They’re Baaack!

The hexagons, that is.

Though, as it turns out, they didn’t stick around for long..

You see at Morning Meeting today our mindfulness teacher gave an adorable metaphor for bringing your awareness back to the present moment. She explained that our thoughts are like puppies: you take them home and you love them and care for them, but then–when you open the door–they run away and you have to chase after them, hug them and bring them back inside.

I’d already been thinking that I was going to have my students “Adopt A Hexagon” and this allowed me to take that idea to the next level. I told them that, just like the puppies at Morning Meeting, their hexagons had run out the door and they needed to create “Missing Hexagon” posters to put up around the school so their hexagons could get reunited with them.

After they’d gotten just about finished I upped the ante by letting them know that the local news station had decided to give them airtime to make an announcement about their missing hexagon, but due to scheduling requirements they only had 10 seconds to make their plea. Therefore, they needed to condense their description down to the one essential criteria of their hexagon.

It was lovely.

As you can see from their lovely posters.

.Hexagons Benz Hexagons Chrystiee Hexagons Ciri Hexagons Foxxi Hexagons Precious

Being Wrong

I had an interesting experience earlier today* that reminded me of Grace’s recent post about what she calls the “culture of correctness.”

A teacher was giving a demo lesson in a neighboring classroom and I popped in for a few minutes to observe. The tiny slice I saw gave me quite a bit to chew on. A warm-up problem asked students to vote with their feet by moving to one side of the room or another based on whether or not they thought a statement about vertical asymptotes was true or false. I happened to be sitting at the “true” side of the room. A handful of students joined me (though I was not voting); most students, however, moved to the “false” side of the room. The prospective teacher asked students to talk to someone near them about why they were standing on that side of the room. At this point a couple of students decided to switch from false to true. After the students shared with their partner, the teacher asked for a representative from the false side to explain her thinking and then for a representative from the true side to explain his thinking. Again, several students decided to switch their answer from false to true.

In this particular shift several students began “explaining” to those around them (or just talking out loud to the room in general) about why they had made a mistake. There was clearly some embarrassment and chagrin from these students, who seemed to feel compelled to share about their reason for making an error. I was a bit concerned about the activity making it highly public for students who got the question wrong–even though this was well over half the class–and was curious to see how the prospective teacher would deal with this.

From what I saw, this teacher did really well, especially considering that the teacher didn’t know any of these students. The teacher noted that several students had changed their mind–from the tone it was clear there was no judgement about this–and asked a couple of the students to explain what had happened in their thought-process that made them decide to switch places. One of the students who shared why she changed her mind was one of the ones that was most vocal as she walked across the classroom. As she had walked over I heard her downplay her abilities (“it’s because I’m so bad a factoring”). But when she explained to the class that she had neglected to factor the numerator, it seemed that she had come to a more comfortable place in her mistake-making. She no longer sounded like she was beating herself up over it.

After this activity I left to go back to my own class but I am looking forward to talking more about this moment and hearing this teacher’s perspective on it.

*I have delayed publishing this post as it talks about a prospective teacher’s demo lesson

Cryptography, Weeks 2 & 3

These past two weeks of school have been a bit brutal. Partly due to outside of class stress, partly due to said stress leaving me with some sleep-lite nights. This past week I had 4 meetings during my prep periods during the first two days. Like I said, brutal. Luckily I have a bit of a break coming up now. I get to spend a week making and eating cheese. And then I fly off to Maui for a week!

I spent Monday of week 2 working on Polyalphabetic Substitution Ciphers, but not really going into the Vigenère Cipher, which I fleshed out on Tuesday. I had my dentist appointment on Thursday–no cavities, yay!–so I gave students a day to work on their Crypto Contest, an idea a lifted from Avery. Students work with a partner to come up with an encryption/decryption algorithm and encode a message which I then shared with the rest of the class (in week 3). They will spend the next several weeks attempting to crack one another’s codes. Friday had students taking a quiz, which took about as long as I predicted, despite never giving this one out before. I’ve gotten pretty good at this teacher-thing. Maybe. We finished by discussing the first half of Chapter 2 of The Code Book.

