I have no idea

I have no idea how to teach problem solving skills.

I have no idea how to teach the creativity needed to come up with a novel solution to a math problem.

I have no idea how to teach how to be a mathematician.

I know how to explain a concept.

I know how to create a task that will help illuminate a concept.

I know how to teach an algorithm.


I don’t know how to make students better mathematicians. I only know how to teach them math that has already been done.

I am feeling a little lost here.


Second Breakfast: Day 74 Or Bad Lesson

My geometry lesson did not go well today. It wasn’t the class (although I did have to ask a student to leave) but me.

I had some short notes planned and then I got excited and wanted to show the class the proof of the Pythagorean Theorem that uses similar triangles.

I should have rehearsed it. I had read it and understood it before class but I didn’t really think about the best way to do an exposition of the proof and it was sloppy and confusing and the students were clearly lost. And my gut is that even if I had presented it well it was just a little bit too complicated for a direct presentation. I should have had them read it and then work on explaining it in groups instead. It just didn’t go smoothly at all.

Ah well. Now I know.

Thanks for reading.


Second Breakfast: Day 73 Or Taylor Used Classroom Management. It’s Marginally More Effective!

I met with my two supervising administrators last week to conference about how my semester is going. The meeting went well and they were complimentary about my improvements in classroom management. (They said I looked more “comfortable” this year compared to last year. Which I think is true.)

But this is still an area I need to grow in even though I have made progress.

I was thinking about what changes I was going to make from this semester to next semester since I will get all new classes and a fresh start. (Which honestly has been really nice and has helped my growth as a teacher. Four attempts at starting a class in the first two years of teaching instead of just two attempts has really been great.)

While I was thinking about this I realized that part of the reason I have been frustrated with myself when it comes to classroom management is that I had a belief that once I get it right, once I find the perfect rules, I will never have problems in class. That if I was just a little more consistent and found the exact right rules and expectations and norms, then I would always have good classes.

Which is, of course, wrong.

And I have finally realized that was a rookie mistake. Certainly some rules, expectations, and norms are going to create better and smoother classrooms where more learning will happen than for other rules, but there will always be difficulties. And yes, I am going to get better, and classes will get better. But I’m not going to find the perfect blend that always works.

Classroom misbehaviors are always going to happen. I just need to expect them to happen and know how to respond when they do.

One of my big frustrations the past year and ahalf has been teaching classes where disruptions or misbehavior happen and me wanting to finally have classes where they don’t, but that isn’t the reality of teaching. It doesn’t matter what classes you have. When my administrators said I looked more comfortable, I think part of that comfort was accepting the reality of teaching high schoolers and what they looks like and how I respond when they misbehave.

I had the following conversation with students today:

Student 1: What does WD-40 smell like?

Me: *coming up to check her worksheet*: It smells kinda oily.

Student 1 and 2: *exuberant laughter*

Me: What’s so funny?

Student 1: You just answered so calm and so fast.

Student 3: Mr. Belcher always calm. I want to see him fall down.

Me: What? Why do you want to see me trip and fall?

Student 3: Because you’re so calm all the time. Like if most people fall down they would be like “AHHHH” but I bet you would just like get up and say, “Alright y’all, let’s do some math.”

Me, Student 1, and Student 2: *laughing*

No one was misbehaving there (well, maybe they were a little off task before I walked up) but I found that conversation encouraging because Student 3 actually had me last year during my first year and he still considered me to be a calm person. I am glad that I have created a perception among the students that my responses to them are calm. Yeah, I’ve lost my cool this year before, but it has only been a few times.

I’m going to keep working on improving how I enforce classroom rules, communicate expectations, and build norms with my students, but I know that ultimately this will never completely eliminate the problem. I have to expect misbehavior and be prepared to respond to it.

I’m not good at it yet, but I am working on it.

Thanks for reading.


