I am teaching our “mathematics for liberal arts” course for the first time. This is a topics course, so I can teach whatever I like; I have chosen to do a Pólya-type problem solving course.

In class, the procedure will likely go like this: students get new problems to work on on Mondays and Fridays. Students will work on old problems on Wednesdays.

The grading of the course has five components: problem reports, correct solutions to problems, quizzes, a final exam, and a project. Without going into too much detail, here is how the final grades will be determined:

• Students will get at least a C if they provide a modest amount of evidence that they have achieved the learning goals (see below) and get at least a CD on the final exam (“CD” is like a C- or D+).
• Students will get at least a B if they provide a good amount of evidence that they have achieved the learning goals (see below), do well on the quizzes, do a project, and get at least a BC on the final exam (“BC” is like a B- or C+).
• Students will get at an A if they provide a whole lot of evidence that they have achieved the learning goals (see below), do well on the quizzes, do a really good project, get at least a AB on the final exam (“AB” is like a A- or B+), and get correct solutions to many of the problems.

In short, C students are able to demonstrate good habits of mind, B students are also able to understand and replicate solutions, and A students are also able to generate solutions to problems.

The learning goals are this:

• You will improve your written and verbal communication skills.
• You will be in the habit of providing and demanding evidence for any assertion.
• You will be in the habit of employing supposition when you encounter new ideas (“What if the idea were tweaked to be slightly different. What would happen then?).
• You will be in the habit of employing different perspectives by determining how other people think

• You will be in the habit of making connections between new ideas and old.
• You will be in the habit of planning before acting.
• You will be in the habit of using heuristics (“rules of thumb”) to help you solve problems.

The way students demonstrate evidence that they are achieving the goals is this: each student specifically states which of the learning goals were “used” in the problem report. For example, the first problem in class is a simple variation of the game nim; I would expect many students might claim that had to employ different Perspectives in solving the game, since they will have to think about how the opponent will respond to each move. Additionally, the student might have a partial solution strategy; if the student provides a “proof” of why the strategy is guaranteed to work, the student can also claim that they displayed evidence of the Evidence goal.

So the students are responsible for realizing what they did (although I have a grader who is going to verify that the students did what they said they did). I like this because it encourages students to use these good habits (“I need a Connections, so I had better try to think about whether this problem is related to something I know”), it forces students to reflect on what they did, and this is how most of the “real world” works (When I apply for tenure, I am the one who needs to provide the evidence that I deserve tenure. Similarly if I were to ask for a raise.).

I help my students by telling them where they can often find opportunities to provide evidence of the learning goals. For instance, students can cite each problem report as Communication, although it must be well-written to get credit. I tell students that the Game Theory questions and the Knights/Knaves/Liars/Truth-tellers problems are good for Perspectives. I also tell students to pose new, but related, problems in each problem report (from The Art of Problem Posing); this is good for satisfying the Supposition goal.

Now tell me this: what could possibly go wrong?

### 11 Responses to “Yet another grading scheme”

1. Andy "SuperFly" Rundquist Says:

First reaction: Maybe too much pressure on the final exam (what will that look like, by the way?)
Second reaction: I really like the language of the learning outcomes, especially the use of the word “habit.” I think it’ll be cool to have the students think about which habits they’re using, though I’m nervous for the frankenstein solutions they’ll try to make by using all the habits.

• bretbenesh Says:

Hi Andy,

The good news (although they don’t know it yet): I grade the final exam pretty leniently. I mainly make it on big ideas, and I try to make it so that students can succeed reasonably well. I have had a similar policy for a while, and there have not been any issues relating to a student’s grade plummeting because the student did poorly on the final. But maybe the students were stressed out.

Also, it is only a take-home exam.

Yeah, I think that “frankenstein solutions” will be a concern. Although I hope to really train them about what is and what is not acceptable to submit as evidence. But we will see. Bret

On Mon, Aug 26, 2013 at 3:22 PM, Solvable by Radicals

2. Joss Ives Says:

Hi Bret. Can you tell me a bit more about what exactly a Polya-type problem solving course is?

• bretbenesh Says:

Hi Joss,

Sure. George Polya was a Stanford mathematician who wrote a famous book called _How to Solve It_. The basics are on this short Wikipedia page (which I assigned my students to read for tomorrow): http://en.wikipedia.org/wiki/How_to_Solve_It

Polya was also big on “heuristics,” which are rules of thumb on how to solve problems. Some of these seem pretty basic, like “draw a picture” or “try a simpler problem first.” But not everyone knows these heuristics, which is part of why I am teaching some of them to my class. Bret

On Mon, Aug 26, 2013 at 5:31 PM, Solvable by Radicals

• Joss Ives Says:

So, in practice what does this type of course look like? I’m entirely unfamiliar what a math for liberal arts course might look like anyway.

• bretbenesh Says:

“Math for liberal arts” is pretty well undefined. At my college, it is a topics course. I just happened to choose “problem solving.”

The first two weeks of the course are to introduce the “heuristics,” or rules of thumb for problem solving, to the students. So I am having them work briefly on problems, and then showing solutions. In showing the solutions, I focus on how to get started by using the heuristics (“draw a picture,” or “solve a simpler problem first”).

For the remainder of the course, most of the class time will be spend on working on problems in small groups in class and/or seeing student presentations of potential solutions. I plan on giving them a new problem every Monday and Friday, and Wednesdays will be spend working on selected old problems.

I also hope to finally get around to some version of Stump the Chump, where students can find problems and ask me to solve them cold in class.

In short, much of my summer was spent collecting interesting problems. Bret

On Thu, Aug 29, 2013 at 2:52 AM, Solvable by Radicals

• Joss Ives Says:

If a person is going to take a terminal math course, that sounds like a great one.

Have you tried to do Stump the Chump before? I have never formally done it, but my advanced lab course feels like a 4-month-long session of stump the chump.

• bretbenesh Says:

It is definitely a terminal math course; we will see if it is great (although the first two days went well).

I have never tried Stump the Chump before, although I had previously planned to. I definitely won’t try it for an entire semester, as you did in your lab.

On Thu, Aug 29, 2013 at 11:57 AM, Solvable by Radicals

3. suevanhattum Says:

I don’t know what might go wrong, but I want to join your class! :^)

• bretbenesh Says:

Hi Sue!

I have seats available in my 9:30 and my 10:40 classes—come join us, Sue!

(Sorry, but my 11:50 class is full). Bret

On Mon, Aug 26, 2013 at 7:43 PM, Solvable by Radicals

4. Update on Problem Reports | Solvable by Radicals Says:

[…] Just another WordPress.com weblog « Yet another grading scheme […]