There's been lots of online discussion and articles lately about holding students accountable, while still showing grace and compassion, especially during the pandemic and as we move out of it. My school has chosen to eliminate semester exams entirely, even after we are back in school full time next year. We're also moving to block scheduling.
I've been thinking about alternatives to testing, because what I really want my students to learn is much more than some math facts and procedures they can quickly produce on a timed test. So I'm wondering if portfolios might be the way to go, for at least part of the grade. But what do I want my kids to learn, and what goes into a portfolio?
First, I do want them to know some math when they leave my class. It would be horribly unfair of me to send them on to the next level without making sure they can perform some of those procedures. (And I'm also thinking about how I can put some of those into a historical or cultural context; students will be far more likely to buy into procedural stuff if they understand its context. I'm not talking about "making math useful" - I find the useful math becomes really boring really quickly, especially since we can always whip out our pocket computing devices and find answers.) The other things I want my students to be comfortable and confident with are perseverance in the face of uncertainty and imagination in using their backgrounds and skills. These last two would be really hard to show or evaluate on a timed test.
Here's what I would want to see in a portfolio problem:
- A significant problem. Not just an exercise of a math procedure, but something the student had struggled with, revised, and thought about.
- Evidence of their problem solving: persistence, creativity, use of prior knowledge, verifying their results, finding further questions.
- Evidence of metacognition: What were their main struggles? What are the key learnings they take from this problem?
- Evidence that they understand some of the important math of the class. For this, I'm thinking that each portfolio problem must address a different topic, and the work must demonstrate an understanding of that topic.