The Roots of the Equation

When I started at my current school two years ago, one of the first conversations I had with my coteacher (Sam Shah!) was about grading, and coming to a compromise on our different grading systems. Often teachers will break down grades into categories, the weights of which can vary. But during that conversation I came up with what I thought of as the supra-categories, which I now use for all of my classes.

The first is Knowing Mathematics. In a standards based grading system, this would be the standards for content knowledge. In a traditional grading system, this would include things like tests, quizzes, projects, presentations, interviews – anything that shows what the student knows about the math itself.

The second is Doing Mathematics. In SBG, these would be process standards. In a traditional system, this might be classwork & homework, or class participation. I evaluate this typically with a portfolio of student work. (More on that below.)

The third is Being Mathematicians. I was doing Knowing/Doing before this, but this third category was how to incorporate some of what Sam had been doing with his portfolios, that I loved (and served a different purpose than mine). The assignments are about reflecting how the student fits into mathematical society – both on a small scale (in the class, reflecting on groupwork) and a larger scale (learning about other mathematicians, especially those from underrepresented populations, and about other mathematics outside of the scope of the class). This is also evaluated with a portfolio.

I first wrote about my portfolios in this post, and the general idea there still applies to my Doing Mathematics portfolio, but the structure is different.

Now I do the portfolio as an ongoing Google Slide. You can see the template for the portfolio I used for Calculus last fall here. Our school has a 7-day cycle, and once a cycle we have a double-period. So for that class, in the second half of the double I’d have a quiz about that cycle’s content (counting for Knowing Mathematics), and then afterwards they would work on their portfolio, picking one piece of classwork and one piece of homework from the cycle to reflect upon and include. This let me keep on top of the grading of the portfolio better than saving it for the end of the quarter/marking period, and also made it easier to make sure the portfolio was actually a collection of their work from the whole semester. They had to do two pieces per habit of mind, although usually I would wind up with only 16 done for the semester, not 18, to have a little wiggle room (because it’s hard to get them all). To make up for that, I include two extra slides for the work they were most proud of that quarter.

The Being Mathematicians Portfolio has a wider variety of assignments. Some will be reflections on how they work with their peers:

Some will be about mathematical debates:

Some will be learning about mathematicians (usually from underrepresented groups) or mathematics from underrepresented cultures.

Sometimes news in the math world, or other modern mathematics:

Sometimes about what it even means to do mathematics:

Students will occasionally get these as homework assignments, and we’ll usually discuss them the next class. (I’d like to be more consistent about it, as I am with the Doing Math – maybe that’s a goal for this year.) I’d also gladly take suggestions for assignments in any of these categories, or if you think there are subcategories I didn’t really hit on!

Here you can find the entire year’s worth of BM Portfolios for Geometry and Calculus. (About half of the slides were made by Sam. Wonder if you can guess which are made by whom!)