About Michael Fenton

Hi there. I taught junior high and high school math for 11 years. I’m now a Lead Instructional Designer at Desmos where I explore the intersection of mathematics, technology, and curiosity.

AP Calculus AB • Quarter 1 Benchmark • Michael Fenton

Introduction

Up next: first quarter benchmark assessment from Michael Fenton’s AP Calculus AB class. 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 Michael?

Submission Type

“Share an assessment you don’t hate…”

“Share an assessment you do hate…”

Okay, I’m really in between on this one. The reason I started the Better Assessments project is that I’m disappointed in the quality of nearly all of my assessments. I’ve already benefitted so much from those who’ve shared their assessments. (Thanks Stephanie, Jim, Jennifer, Luke, and Sam!) This one is certainly better than a lot of my assessments, but I know it could be so much better.

Assessment

The assessment is here.

The solutions I provided to students after the assessment are here.

Author’s Commentary

I gave this benchmark assessment to my AP Calculus AB class nine weeks into the 2012-2013 school year. We use Paul Foerster’s Calculus book (here’s a look at my course outline). The benchmark addresses Chapters 1-3

  1. Course Overview
  2. Properties of Limits
  3. Derivatives, Antiderivatives, and Indefinite Integrals

When I first started teaching from Foerster’s books (I also use his Precalculus text) I was quickly drawn to his fourfold approach: Verbal, Numerical, Graphical, and Algebraic. (As a student, I didn’t have a sense of this multiple representations framework.) I tried to include questions that would require students to demonstrate understanding in each of those four categories.

In reading through the questions again, I see myself leading students and offering hints where they shouldn’t really need them. I may have been trying to guard against poor results based on the weakness of that class, or the gaps I perceived in my teaching.

The assessment was given in one 50-minute class period. It was quite a few months ago, but if my memory serves me well, then my stronger students needed only about half the period, while several of my struggling students took the entire allotted time.

Thanks in advance for your comments!

Assessment on Rational Functions • Sam Shah

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.”

Precalculus Quiz on Law of Sines, Law of Cosines • Luke Hodge

Introduction

This week’s assessment (a Precalculus quiz on the Law of Sines and the Law of Cosines) is from Luke Hodge. 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 Luke?

Submission Type

“Share an assessment you don’t hate…”

Assessment

Behold!

Author’s Commentary

“I was reasonably happy with the quiz because a couple of the problems (#4 & #6) allowed for different levels of insight and I got a wide range of answers. Questions #1 – #3 were things we had looked at a bunch. We had done optimizing problems like #4, but this was a new set up. Question #5 was not new, but I had not put much emphasis on “hill” problems. Question #6 and the bonus were completely new.”

On Deck

Sam Shah’s assessment on rational functions

Algebra 1 Mid-unit Test • Jennifer Silverman

Introduction

Our next “in-the-spotlight” assessment comes from Jennifer Silverman’s Algebra 1 class. It’s a mid-unit test on linear functions. 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 Jennifer?

Submission Type

“Share an assessment you don’t hate…”

Assessment

https://www.dropbox.com/s/rxj0fzx5k07zqh3/4.3.9%20Midunit%20Test.pdf

Author’s Commentary

“I liked this assessment for its multiple representations and open-ended questions. I feel it gave me a good picture of what my students understood. The red barn was painted by my dad, who passed in 2011.”

On Deck

TBA later this week.

Call for Submissions

With only one assessment in the queue, I would love to receive your submissions this week. For details on submitting assessments, check out this post. I’ll have an easier submission process in place later this summer, but this should do for now. If you’re frustrated with the current submission process, feel free to send your submissions via email (mjfenton at gmail dot com).

Precalculus Test • Jim Doherty

Introduction

The second assessment in the spotlight is a Precalculus Honors test on conic sections and parametric equations from Jim Doherty (a.k.a. mrdardy). Questions to consider:

  • What do you like (and why)?
  • What would you do differently (and why)?
  • What questions do you have for Jim?

Submission Type

“Share an assessment you don’t hate…”

Assessment

https://www.dropbox.com/sh/geof1hp8yab8gdt/efJg4O0OX1/PCH%20Test%2011.pdf

Author’s Commentary

“Here is a link to my most recent Precalc Honors test. We just finished our long slog through trig and have emerged on the other end with a conics/parametric unit. I stole some ideas from Sam Shah in class and we kept referring back to polars but I chickened out about including them on this test. I’d love to hear any opinions/questions/advice here!”

