Your Trees are Blocking My View of the Forest

Dead Tree


I feel like one of the dangers of teaching is over-inflating the importance of small groups of students with respect to behavior, mastery of material, or what have you. I can’t count the number of times I’ve heard a colleague lament that “they just don’t know any algebra” and upon further questioning the teacher admits that “they” consists of maybe 2 or 3 individuals. I fall into the same tendency–fixating on the (small amount of) negative and ignoring or glossing over the (majority of) positive.

Now, I’m not saying that we shouldn’t be aware of and focus in on those few students who are struggling–of course we need to work on improving things for these students. I’m just saying that we need to do a better job of recognizing and appreciating all of the good things our students are doing and that we are doing for our students–News Flash! It didn’t just come from nowhere; we did something good.

This is of course a long-winded way of saying that I am not doing a good job at all of the things I’m chastising you for above. I fell down the rabbit hole this afternoon. Luckily, I recognized it really quickly and I’m picking myself back up (well, I’m trying!).

My school moved to a new report card system for end of the trimester grades this year. We modified our rubrics to make them uniform across disciplines and added a space to include strengths and areas for improvement (selected primarily from a drop-down menu). There’s also room for an optional comment from the teacher and a space for students to submit their own self-reflection.

I was on the committee that worked to change the report cards and I’m really proud of how they turned out. There are some details that I don’t love, but overall it is a positive change. One thing I didn’t have strong feelings about was the student self-reflection. Some teachers were adamant that this be included on the report cards. I was fine having it in, but I didn’t particularly care if it wasn’t there.

I have to say, having gone through this system twice now (okay, okay; I’m not *actually* 100% done with my report cards from this trimester yet), I have changed my mind completely. I LOVE the student self-reflections. They are already there, up at the top of the page and I can read them (misspellings and all) before I fill out their report cards. So when a student says that they need to work on showing their work, I can say to myself–yeah, that’s true–and then include that in their “areas for improvement” knowing full well that we already agree on this. It’s also really great seeing how they write about their progress over the term and what they want to work on in the future. It’s super heart-warming.

At least, until you get to that one kid who just totally yanks your chain.

The kid who blames everything on the fact that they don’t like working in groups and the tests didn’t match what they learned in class and the whole way the class was formatted just didn’t fit with their learning style. Of course, nothing is the fault of this student–it’s all external issues.

Basically, it’s all my fault that they didn’t do well in the class.

And of course, once I read that, all of the other good things that students said, the thoughtful, reflective, growth-mindset, honest, insightful things, all that just flew out the window. All I could think about was this one kid’s annoying NON-reflection.

***Deep Breaths***

Okay. Time to step back and look at the big picture. This is one student.

One kid.

At this point I have written up 30 or so report cards. And out of 30, there was 1 student who didn’t take responsibility for their own learning. One in thirty. So, like 3% of all my kids. And that’s just so far. Odds are good that the next group of kids will make that percentage even lower.

So, while it’s no fun to have someone shift the blame onto your head, I’m going to spend the rest of my evening–and the time tomorrow finishing up my grading for the week–focusing on the 29 out of 30 students who took ownership of their learning and who are actively striving to improve as students. That’s who I’m going to think about.

Once my teeth stop this reflexive grinding motion.

Interdisciplinary Course Ideas

This is more of an invitation to brainstorm with me, rather than a blog post:

Imagine you had the opportunity to team teach with a teacher from a different department. What course would you create?

…if you were teaching with a Humanities teacher?

…an art teacher?

…a science teacher?

…a language teacher (you choose the language)?

Hexagons, part III: Talking [Points] ’bout Hexagons

Apologies for leaving you hanging after my last post. The weekend. The football. These vital, important events sometimes push aside things like writing blog posts about hexagons. But I’m here now!

Let us recommence playing in our hexagon sandbox.

With the success of the Bongard Problems during the previous class, I felt empowered to try yet another new activity: Talking Points.

First we did an introduction to talking points:

And then we did a set of talking points specifically around our hexagon definitions:

During both I realized that it is pretty challenging to manage a group of students and make sure they are following the procedure correctly. My students are really good at dialogue, not so good at taking turns. My hat is off to @cheesemonkeysf on this one!

Once the hexagon talking points activity was finished we segued into some work with conditional statements. Nothing terribly innovative or exciting. Students did a quick warm-up deciding whether statements were true or false, then we discussed the similarities in all of the statements (they were all “If…Then”, they were all either true or false, they were factual). I gave a little lecture and defined some terms. Students did a worksheet to practice finding counterexamples and writing converses.

And then we were out of time. More of the same for homework.

