Trying to find math inside everything else

Set Building Game

So I came up with this semi-game last year, based on Frank Noschese’s Subversive Lab Grouping activity. My students had already done that activity at the beginning of the year, so they were familiar with the cards and the idea that the groups were not always what they appeared.

This time, I gave each student a badge that had two words on it: one word on the front, and one word on the back. I asked the students to create groups of 3-4 students using either of their two words. After they formed a group, they had to come up with a description of their group that applied to ALL of their members but ONLY to their members.

This was tricky because of the set of words that I chose, which I had displayed at the front of the room.

Almost any group of 4 you could create would have some errant fifth member that would fit. And I was VERY adamant that they could not have more than 4 people in a group, no matter how much they asked. So the students needed to use set operations to include or exclude other words. For example, if the students were {Arizona, Brooklyn, Georgia, Virginia} they might say “Our group is the set of x such that x is a girl’s name AND x is a location AND x is NOT Asian.”

Often students would give sentences that weren’t quite precise enough, so I (and later other students in the class) would push back. “Wait! China is a girl’s name and a location.” “Okay, so we’ll add ‘AND x is not Asian.” This caused them to think deeply about what the actual definitions of their group were, and to be careful with being precise. If they weren’t precise enough, they would let other words into their group.

After we got the gist, the groups would then either come up with a description and see if the other students could guess their members OR list their members and see if the other students could figure our their description.

Each round, I had the groups write down on an accompanying sheet their group in Roster Notation, Set Builder Notation, and draw a Venn Diagram where they shaded in where their group lies. So through this I introduce the different notation we use, intersections, and complements. (That left only unions and interval notation for the next day.) I also included pictures of 4-way and 5-way Venn diagrams, in case they needed it.

Stuff

Set Cards (pdf – formatted for name-tag size)

Set Game Worksheet (pdf)

Set Game Worksheet (pages)

Rubrics for Standards

So my grading experiment has been going on for a month now, and so far I think it’s going well. But I was pretty stressed about getting it up and running, because a lot of the work was front-loaded. The thing I was particularly working to get done was my mega-rubric. I wanted to make a rubric that showed what exactly students needed to prove they understand to move up a level in a particular learning goal.

So here’s what I made (I call it the SPELS Book to go along with the students’ SPELS sheet):

I started by making the proficient categories, and for the first 8 (The Habits of Mind/Standards of Practice) it was pretty easy to scale them down to Novice, and then to add an additional high-level habit to become masters.

I was stuck, though, on the more Skill-Based Standards. I had all the things I wanted the students to show in each category, but how do I denote if they “sometimes” show me they can graph a linear equation? If I was doing quizzes all the time, like in the past, I could say something like “70% correct shows Apprentice levels.” But I wasn’t, and it seemed like a nightmare to keep track of across varying assignments.

So instead, my co-teacher had the idea that, if each topic had 4 sub-skills that I wanted them to know, we could rank them from easiest to hardest and just have that be the levels. So my system inadvertently became a binary SBG system, but still with the SBG and Level Up shell. Now if a student shows they understand a sub-skill, they level up. If they don’t, I write a comment on their assignment giving advice on what they should do in the future. What remains to be seen is how much they take me up on that advice. We’ll see.

Also, I’d LOVE any feedback you have on the rubric, and how I can improve it. Thanks!