Is addition commutative? Explain. Support your answer/explanation with an example.”

# Wrap Up

So, was that terribly longer than a minute? Or was it simply a terrible minute? Let me know what you think about this feature in general and/or this question comparison in particular in the comments.

Cheers!

## Comments 8

Michael

You are certainly correct that the second batch of questions is more thoughtful, However, I think that the True/False can also be salvaged (somewhat) by asking something along these lines – If you think that the statement is false, correct it so that it is a true statement. Or, use something closer to what you did in your modification – If you think that the statement is true, show this with a specific example.

This would work whenever your original T/F question is framed with unknowns in the question.

I’m having similar thoughts about arithmetic and geometric sequences questions which have always been mostly plug and chug formula problems. One question I thought of is explain why a1 + (n-1)d gives you the nth term of an arithmetic sequence.

@mrdardy I like your line of thinking there, both in general (trying to salvage a poor question, rather than abandon it completely) and in this particular case. If I go with the “correct the statements which are false” approach, I would still want to “upgrade” the statements in question. You might need to glance at some of the other forms (I’d be happy to share, if you want) to see just how bad some of this first round of T/F questions were. Rather than simply getting a read on student understanding, I think I introduced some extra layers of confusion by asking things in a strange way. For example, a*(b+c)=a*b+a*c because of the commutative property of addition. Ugh. For shame.

@mathnerdjet Nice! I’d love to see a few more questions along those lines for arithmetic and geometric sequence/series questions. If you write them sometime, will you share?

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Michael,

Very interesting post. One thing I tried this year with the properties was similar to what mrdardy suggested. We would ask is something like the following. Is the equation below always true? Explain how you know. If not, provide a counter example.

a/b = b/a

we were trying to get through the idea that the properties allow us to verify a statements without having to check for all values of the given variables. Then, if a property does not apply it only takes one counter example to indicate that something is not always true.

Thanks again for the thought provoking post.

-Peter