Group Exams and Assessment in General

Exams are over! As a teacher, I secretly love exams – I love grading in brightly-colored pens, noticing trends in student performance, and somewhat shamefully, I enjoy a few days of just sitting. It is a really interesting balance, though, of stressing the importance of demonstrating knowledge on a culminating assessment without heightening any students’ anxieties. All last week and now this week I’ve been on the verge of sending mixed messages, applauding students for doing well but reassuring ones who didn’t knock it out of the park that their grade won’t drop down catastrophically.

The rest of the year I give short, low-pressure assessments as soon as students feel they’ve mastered a particular objective. I think that making these as small a deal as possible helps get more accurate data – students aren’t nervous about their performance, they’re just demonstrating their knowledge.

I tried to make the exam pretty non-threatening as well, even though it inherently feels high-pressure. A big part of that is the group exam. This is usually a multi-part task with multiple entry points to maximize student participation. This year for math 4 I had them build three iterations of the Koch snowflake out of craft sticks. I was going to have them build 4 but we would NOT have had time, or probably space. Then they had to find the area of each iteration based on the patterns of exponentially-increasing triangles. It turned out very nice!

snowflake1 snowflake2

My favorite part about this was that they walked in for the exam to see all the tables pushed to the walls and just knew something was up. I’ll attach the text of the group exam as well: Math 4 Group Final 2015

I should note that I do a group final as well as a standard individual final because of the way exams are scheduled at my school – I have each class for 1.5 hours before lunch, then another 1.5 hours after lunch. I didn’t think that it would benefit anyone to write a 3-hour math test. These tasks could work in a non-assessment situation, too, though.

For math 2, we’ve been doing all this great work with polyhedra so I had them continue for the group exam. As a sidenote I’ve been very inspired by this myself and have been hard at work crocheting pentagons for a dodecahedron – I hope to post that at some point. This exam was centered around the tetrahemihexahedron, which I think is amazing. I had them cut out nets and fold them with basically zero guidance – they did an amazing job intuiting how these should be folded. Then I asked them to create toothpick-and-marshmallow structures with things in common with this concave shape, such as the cuboctahedron below with the same vertex figure, 2 squares and 2 triangles:


That’s actually one I made, theirs was kinda lopsided, but they tried SO HARD. Most of the time my philosophy is that trying hard is NOT the same as doing good work, but sometimes I let lopsided polyhedra and the like slide.

Here’s the full text of the task: MATH 2 GROUP EXAM final 2015

So I’m almost done in the classroom, but I still have enough odds and ends to be posting well into the summer. I’m actually about to head back to school now to see the seniors present their projects, which is always a really nice culmination of some interesting independent student work. Plus I made cookies!