Reflecting, one week in, on the idea of using the hexagons to introduce our geometric proofs unit I am uncertain whether or not it was a good idea. I think it remains to be seen how I tie the hexagons back in further down the road. If I stopped here and we never used them again, this probably wouldn’t be a plan I would use in future iterations of this class. But the unit has only just begun and so hopefully I will find ways to circle back around to hexagon proofs later.

I’ll be sure to report back about when and how I do that.

Hexagons, part II: Return of The Pakman

When we left our intrepid adventurers they were faced with the perplexing question:


The class was divided. Consensus seemed impossible. The original group was adamantly opposed to the idea; the rest of the class seemed open. Some students–*gasp*–seemed not to care one way or the other!

Ambiguity in a math classroom. It must have been a cold day in a very hot place…

However, that place was not San Francisco:

weather 1.6

Clearly *we* did not have school off because it was “too cold.”


Before re-addressing this delightful question, I began class by using Bongard Problems. This turned out to be a genius plan. The big idea of Bongard Problems is that there is a common defining characteristic that differentiates the left hand side from the right hand side images:


Thinking about what makes something a defining characteristic, rather than being a property of the object, helped to create a much more streamlined definition of each of our hexagons. We returned to the question from yesterday’s class.

We looked at our exemplar Pakman card again. We went back and forth, forth and back. Until finally we agreed that a Pakman was (drumroll please)…

A hexagon formed by reflecting a parallelogram across one of its sides.

Much rejoicing was had by all–though come to think of it, maybe that rejoicing was due to the fact that I said we didn’t have to go through this process for all of the other hexagons…

I passed out the remaining hexagons, printed on regular paper this time as I have just about used up my school’s entire supply of cardstock by now. Students determined whether any of the new hexagons belonged to an existing group and created new names and definitions for those that needed one.

Our final collection of definitions looked something like this:

The Hexagons

At this point we had officially run out of time. However by this point we had created a very rich and interesting sandbox to play in. Stay tuned for tomorrow’s final (at least for now) installment in the saga. In which the Hexagon Talking Points will make an appearance.

Hexagons: The First Day

The first day back from break can be a little rough.

Trying something new you’ve never done before can be a little rough.

Doing both at the same time?

Can be a magical roller-coaster of the good, the bad, and the who-even-knows-how-that-went.

On Monday I introduced the hexagons. Not having planned ahead enough to create a wooden set on the school’s laser cutter, I resorted to good old-fashioned cardstock.


I used the cards to separate kids into random groups and then each group named and defined their hexagon. This is the part that didn’t go so awesomely. Funny thing is, kids don’t know what a “definition” is. So, what they did was:

  1. Ask me if I wanted a definition of hexagon. [Thank you, but no.]
  2. Write a list of every single characteristic of their hexagon they could think of.

Not exactly what I had in mind…

But I went with it. Students wrote up their characteristics on chart paper and posted their “definitions” around the room. Then I had everyone do a Post-It activity where they drew a hexagon based on the written description. Another flaw: everyone said they remembered what the hexagons looked like from the grouping shuffle at the beginning of class, so there wasn’t much gained from this part of the class. Oh well.

Next step was to create Venn diagrams of each group’s hexagon and the hexagon to their left. The goal was to discover if it was possible to create a hexagon that fit into the intersection of the two circles. I don’t think any group was able to do this based on their definitions. We repeated with the group to the right. Same story.

That’s when things started to pick up.

I grabbed a marker and set up shop at the hexagon in the front of the room, the Pakman (aside: this group took freaking forever to come up with a name for their hexagon). I asked if there was any way to simplify their list of categories into one succinct description that contained the essential characteristics of a Pakman without additional or redundant information.


After some debate and discussion we settled on the idea that a Pakman’s essential element was that it was a hexagon composed of two congruent parallelograms.

I ended the class by asking:



And, just like the class itself, this will be continued tomorrow…

I Notice Awesomeness

…because there really is no way to have too many posts about the “I Notice/I Wonder” process.

My Math 3A (geometry) students had never done an I Notice/I Wonder before. That is the beauty of this process–it’s practically bullet-proof.

Here’s what they noticed and wondered about the side-length ratios of a 30-60-90 triangle that we played around with in GSP:







In which I write a blog post comprised primarily of tweets from other people. I think normally we call this “being lazy.”


At Asilomar this year I gave a talk on math electives, which was kind of fun:


Also I Ignited…[Alternative Title: Help–I’m On Fire!]

Embedded image permalink

But unfortunately my Ignite talk didn’t include any unicorns.

Instead, I talked about raising the value of mistake-making in the math classroom:

Some people were kind enough to tell me I did okay (even without the unicorns).

Holy crap, there were a lot of people…

Embedded image permalink

All in all, it was a fun time. See you next year!