Second Breakfast: Day 72 Or Which Came First? Equality or Congruence

This is the second day in a row that I thought to myself “Oh I should blog about that after the last class” and then when I sit down to write I have forgotten it. I guess I will need to start writing quick reminder notes to myself while teaching because I cannot remember what I wanted to say about Foundations at all.

On the bright side, a student in geometry asked a very interesting question, which I would like to pose to the internet because I was not certain about the answer.

I started teaching similarity today and I was connecting it back to congruence and equality as they are topic we have already investigated. A student raised his hand and asked “Do you think congruence came before equality?”

Man, what a great question.

I told him that I would need to look up some materials and think about it, but that I think you could make the argument that congruence as a concept did come before equality given how the Greeks conceptualized number and area.

And now that I am sitting here writing this and thinking “What about math, such as it was, before the Ancient Greeks” and I thought of the theory that ancient peoples would count livestock by piling stones and using a 1-to-1 correspondence. Which is also like a congruence rather than an equality.

But I am curious to here what more knowledgeable people think. Please tell me!

Thanks for reading.


Second Breakfast: Day 71

I introduced slope-intercept form today by having Foundations students graph a given equation using Desmos and then identifying the slope and y-intercept. They repeated this for 6 graphs. Then I asked them about any patterns they noticed.

It didn’t click.

I will have to redesign the task for next time.

I asked very pointed questions to first block and they finally got it. But second block still didn’t get it and still didn’t get it.

I moved on to some small direct instruction with notes on slope-intercept form.

I like the strategy of discovery activity and then class summary but it doesn’t always work. Sometimes my task design isn’t good and other times it works for some students and not others.

Tomorrow I will reinforce with practice.


Second Breakfast: Day 70 Or Is Oatmeal A Soup

I underplanned Foundations today. That hasn’t happened in a while. I scrambled with some Kahoots and turned out terribly because I didn’t have time to vet / edit them and some of the Kahoots out there are just plain old bad. I managed to correct the problem by the time second block rolled around, but it was a little dicey near the end of first block as I tried to find a new task for the students to do. They behaved surprisingly well.

I stole a great warm up from Sarah Carter (@mathequalslove) that went great in all of my classes. I am pleased that I have convinced most of my students to buy into debate in math class. I still have some work to do in getting everyone immediately on task at the beginning of class, but once they got started they did a great job. And speaking of debates in math class, a first block student cracked me up this morning by walking buy, holding out a packet of instant oatmeal, winking, and saying “Soup!”

I was confused at first, but then I walked in to find my first block arguing about whether oatmeal was a soup all on their own.

It was so great.

Thanks for reading.


Second Breakfast: Day 69 Or Doing What You Can And It’s Okay

Now sometimes you just have to do what you can and it’s okay.

I used a Visual Pattern from Fawn Nguyen’s website for the warm-up (Again. Thanks, Fawn. You’re the best.), but I was struggling to come up with the energy this Monday morning to moderate a whole-class discussion on the correct answer. I was tired. It’s okay.

Class behavior wasn’t bad, but  I decided that it was okay every once in a while to let the students try the warm up and then move on to the next thing to do without a whole class summary. It’s okay.

Even though they were a little slower to start Quizlet than I would prefer, they eventually did it and worked together. I don’t have to be riding them hard to be maximally efficient with classtime every day if I’m a little slow on a Monday. It’s okay.

We practiced slope a whole bunch afterwards using a worksheet. Because the kids need to practice slope. We already did a conceptual exercise last week. It’s okay to use a worksheet to practice the skill. It’s really okay.

I went through some answers in second block and we didn’t have time to show the work on every single problem. It’s okay.

In geometry I met individually with every single student because the last unit test scores were




and this conferencing took up longer than I wanted. And that’s okay.

I lectured on kites and trapezoids from the whiteboard without making a slide deck or interactive google forms because I didn’t have time to prepare them this week. It’s okay.

Sometimes you just do what you can do.

It’s okay.