From my first year at my school, seven years ago, whenever I taught triangle congruence I did it using an interactive Geometer’s Sketchpad file that had students manipulate virtual triangle configurations to try to make non-congruent triangles. This year I knew I needed a back-up plan in case the wifi was down and they couldn’t download the document onto their laptops. So it was back to good ol’ rulers and protractors!

Talking the idea over with my office-mate, I decided that I didn’t care whether the wifi was out or not, I was going to do the paper and protractor version anyways.

Kinesthetic learning! Using appropriate tools with precision! Decorating triangles!

The decorating was very important, btw.

I had read this blog post, which for some reason I didn’t clip to Evernote (why?!?), that talked about giving students the following scenario:

Let’s say I ask Suzy to create a triangle with sides measuring 3 inches, 4 inches and 5 inches for homework. Now, I know Suzy is really amazing with a ruler and scissors, so she is going to come back tomorrow with a really great triangle whose sides are 3, 4 and 5 inches long. Let’s say I also ask Stewart to do the same task. Stewart’s skills with ruler and scissors are equally amazing, so his triangle will also be great.

I want to know, will Suzy’s and Stewart’s triangles be exactly the same or could they be different?

The class discussed this, as well as the second scenario, which is the same except that now the triangle being made is 45 degrees, 45 degrees and 90 degrees. Then the teacher threw out another scenario (don’t remember what it was) and kept doing this until a student suggested “Let’s try it!” Then, out came the rulers, protractors and scissors and away they went.

I didn’t wait for students to suggest the cutting–I gave them time to discuss the first and second scenarios and then I had them construct the two triangles, decorate them and cut them out. In my first class I had them tape their triangles to pieces of paper all at the end of class (it was kind of a last-minute thought) but for the second class I had them do this for each triangle as they went along. I taped up papers labeled “1”, “2”, etc. around the room and wrote out the triangle’s criteria next to the paper on the whiteboard. This worked really well; students went up and taped their triangle to the paper as they finished and then they moved on to the next triangle. I was able to take down papers that everyone had finished and put up the new ones as we went along, which helped keep everyone moving forward without having stress to rush through because they hadtofinishinthreeminutesohmygahhhh!

There were multiple (!) exclamations of “this is fun” from (*unexpected!*) students as they were cutting and measuring and taping and decorating. When class was over we had multiple pages worth of triangles for many of the criteria and a full page worth of all the rest.

That afternoon/next morning I selected triangles to put on the “final sheet”–really I just took off triangles so that there was one page per set of criteria–and photocopied each page. This is where the decorations came in handy. That was my selection criteria–not accuracy, but aesthetics! [also what will show up on a photocopy best]

Day two was our day to come up with some conclusions: Was SAS enough information to determine whether two triangles would be congruent? What did SAS mean, really?

I had students * Trust, But Verify* one another’s work. Which means I passed out the photocopies of the triangle sheets and check to see whether each triangle on the page satisfied the given criteria. This means students needed to measure the side lengths and angle measures as well as figure out

I didn’t anticipate that this activity would address this misconception, but it did. Big time! Students were figuring out on their own that if the 5″ side was touching the 40 degree angle rather than the 30 degree angle this was not the same triangle as the one that was doing the reverse.

By the end of the class we had a set of criteria for determining triangle congruence.

And I could positively kiss the kid who, when we were talking about SSA, asked:

Isn’t this like that problem we did in our last unit?

Yes, little darling.

Yes, it absolutely is.

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Perhaps it was (in part) because of the extra hours of sleep, but this week–despite being a full week after a short one–felt good. I had my students fill out midterm course evaluations (anonymously) on Monday. It took me a few days to get around to reading them. I always am a bit nervous about doing this, so I waited for a time when I knew I could decompress afterwards if that was needed. Turns out it wasn’t.

While the comments were by no means universally complimentary (something I appreciate, because that’s not actually helpful!), the students were forthright and constructive in their feedback. It also seemed clear to me that some of the items I’ve been working on (e.g. providing more variety of tasks) has been noticed and well-received by my classes. So that was good. And I got some usable suggestions that I can try to incorporate moving forward. Also good.

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One of the biggest changes that I see in myself in this year’s version of our proofs unit compared to previous years is that I am doing a good job of shifting the onus of responsibility for checking students’ work from myself as “arbiter-of-accuracy” onto the students themselves. I’ve done several gallery walks where they write comments to one another on the whiteboards about what is effective and what is confusing about their group’s proof. These followed a more structured proof “writing workshop” where they commented (on google docs this year!) on one another’s work and read the feedback from their peers. I’ve done the writing workshop in previous years, but then drifted away from building upon that. This feels so much better!

