cheesemonkey wonders

cheesemonkey wonders

Monday, November 12, 2018

Proof Portfolios: Revenge of the Immersive Project

Some years ago, in a town about 11 miles south of here, I taught both math and English (I'm credentialed in both — shhh... don't tell anybody). Our English department was the single most functional academic department I have ever been a part of. When you came right down to it, what we did wasn't rocket science. We had a method, we used the method, and we assessed together by grade level. The 8th grade team consisted of Alec MacKenzie, Kelly Starnes, Linda Grady, and me. We are all still in the classroom, which strikes me as a minor miracle.

The writing method we used was a combination of the Jane Shaffer method and Six Traits. Every teacher in the district had been trained on the method, and collaborative rubrics and projects had been developed over the years. The method was flexible, but we all agreed on certain basic components. We used Jane Shaffer's method of color-coding, from elementary through middle school. This meant that every student in the district developed a common understanding of what a topic sentence is, what a claim is, how we use evidence to support our claims, and how we use reasoning to tie things together. I believe it is still one of the highest-performing writing districts in California.

One of our signature practices was that we gave a fall writing assessment and a spring writing assessment. In middle school it was a two-day affair, tied to the literature curriculum. Time was allocated for pre-writing and writing.

And then we teachers were given an on-campus release day so we could read and score holistically — together. We double-scored each sample, using a rubric and highlighters.

It drove us crazy, but it also enabled us to see patterns. And because we could see patterns, we could adapt instruction to address the gaps or needs we identified.

Shouldn't this be the norm for instruction?

I have long wanted to use this approach with my teaching of proof in high school, but this was the first year I got my act together to run my own personal pilot program. I don't have a colleague with whom to work on this, so I went it alone. I created a four-day project that and gave them one day's worth of stuff to work on each day.
Here is the zip file with all four days' worth of assignments:
The secret of doing an assignment like this is radical: you have to relinquish control. You cannot be the only one giving students feedback. In fact, there is so much practice here, it is completely impossible. That is good. One thing I have learned as a writer and as a teacher of writing is that you learn how to write by writing a lot. The same is true with proof and proving. Students need space to immerse themselves and not worry about whether every mark they make is "right" or "wrong."

So each day had its "stuff." Four small proofs a day, plus reflection and peer review. Then more the next day.

The complaints and lamentations were filled with drama. "OH MY GOD, DR. S — THAT ASSIGNMENT WAS HARD." But they could tell that they had accomplished something.

My assessment strategy was to be rigorous about completion but merciful with points. It was only worth a quiz grade (100 points), and my default score for students who completed every section was a 95. There are rewards for following instructions. Missing sections or components left blank cost more points.

But none of that matters. My goal was to get students doing a LOT of proof -- writing shitty first drafts, comparing notes with each other, and using a rubric to assess each other's work. Dogen Zenji said, "When you walk in the mist, you get wet."

And it seems to have made a difference.

I am excited to see what happens on the next major test that includes a proof. Photos of student work to follow.

As always, let me know what you think and what happens if you use this!

Tuesday, November 6, 2018

Proof Portfolios

Over the last five years of teaching proofs in Geometry, I have learned two things: (1) the most effective student understanding comes from writing about their proof process, not from the proving itself, and (2) the most effective feedback process for students is a peer-to-peer reciprocal feedback process.

So this year, when I had to be out of school for a few days, I designed a Proof Portfolio project for them to do in my absence.

Each day had four small, reasonable proofs students had to do — and they could collaborate on these. But then... they had to write a number of short-answer reflections to analysis questions based on their own proofs in the day's set.

In addition, they had to find a peer to trade with and to give a rubric-based peer review and reflection.

In my class, they did this for several consecutive days. I made it worth a quiz/project grade.

When I returned, there was a great deal of wailing and moaning and gnashing of teeth about How Hard This Project Was and How Hard They All Worked.

It was clear that this project was a rite of passage for my classes.

But as I'm reading their work, I am blown away by how much they seem to have learned!

Their mastery of proof is not perfect. But it is authentic and it is growing. And to me, that is the most important point at this stage.


I made up four days' worth of activities. Each day is two double-sided pages (proofs & reflections).

Here is a link to the G-drive folder with the four PDFs:

More photos: