Test Questions

 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.

I would want to have each student solve and write about maybe three portfolio problems per quarter?  I want the students to have opportunities to get feedback and make revisions.  But how do I describe the bullet points above on a rubric that the students and I (and their parents) understand?  What's the criteria for success?  And is it even possible for me to provide quality feedback on so many portfolios in a timely manner?

And more questions ... By using portfolios, am I actually grading a student's writing abilities?  What about students who have trouble keeping their work organized?  Might there be an opportunity for an "interview" version where I have the students talk to me about their work?  I'll need to give some sort of homework or some way for the students to practice the skills and procedures; should I assign points to that as well?  And should there still be small quizzes to check progress and give the students feedback on that aspect of the work?

I'm glad I have extra time to think about this, rather than turning it in at the end of the period.