We did some proof puzzles–I wrote up statements and reasons for some problems and had students arrange them in order–and I got to model what I look for when checking a proof.

First, I check to see: do you have the givens?

Then, I check: did you end with the thing you were trying to prove?

Finally, I check the middle: is each statement supported by the ones that come before it?

This has taken place over the past three-ish weeks, but this past week it really felt like things came together. I had students work on the lovely TIMMS problem below and had different students put up their solution method on the board.

I carefully selected students who used different methods (add a parallel line, add a perpendicular line, extend the lines) so that students could see a variety of ways to solve the problem. [I overheard one student say “I think that’s how we were supposed to do it.” which made me shake my head…your way worked too!!!] Then I gave them additional numbers to work, using a method that was different than their own, until they noticed a pattern and a conjecture emerged.

I wrote the conjecture on the board and asked the class, “What do we do with conjectures?”

Class: “Try to prove them!”

And so they did. Afterwards, they exchanged papers with someone in front/behind them (so as to avoid exchanging with someone they may have worked with) and took 1 minute of silent reading time to look over their partner’s work then they talked it over. The room was abuzz with great conversation! They were helping one another hone their arguments and make things clearer.

It felt good.

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I blame Mara.

I stayed home on Wednesday, though I did have childcare in the morning, which allowed me to do a bunch of grading. But my goal of doing all of my comments for Topology–a class of only 5 students–was stymied by doing such important tasks as: going to the park, making chicken stock, washing all of the dishes. Okay, so only one of those chores was really Mara’s fault.

During the day on Thursday and Friday I went into work from 9 to 2:30 both days. I had quite a bit of free hours on Thursday, not so many on Friday. But this pumping thing, it eats up quite a bit of time…

I was able to finish my grading (and Topology comments) on Thursday. On Friday I wrote a few more comments, but I went off campus during my lunch break to attend a breastfeeding support group I used to go to regularly. That was fun; wish I could have taken Mara.

The upshot to all of this is, I have been writing comments today and have one more class-worth of comments to write tomorrow. And I suppose I should figure out what the heck I’m doing for my classes on Monday at some point.

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I got this game from Mathsational–I never would have thought to make the cards up in PowerPoint, but this is a genius move. Making different sets was really easy–I just changed the background in the powerpoint. So simple! I had actually never heard of the game “My Ship Sails”…and all but one of my students hadn’t heard of it either, but the rules are pretty straightforward and no one had any issues with the rules getting in the way of them practicing the math concepts, so that was good. I came up with the idea mid-way through that I should have had students say “QED” when they won, but I had already told them the rules and they were so busy being productive.

Another blatant rip-off from the MTBOS that I did on the very same day was Attacks and Counterattacks. I added a few more words for students to define, but in my final debrief I stuck to the three that Sam defined: circle, polygon and triangle. I didn’t do the best job of the debrief in my first section, but I think I did a good round 2 with my second section. Nothing fancy, just had each group put up their three definitions on the whiteboards and then when people raised their hands that they had a counterattack, asked them to put them on the whiteboard. We did one word at a time, partly because I wasn’t sure how many we’d get through before the class was over, partly as an organizational strategy to keep everything focused. It worked.

My favorite word–which we did not put up on the whiteboards–is the narwhal. I have had classes in the past (lame, boring classes) who purposefully *skip* this word, because “it’s not serious.” GEEZ, KIDS! THAT’S THE WHOLE POINT!!! But this year the kiddos were into it and we had many fabulous definitions of narwhal.

My favorite one was my favorite because I had an awesome counterattack for it: two kids defined narwhal as “the product of the marriage between a unicorn and a dolphin.” My counterattack stated that the unicorn and the dolphin were not heterosexual, and therefore were unable to have biological children. The kids loved this by the way; they even took a picture of my sentence–though I shudder to think where that image wound up going… Whatever. Score one for the fight against heteronormativity!

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One thing that really made me happy this week was a new thing I tried with students. I had pairs of students put up a solution to one problem from the sheet they’d worked on the day before with the instructions that they would not be presenting the problem so there had to be enough information up on the whiteboard for people reading it to follow along without being able to ask questions. Everyone grabbed a dry erase marker and did a reasonably silent gallery walk. Since it was the first one we’d done for the year I prefaced it with a discussion about what type of feedback would be good. One class did a much better job about giving thoughtful responses than the other, but I digress.

