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.
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
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
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
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
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