Now I want to say that I am the same me both times, but now I am wondering if I react and compose myself in different ways based on how classes go. I think ultimately there are several variables outside of my control, but I do still have control of the classroom no matter which class is there.

Anyway, I didn’t do anything innovative or exciting today.

In Foundations I gave them a set of multi-step equations from the maze activity we completed last week. They didn’t recognize them until I dropped very obvious hints. Foundations is currently grounded from Kahoot because someone stuck bots in and messed up the data last time. This has made reviewing a little tedious, but I holding them accountable. I said no Kahoot for two weeks so we are doing no Kahoot for two weeks.

In Geometry I gave them a short group activity (they did well) and them an individual / pairs worksheet. Then we reviewed and then a skills check.

Sometimes learning is just a grind.

Thanks for reading.

]]>I am just the worst.

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I gave them the following activity as a way to review properties of equivalence and congruence and push them to think and apply the concepts without having to understand a new definition.

The activity itself just went okay. My 3/4 suffered through me fumbling it the first time. I overexplained and didn’t give them time to try it themselves. I did a better job for 6/7, but I was still maybe giving too much help.

What I want to talk about is what happened during this activity in 3/4 though. I asked the students if a line could be perpendicular to itself. They said no. I asked why not. They said it would have to intersect itself. Great so far. Then I drew a line that intersected itself. A student said “That looks like a ribbon.” This inspired me.

“Okay. So lines don’t intersect themselves, but these ribbons do. What if they intersect themselves at right angles? Then they would be right ribbons. What else could happen?”

Student: “It could be less than 90!”

Me: “Exactly! And what else?”

Student: “More than 90 degrees. Obtuse ribbons!”

I was really excited about this and tried to convey the fact that they were doing brand new math with me. (I mean, someone has probably studied something like a ribbon I am sure, but I was really trying to get them to see that we were doing what mathematicians do: defining a new object and then playing around with it.) They weren’t nearly as enthusiastic as I am. I may create an assignment in the future that tries to help them discover some loop properties. The students were excited, but they did come up with some new ideas or at last connect new ideas to old ideas.

I have been really lucky with that particular class.

Thanks for reading.

]]>But this semester hasn’t been that way.

Part of it is that is just the luck of the draw with the students I have and what classes they are in together, but I also think that I have gotten better at building and sustaining culture.

So. Norms.

Mr. Dr. David Butler has a great shirt. It says “A line is a line if I say it’s a line” and it has a picture of the Fano plane. It’s fantastic. I bring this up because I stole a lot of my classroom norms that I want to build in my class from David’s 100 Factorial Norms for Working Together. You can see his norms reflected very closely in mine from the first day slide.

In particular I want to point out the “Say you don’t understand”, “Ask what’s happened so far” and “Say that you still don’t understand”.

Because today after I had given the students time to work individually or in pairs on some conditional logic questions, we were going over the solutions as a class. We finished up and I asked the students to submit the work in the bin. One student raised his hand and said,

* “Mr. Belcher, I have a question.”*

*“Yes?”*

*“What are the answers to five through seven?”*

*“Five through seven?!”*

*“Yeah. Five through seven.”*

**“What were you doing for the last 10 minutes?”**

*“Mr. B, you know I don’t be paying attention.”*

*“Y’all. Someone help [name redacted]. The rest of you, submit your work and get ready for notes.”*

Now.

A line may be a line if I say it’s a line, but is a norm a norm if I only say it’s a norm? Does his question count as “Ask what’s happened so far”? Is it a case of saying he doesn’t understand?

Clearly in the moment my gut reaction was no. I handed him off to another student to effectively copy the answers and I blew off his request for help.

Was I violating the norm? Or is the idea that you have been actively engaged in the activity implicit in the norm? And if it is implicit, it is still clear? Do I need to clarify that my willingness to answer a question I have already answered is contingent on you trying to understand the first time or the tenth time? Because to me it is obvious that a norm isn’t a norm if I only say it’s a norm. It’s only a norm if, well, if you’ll forgive the tautology, if it’s a norm!

I don’t know if I really broke that norm today, but I think I should have pulled that student aside today after class and spoke with him about expectations and why I moved the class on without helping him.

Thanks for reading!

]]>And followed me.

Right after making accounts.

Normally when you get followed by a bunch of blank accounts it means that you have caught the attention of some bot-net that is aggressively following you and that’s what I thought it was.

So I started blocking them.

Howie’s bot students.

But then I noticed Howie followed a couple of them and I see education retweets and I put 2 and 2 together since Howie had mentioned I had come up in his class recently. (I was probably being an idiot on Twitter because, let’s face it, when am I *not *being an idiot on Twitter.)

So, sorry for blocking you, Howie’s not-bot students. I thought you were not not-bots. I unblocked you.

Anyway.

After I realized they were students and not bots I decided to ask them a self-referential multiple choice question, which are fun. But then it inspired me to ask my own students the same question.

So this was today’s warm up. Go ahead and answer with a real or fake name if you want. I already collected the data I need.

Here’s Foundations Of Algebra

CP Geometry (3/4 Block)

And CP Geometry (6/7 Block) (Who I cajoled the most to really be careful and talk to each other. They also listened the best but alas one student didn’t cooperate, which was funny.)