The part that was new was the last bit. I had students return to the problem that they’d written up on the board and read the comments with two things in mind:

- Look for any questions that classmates asked.
- Look for common themes in the comments.

As the final step I had groups share out the common themes they noticed on their boards. I really liked this because it got at some good stuff about communicating your ideas clearly and highlighted points of confusion while taking the focus away from simply getting the correct answer. We did talk about the correct answer in at least one problem in the end, either because a student asked about it or I brought up the fact that no one had made a comment about a certain mistake that was made, but it was not the focus of our conversation. Which was really awesome.

After we finished the activity I asked students what they thought about it. In both classes, the handful of students who spoke up commented that they liked it; that it was nice to think about their work in a different way. One kid from each class mentioned that they liked our “regular” debriefs too and I reassured them that we would still be doing those as well. I shared that what I liked about this activity was that it allowed everyone to share their thoughts, even the people who are less frequent speakers in our class conversations, and so each group got more feedback, from more people, than if we had just talked about their problem.

In the second class, one kid commented that “parts of [the activity] felt a bit rushed” and, just as I was acknowledging that I heard and appreciated his feedback, the announcement of our earthquake drill came over the intercom. I smiled and said “now you know why it was rushed!”

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I know lots of teachers–some of them my amazing colleagues–complain about BTSN, and on occasion I feel grumpy about it too. But for this week’s post I am going to reflect on all the things I am grateful for about BTSN:

- For some reason, I really like the abbreviation BTSN.
- That moment when you meet a student’s parent(s) and you go “OH! I totally get why such and so does
*that thing*now.” [In your head, obvi.] - Seeing parents do the first math lesson they’ve done in [insert large number] years.
- Whatever activity I throw at parents–in one class this year it was learning about radians!–at least some are ready and eager to engage, even though it’s 7:30 at night.
- Getting to introduce grow-ups to the cool things that happen when you play around with Möbius strips and hearing them audibly say “neat!”, “whoa!” and the like.
- Parents who just want to meet you and shake your hand and tell you that they’re Stu’s mom/dad.
- Getting to see parents of students you’ve had before again!
- Parents who ask you “how’s
*your*baby doing?”❤

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I jumped on that one!

“Yes,” I said, “explaining your thinking is really hard. And that’s why we practice it.” I went on for a bit about building neural pathways in your brain and about how this feeling of not knowing exactly how to say something felt uncomfortable, but that just meant that they were learning new things. “It’s hard,” I concluded, “so what are we going to do?”

“Practice it!” the class responded.

***

I had some great moments with colleagues this week. Like, really awesome moments. I haven’t had this kind of collaborative partnership with other adults around something not involving baby-stuff for over half a year now, so it feels really good.

I had a colleague who has been notoriously difficult to work with reach out and ask me for advice on a quasi-personal, quasi-professional topic. I felt respected by this person in a way that hasn’t been obviously apparent previously. I also brought up a challenging issue with this person, basically seeking out a potentially difficult conversation and it went well. Double yay!

***

Another colleague and I worked together to develop a set of reading questions for students to ensure that they grappled on a deeper level with a text about radians. I felt like the questions I wrote were meaningful and allowed students to access ideas in the text at a level they haven’t in previous years. Discussion was rich and students asked really good questions.

***

I tried a new activity and felt like the directions could be a bit confusing for students…so I made some visual instructions and threw them up on google slides. I think I blew at least one student’s mind when I mentioned the z-axis.

***

Another teacher stopped by to leave me a note regarding one of his advisees, who is my student. After class was over he talked with me about the part of the lesson he’d seen whilst he was writing his note and was super complimentary on my use of technology to record class notes about a discussion of the task. It felt really good to hear someone say nice things about what I was doing.

***

Both my department chair and my dean of students observed me on the same day (not the same section, but the same class)! They didn’t realize that they had done this, and they were both apologetic about it once they did know. But I responded with enthusiasm–hey! now I get two different perspectives on the same lesson, awesome! Lack of feedback on my teaching has been one of my criticisms of my school in the past, so I’m totally willing to go a bit too far in the opposite direction before things get totally dialed in. Yay, observations!

***

My kiddo had her first fever this week.

But she got better really quickly and is back to her energetic, delighting-in-the-world self now.

And it’s the weekend.

Hell.

Yeah.