(More commentary may follow soon is included below.)

Additional Author’s Commentary

“I have long used this structure for tests in this course where there are some quick fact/skill questions at the beginning worth 5 points each while there are longer, multi-step questions worth 10 points each. Based on some reading I’ve done lately (especially from the mathymcmasterson blog) I am thinking of inverting this model so that the majority of points earned are at the skill/recall level while the multi-step problems take a smaller portion of the points on the test. I’m interested in feedback on this balance.

Our text has the conics unit after a long trig unit. My students know that all of my tests are cumulative in nature with some general ground rules in place about what might appear. The central focus will be on the most recent material discussed with one or two questions directly representing material from the most recent test. Often, these will be questions that caused some problems and were the focus of our post-test briefing when I return papers. For some reason this year we had repeated questions about circles and it became a bit of a running gag during the year. I was happy about tying together questions 2, 3, and 8 but on reflecting about this, I’d make them closer to each other in the formatting. I try to write questions like #7 as often as possible. I think it gives me some insight into the kids ability to process some of this algorithmic information in a non-standard way. I started including the editorial note about multiple solutions in reaction to NUMEROUS questions along those lines. I kind of wish I had not done that. For questions 10 I fully expected students to simply solve for t in terms of y and then come up with a non-function parabola. A number of them solve for t in terms of x then had a function square root curve as their answer. Both approaches earned credit with clear support. I typically make the last problem a bit of a giveaway when I am concerned with time. We had a 40 minute class that day and I was worried about time on this one, but the kids did just fine as far as time was concerned. Looking back, I wish it was less driven by straightforward algebraic manipulation of the con is material, but I know I had seen some struggles with the types of word problems where the kids are given clues about a conic and they are to find its equation.

By this point of the year, my class was starting to really stretch out along the grade continuum with scores on this assessment ranging from 50 to 98 in a 10 student class. The mean was 83 with a median of 87.”

On Deck

A sweet-looking Precalculus quiz on the Law of Sines and the Law of Cosines from Luke Hodge.

Algebra 2 Quiz • Stephanie Reilly

Introduction

Our first assessment submission comes from Stephanie Reilly (@reilly1041, mrsreillyblog.wordpress.com) in the form of an Algebra 2 quiz on exponents and adding polynomials. Links for the assessment and commentary are below. Questions to consider:

  • What do you like?
  • How would you make it better?
  • What questions do you have for Stephanie?

Submission Type

“Share an assessment you don’t hate…”

Assessment

https://docs.google.com/file/d/0BytS9twTZ9tlVElfUGZ2MHp6aW8/edit

Author’s Commentary

https://docs.google.com/document/d/1o71FlRPQ5LdyD3B0k-LZjgXdEWiT0HUnzFC1slftaPc/edit

Bonus Request

Since this is the first assessment submission post, please let me know in the comments, via Twitter (@mjfenton), or via email (mjfenton at gmail dot com) if you have any suggestions for how better to facilitate this assessment conversation.

Coming Soon

Next in line: A Precalculus Honors test from Jim Doherty.

Another Way To Play

Create an assessment you don’t hate…

According to this, that’s Step 1 in the Better Assessments rulebook. But I wonder if we’re cutting out half of the assessment conversation by making the first step the submission of something awesome. I don’t know if I have anything I’d be comfortable sharing right now if that’s the requirement.

So how about this as a second way to play along…

Share an assessment you do hate.

Have you been giving an absolutely terrible assessment in Algebra 1 (or some other class) for years? Is it time to make something better, but you’re not quite sure how? Throw your assessment in the ring and we’ll do our best to help you make it better.

And while we’re at it…

Why not have a third point of entry, a sort of combination of the first two. If you’re already revamped a sub-par assessment and ended up with something notably better, share them both, along with some commentary on the transformation. Think of it as the math assessment equivalent of those annoying P90X before and after infomercials.

However you want to play…

Whether you have something great to share, something terrible to work on, or a before and after comparison, if you’re interested in contributing, go for it!