Week 3 felt like a bit of a stretch. Like I had about 2 weeks worth of material that I was trying to fit into 3 weeks… We did some somewhat random stuff. Monday I had us turn to the back of The Code Book and we looked at the Playfair Cipher and the ADFGVX Cipher. On Tuesday we had a discussion about the second half of Chapter 2. BTW: In case you haven’t noticed yet, my Cryptography class doesn’t meet on Wednesdays. On Thursday we talked about “book ciphers and ciphers in books” which was kinda cute. I found links to two short stories, mentioned in The Code Book, which featured ciphers–The Adventures of the Dancing Men and The Gold Bug–and had students either read the text and attempt to decrypt the code in the story or to use the story as a cipher text to encrypt a short passage. We didn’t have school on Friday, to give us time to prepare for Intersession.

And now, I shall go make cheese for a week. I canNOT wait!

Cryptography, Week One

I first proposed this course a little over 2 years ago…and now it’s finally made it into reality.

Which–of course–comes with the drawback that now I actually have to *plan* the course each week. Funny how that works, right?

But, I have to say, it went really well the first week. I totally under-planned for the first day, but somehow I managed to swing an off-the-cuff lesson on modular arithmetic that had me looking up at the clock and saying “has it really been an hour already?” and my students saying the same. You know it was a successful day when students are amazed by how fast the class went by.

I know I’m probably not the only one who has a secret yearning to teach Crypto, so I’m going to try to post everything I do in class here. Added bonus: when I teach it again next year, I’ll actually know what the heck to do!

Day One:

Say hello, confirm that everyone knows everyone else (at least enough to say “hello” to), tell students their first assignment is to read the syllabus. Then give students the syllabus–which they quickly note is IN CODE! They are intelligent enough to realize that they are supposed to decrypt the message. This didn’t take very long (good to remember!) as I kept in all sorts of easy hints–it was pretty easy to realize my email address was going to end in for instance.

When they got the code, I passed out the plaintext version of the syllabus and had students read it. While students were decrypting and reading, I put some vocab up on the whiteboard. After asking about questions relating to the course, we went over the definitions. Then, a mini-lecture on inverse functions and how encryption and decryption functions are inverses. Talk about ROT13 (the algorithm I used to encrypt the syllabus) and how it is its own inverse. History of Caesar shift also happens here at some point. Then I connected the Casesar shift to modular arithmetic and we did a few examples. To end the class I had students each encrypt a message using a Caesar shift–I gave them “decoder ring” to help–and exchange with a partner to decrypt.

Homework was to write me a letter.

Day Two:

I use this PowerPoint, which takes up basically the whole class. The lecture is on frequency analysis, the second to last slide is from The Code Book. Students work on decrypting the message–this takes a while and students don’t finish before class is over. We don’t get to the last slide.

Day Three:

We start by having a discussion about the first chapter in The Code Book. I push the tables together so we’re sitting in a circle. They are well-trained from their Humanities class in having a discussion, so I don’t have to work very hard. Then we do slide 9 from the previous day’s PPT. I give each group of students a set of Scrabble tiles and they compute the relative frequencies of each letter. Then they decide whether they agree or disagree with the point distributions for each letter. Their assignment, which they finish for homework, is to write a memo to Hasbro Co. giving their recommendations for changes to the game (or, if they think no changes are necessary, they write explaining what they think is good about the game design).

Day Four:

Warm-up is a few problems on evaluating several numbers in mod 6. I somehow forgot to mention that modulos can be evaluated using division with remainders, so I choose my numbers to (hopefully) lead up to this insight. I make sure we talk about this now. In the previous class someone had mentioned a misconception about anagrams, saying that the reason they did not get used often for encryption was that they were too easy to decrypt. So, we used the Scrabble tiles again to do a lesson on permutations.

And that was it for the week.


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.