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It’s been a long while since I have updated this blog. Something which I have many reasonable excuses for (see below for the cutest one). However, this is something which I would like to change this year.

While I can’t possibly wrap my head around the idea of doing a daily blog, like Justin, or even around blogging every day for a month, like Anne, I want to make a small commitment. And so I have decided that this school year I will blog each week. Probably on the weekend, probably during someone’s nap time. It might be short, it might be long. I don’t know yet.

There will probably be talk about parenting, certainly infinitely more about that than in previous postings! It is kind of big deal, after all, becoming a parent who teaches. I’m not sure yet how teaching fits into my new role of being a mom, and how being a mom fits into my old role of teaching. It’s only been one week back in the classroom so far.

Speaking of that week, it was…tiring. Every beginning of the school year is tiring, though this is the first year I’ve been getting up every night in the wee early hours of the morning to feed a baby. The start-up felt more clunky than usual this time around. It’s been half of a year since I was last in the classroom, and I haven’t gotten my sea-legs back yet.

I had a moment midway through the week where the thought crossed my mind, “I’m not having fun yet.” And I had to remind myself that I * always *feel this way during the first week–I don’t know these kids yet and I miss being on summer break. It’s hard work and I haven’t gotten back into the swing of things.

But despite this, I feel like I had a solid first week. I absolutely love my new batch of freshman advisees. They talk to each other! From the first moments of orientation!! My last group took about a year and a half to start having conversations. This is so much easier. Plus, we have a snack rotation already in place–score!

I’m teaching two preps, one of which is Topology. I got an email Friday afternoon that my new ~~doughnut~~ coffee mug has arrived. Very exciting. Topology is a class of only five students, which can be either totally awesome, or a complete failure depending on how the group meshes. And I can tell they are all willing to dive in and talk about big ideas. I broke them up into two groups at one point to discuss a problem and they kind of half-heartedly did so until I asked them whether they would rather just talk in the whole group. “Yes!” they responded. And so we did, and shall. We’re using Shape of Space as our primary text and reading selections from Flatland. I’m trying to channel Sam’s book group.

My other class is an integrated math class, mainly sophomores but with a few juniors who I last had in math 1 their freshman year as well as one freshman. We started off with one of Dan’s textbook makeover problems, the one with the dock ramp going up and down with the tide. Our goal was to do an informal assessment of what students remembered from their trig unit the previous year. Turns out they remember bits and pieces of information, but they don’t have it put together in any meaningful way. Some of them remember the definitions of sine, cosine and tangent in relation to the unit circle (which was the definition they were taught), but none of them have an idea of why that definition is meaningful. So that’s my goal for the next few weeks. I started by going back to triangles–justifying this because the word trigonometry means triangle-measure–and then connecting the triangles to the unit circle. I feel like it’s starting to gel a little for some of them. We’ll keep working on it next week.

Oh, and thank goodness we have a three day weekend! More time to spend with this amazing person.

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But it was really strange noodling around about conference session ideas for a few months now and coming up with zilch. I even consulted a list of ideas I’d written up a few years ago. Looking back on that was kind of nice, as most of the ideas I’d written down I’ve since presented on. Go me! A few others that I haven’t (yet) presented struck me a kind of meh on this reading.

All I could really think of as a compelling idea was that I’d like to spend some time talking with people about balancing work/life as a new parent. Now, I didn’t think that this is a topic that would necessarily get chosen and I certainly didn’t think that I would be an expert on this by the time November rolled around, so it was a no-go for a conference proposal. However, it got me to thinking…

I would love to have a mechanism in place to set up informal conversations–maybe lunch groups?–who could come together to talk about a topic that is interesting to a certain segment of the conference-goers. For me, it could be talking to other parents about how to juggle everything. Maybe for someone else it would be about homework policies or how to implement standards based grading. The more I thought about it (and talked it over with Avery) the more it started to sound like setting up a mini-EdCamp in the midst of a “real” conference.

So that’s what I’d *actually* like to do for my workshop. For logistical (and economic) purposes, I went ahead and submitted a “regular” session proposal. But this idea is the one that makes me go “Hmmm…that sounds intriguing.”

I guess I’m putting this idea out here just to see if there is in fact any interest in doing something like this.

Or if I’m totally bonkers.

Though I suppose those things are not mutually exclusive…

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But indeed, there is a powerpoint! And here it is, links and videos and everything:

Asilomar Classroom Routines to Support Mathematical Discourse

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