# Introduction

Up next: an assessment on rational functions from Sam Shah. As you read through the assessment and consider adding your comments to the discussion, keep these questions in mind:

- What do you like (and why)?
- What would you do differently (and why)?
- What questions do you have for Sam?

# Submission Type

“Share an assessment you *don’t* hate…”

# Assessment

# Author’s Commentary

“I have a lot of not-so-good assessments, ones that I would be embarrassed for any of y’all to see. But I’m not sharing those because I know they aren’t so good, and I know I can come up with ways to improve them. (Mainly that will involve improving how I teach/introduce the material, which means that the assessments themselves will be better because my kids will have done more and better thinking, so I can ask more and better questions.) So I’m going to share a strong assessment that I just gave, on rational functions.

I am teaching an advanced precalculus class for the first time this year. And so they get things pretty quickly, and are a strong bunch. You can see how I introduced/taught rational functions here in this blogpost. This was the assessment I came up with to cover the unit.

I don’t have too much to really say about individual questions.

The goal of this unit was to be highly conceptual, and the goal of the questions was to uncover misunderstandings.

For example, when I asked the vertical asymptote question (#3), only about a 1/3 of the kids got full credit. I was looking for something like: “when x gets close to zero, you have a fraction that is 1/(small number) which results in a big number. So for example, 1/0.001 is 1000. The closer the x value is to zero, the larger the output! That is why the function approaches infinity as x gets close to zero!”

However, what was clear to me in hindsight was that we talked about that idea briefly, but then we spent a long time talking about why horizontal asymptotes appear (or don’t appear). And so kids would say things about not dividing by zero, and then almost in a non-sequitor switch their explanation to something like “for large positive and negative x-values, the output is close to 0.” So I was able to see where their misunderstandings were through this question (and also where I need to shore up my own teaching next year).

Overall, though, I have to say I really am proud of this assessment. Not only that, but my kids did quite well on it — I think I had a B+ average! That being said, I’d love ideas on places to improve it.”