Why do I keep seeing all these pictures of students working on whiteboards?
ProofBlocks is all about removing the fear and the failure from the process of learning proof. What better way to do this than to make the first several days erasable? And what kid can resist a giant whiteboard? (Reel ‘em in…)

A word to the wise though: find non-smelly dry erase markers for them to use or the fumes will drive you out of your room! Definitely have fans ready and windows open if possible.

Aren’t whiteboards expensive?
Sure. But these aren’t really whiteboards. They’re called “tileboard” which you can get from places like Home Depot for about $50 per class set. It comes in 4’ x 8’ sheets, but the guys there are happy to cut it down to 2’ x 4’ boards for you. (We once had them cut it in thirds instead… please learn from our mistake. They’re horribly heavy to carry, as well as bulky and awkward to move or use in our cramped classrooms.) As it is, we recommend finding someone big and burly (or too young to know better) to carry them from your car to your classroom.

If you’re thinking that you’ll never use these outside of ProofBlocks, think again. We LOVE them! They’re especially great for all that work on simplifying rational expressions that we do at the end of the year in the Algebra I and II classes.

How do you group the students?
For most of the unit, we have students work in pairs, one whiteboard per pair. (Some classes are too large to provide this much space for pairs of students. In these instances, we triple students up at the whiteboards.) Because the ProofBlock format is so visual, with theorems and connections drawn all over the place, it’s pretty easy for students to see what their partner is thinking and collaboration is relatively natural. One way to encourage discussion, and control doodling simultaneously, is to give the two kids just one marker and have them take turns. (Sometimes it’s the kindergarten skills that are the hardest…)

While we don’t feel it matters much how students are grouped initially with regard to ability (and frequently students who understand the early proofs are more than willing to go help out other pairs of classmates), after a few days, students who clearly get the idea and are excelling should be allowed to work together on longer proofs with more complex figures.

How do you monitor student understanding?
It’s all right there on the boards, practically larger than life. It depends on the class, but for the first couple problems of each day, we have been known to keep the class mostly together by forcing pairs to check their answers with us (or a student who already got it right). We require them to draw the picture on their board and put the marks right on that before ever starting the proof. Frequently, it’s there that you see the mistakes, more than in the proof itself even.

Once they get the hang of it, most students can tell whether or not they did the proof correctly just by checking inputs and outputs. As these students become self-sufficient rapidly, we have found that very soon we are free to turn our focus to the handful of students who are lost in the geometry of the problems.

In addition to just listening to the partners debate their proofs, class discussions themselves are also helped by the ProofBlock and whiteboard combination. Sharing work with the group is easy with the big boards, since when students prop them up, they can usually be read across the room. (While we don’t usually share solutions in this way, there are times when it is extremely valuable. For instance, as the students are transitioning to two-column proof, it’s interesting to have them put up their versions of the same proof so that the class can talk about the ordering of the steps and see just which ones can be rearranged and which cannot.)