October 17, 2012

Geometry Proofs: A New Approach

This year I have re-organized the Geometry curriculum.  I'll tell you more about how that's going later, but for now just know that we have studied patterns, lines and angles.  When we did angles formed by parallel lines and a transversal I introduced the word 'converse' but otherwise haven't done any logic.  Students have been asked to justify all of their answers, but Friday will be our first introduction to more formal proof.

In my class the goal of proof is to show a logical sequence and explain reasoning.  I hated proof when I was in Geometry in high school since they were all fill in the blank proofs- I could have proven the statement myself but could never follow the disjointed outline that the book offered.  However, I appreciate the scaffold that offers, which is where Proof Blocks come in.  People have mentioned them to me on a few occasions and I made a weak attempt at them last year, but this year I'm hoping to use this format faithfully.  The idea is that students have a set of cards which represent all the possible reasons they can use in a proof, then they arrange the cards in a logical order and fill in the information specific to the problem they are working on.  I didn't love that the provided cards tell students exactly how to use each theorem since I would like them to remember the definition of perpendicular on their own, so I reformatted them slightly to have hints on the back that students can check if they forget. (First column: front, Second column: back; which I just realized won't print double sided... this version will - I think - but it's not nice to look at.)

Proof Blocks 1
(On my computer all the words fit on one line and the perpendicular symbol shows up, hopefully that will be fixed if you download the file rather than viewing on scribd?)

On Friday I will give each pair of students a laminated set of card (and recommend that they print their own for use at home) and each student will have a page of proofs to work on.  I will pull the proofs from the book, but won't include any of the extra information (my book either makes them fill in the blank or offers a 'plan for proof' that eliminates all the thinking!).  Then I will offer a brief explanation of how the cards work and set them loose.  Hopefully this will be a nice way to bring together all the ideas we've studied on lines and angles.  I'm also hoping that proofs will be fun puzzles rather than onerous tasks.

So, have you done anything like this before?  Do you have any suggestions?  Did I miss any important reasons in my cards?  Thanks in advance.

Edited 10/21 to add: I tried it and was successful!  Read about the outcome.


  1. A small idea that might help scaffold this kind of task is to ask them to pull from subsets of the larger pool of cards in the first few proofs you ask them to write. I feel like having all of those cards "in play" from the beginning might be a little overwhelming.

    But you'd probably want to include in those smaller subsets some cards that are "wrong"--ones that won't be useful in constructing the proof at hand. Otherwise it'll probably feel too fill-in-the-blank and not as fun.

    Also, it might be interesting if you or your students were to assign colors to the cards according to some kind of categorization. Maybe something like: given, definition, algebra, diagram, theorem. Or maybe by subject matter instead.

    Hope something of that is useful. Excited to hear how it goes!

    1. Thanks for these great ideas! The first couple proofs we did were about angles (and not lines), so I suggested students pull out the ones related to angles and just deal with those, which did help narrow things down. I printed them all on yellow and am planning on using a different color when I print triangle theorems. However, I wish that Given was really bright and easy to find since it's used every time. I could still print one page of just Givens and that would be enough, so maybe that will happen, eventually...