A Few Problems of My Own

Some of my favorite assessment problems from this semester in College Algebra. Each problem is labeled with the standards it mainly addresses. The main function families for our course are:

• Q - quadratics
• P - polynomials degree 3 and higher
• R - rational functions
• E - exponential
• L - logarithmic

And then there's a category of function concepts and special functions.

For each function family, there's four repeating standards:

1. Basics - vocabulary, characteristics
2. Representation - being able to move amongst table, graph and equation
3. Symbolic - traditional algebraic skills, solving and simplifying.
4. Context - solving in application. Being able to mathematize situations.

I like having a structure, as students getting used to the Standards Based Grading is one of the big hurdles in the course. That's why all the problems are labeled with standards, too.

These problems are different than the ones I use in class or for homework, with more scaffolding, and often reminiscent of things we've tried in groups. They also choose problems on which they're ready to be assessed. They can write up longer responses at home to turn in on problems that they do not do in class.

This first one's not mine. They read a Glen Waddell post on the Exeter method, so I thought it was a nice connection to put on an assessment.  The element of the cup really made clear which students understood what the height function was saying.

We did a fun activity in class on sound frequencies that you can hear at different ages (due to hearing loss/damage) in class when we were talking about decibels. Frequency is not logarithmic, of course, but I love using a topic as arcane as logarithms to make sense of something they've heard of (get it?) as much as decibels.

One of their favorite application problems in the semester was using exponentials to model weekend movie grosses, which are roughly exponential decay. But of course the sum of geometric sequences is also a transformation of an exponential. This problem unfortunately highlighted careful reading or the lack of it, which is not super-useful, so that some people tried an A*k^x model. But it did show the people who were making sense of that not working, and the people who blindly accepted the results. Desmos reliers (as opposed to Desmos-only-if-my-calculator-can't-do-it) did better on this.

This problem was another great one for function notation. The difference between evaluation and solving was crystal clear. And it was such a nice pattern for the people who correctly interpreted the problem that there was a good payoff.

The top problem here is also not mine, of course, coming from WODB.ca. Well, originally. The task of making a function to look like it is a great representation prompt. Students who made sense of marble slides were really able to strut their stuff.

 It was the second and third problems that were really interesting to me here. They were open middle-like in the variety of different methods people used to solve them. Recursive rules, which we never used in class, really, excellent table use, some regression... such a nice mix.

I liked it enough that I wrote a follow up for the last SBAR opportunity. (AKA the final.)

One thing that we never addressed directly that we got to the last time I taught this course is that the sum of a certain degree polynomial sequence gives the next degree. Much like the differences give the next lower degree. I LOVE that structure.

For the special function types they only had to demonstrate one of the four kind of standards that they did for the main function families. Both of these offered a lot of opportunities for sense making. In particular the normal distribution question highlighted whether people understood mean and standard deviation as descriptors.

If you have feedback on writing assessment questions for SBARs, I'd love to hear it. Whether it's modifying these or a whole different direction. Here's all my assessments from the semester in a Google folder, if that could be of help or interest.

PS. Thanks Ann and #MTBoS30 - I've now blogged more in May than I did all January to April.