I didn’t draw as much out of my classes as I wanted to / should have with this activity but it was still fun. I may do another self-referential / game-theory question in the future and make it competitive rather than cooperative and offer bonus points as an incentive.

In any case, hi Howie’s class. @ me anytime on Twitter!

]]>It’s like Staggered Submission or Delayed Collection or something like that.

I give the students an assignment and time to work in class on it.

I follow the assignment up with a Kahoot or Google form that matches the assignment exactly and they enter the answers.

A problem that I would run into using Go Formative every single day last year (my first year) is that students needed their computers for it. I love computers. Computers have done wonderful things for math education. But sometimes I just need device free desks with paper and pencils and kids writing down the math. And the computer (even computer collection) can get in the way of doing that.

But if you go full analogue it’s a pain to collect answers. You have get a stack of messy papers for which someone forgot to label properly their name, date, and assignment and you’re carrying them around and you have to manually grade. You can’t get away from that completely and I don’t think we should. There’s value in grading some written work. But! But. It sure is nice to have a problem set auto-graded and get an instant picture of who did what and who maybe understands what.

So I stagger it.

“No, not tech right now. Just these problems. Think about them. Try them. Write stuff down.”

*later*

“Okay please take this quizlet / kahoot / google form and answer the questions. They should look very familiar.”

I don’t have a catchy name for it. I’m just saying. Stagger it a little. It helps.

Thanks for reading.

]]>I know lecture isn’t everything but it has been nice to work on improving my skills as a lecturer this semester because I have had more attentive classes. I still need to improve on my facilitation of group activities, but I am making progress there.

Anyway I know I haven’t written much about my actual lessons today, but that’s because they were pretty boring and routine.

Warm Up

Homework Check

Review and Practice from previous day

Introduce New Material

Practice New Material while integrating old material

Skills Check

The bread-and-butter as it were.

Thanks for reading.

]]>My foundations students responded pretty well to my follow-up lesson introducing the three fundamental rules of algebra for solving one-step equations. On Monday we will revisit them until we’re sick and then move on to two-step equations.

It’s been a full and busy week and I am tired so I think that’s all I am going to write for today.

Thanks for reading.

]]>I felt really lucky that all of my lessons turned out so well because after giving a test Wednesday I didn’t really think about what I was going to follow up with and so I was scrambling this morning to prepare for all of my classes.

I really love the unit we’re starting in Geometry (Reasoning And Proof) since I get to really get on the soap box about how reasoning and proof is what all of math is. I could tell I was really waxing poetic today in class because my students’ eyes were glazing over as though covered with wax paper.

ANYWAY, I started today with a nice warm-up that I adapted from a John Stevens Would You Rather? tweet. I adapted to how it reads below:

I changed it to read this way because I was concerned about some of my students who can be mean to each other. Although I enforce kind language in my class, I was hoping to avoid the problem and I was afraid that there would be hurt feelings if we started discussing weight.

The downside to this version is that it takes some nuance out of the problem. A very tall and very skinny person might choose differently from me, a stocky guy that’s only slightly above average height.

But as it was it was still good. I was once again amazed at how the same problem can cause such varying reactions among different classes. All three blocks responded differently to it.

After the warm up I went to well that I have often go to before, Jo Boaler’s YouCubed Pascal’s Triangle activity. Asking students to complete the triangle has worked really well in the past when I wanted to show them that math is more than just following an algorithm to find an answer, and I think it’s a great way to start a lesson on inductive reasoning and finding patterns.

This went really well in both blocks. In fact, one student pointed out a pattern in the triangle that I have never seen before and I was blown away. I was very excited.

I let the students explore while I circulated the room. Every time I have done this I have been pleased with the results. Students naturally start sharing ideas and answers with each other. There is something about completing the triangle that hits exactly in the right spot: easy enough that students get started without fear, hard enough that they don’t realize the answer right away with plenty of extensions and side-trips to make even if they realize the basic pattern building the triangle. (What we call a low floor, high ceiling task.) For some things you have to train and help and remind students, but a task like this seems to naturally activate some innate human mathematical ability for pattern recognition. I love it. It’s great.

After a whole class summary and some sharing from students, I moved to a slide deck that started with some GH Hardy quotes about mathematicians being makers of patterns and so on.

I then gave the definition of inductive reasoning from their textbook and followed it with my “simplified steps for inductive reasoning”:

- Look for it
- State it
- Prove it

Where it is the pattern or conjecture. I think this went over pretty well. I really wanted to emphasize with the students that proving a conjecture required showing it was true for all cases or by finding a counter-example. So I introduced the Goldbach Conjecture. I think it’s perfect for this lesson because the conjecture is easy to state and understand and then it’s a bit mind blowing when you see on the Wikipedia article on it that we’ve checked over 400 trillion (400 TRILLION!) cases and we still don’t have a proof. And then I immediately followed this up with patterns from Ben Blum Smith and James Tanton that break very quickly. I think this really drove home the point.

We finished up the last 30 minutes or so with a problem set from the text and then a skills check over some unit 1 ideas.

All three classes today went well but now I am sitting here at home writing my blog at 1030 PM and once again I am going to have to get up in the morning and come up with something. It’s hard to get ahead, but I really love this job on days like today.

Thanks for reading.

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