Second Breakfast: Day 34 Or We Don’t Believe You

To follow up on yesterday’s discussion in 1st block about whether 0.999… was equal to 1, I made the Warm Up to discuss whether the two numbers were equal using the Talking Points format.

It was very clear that I have not been using the Talking Points format enough, because the students either forgot how to do it or just plain old ignored it. However, I finally got everyone on track and they discussed the idea and we got some good math talk out of it.

At the end though, I tried to convince them with a few different tacks and for the most part they didn’t believe me. This warm up worked best with my 1st block because the topic had come up naturally, but 2nd block pushed back the hardest. The could follow each step in the argument, but wanted to know WHY I was doing the things I was doing. It felt random and disconnected to them.

My geometry block accepted the arguments the quickest, but I am not sure if that was a good thing or a bad thing.

My brain is feeling a little cloudy today so I don’t think I am going to write any more.

Thanks for reading.


Second Breakfast: Day 33 Or Clothesline Math Returns!

Today for Foundations I wanted my students to explore the solutions to one-step inequalities BEFORE I gave direct instruction on how to solve one-step inequalities.

Starting last week I introduced simple inequalities (and as I told my students, by simple I do not mean “easy”, I mean there is just a variable being compared to a number and nothing else) and we practiced translating between algebraic, verbal, and graphical representations of the simple inequalities. I emphasized that a solution to the inequality is a value for the variable that makes the inequality true.

So! For the lesson today we did a short review of translating between representations and then I got out the Clothesline. I wrote a one-step inequality on the board.

z + 1 <= 5

I then asked every student to think about a possible solution to the inequality and then write it down. I had the computer randomly generate numbers between 1 and my class size and then I asked the student whose number (going by the alphabetical roster) to go up and place their solution up on the clothesline. Then as a class we evaluated whether or not the number was a solution to the inequality or decided where to move it so it was in the appropriate place on the number line. (I placed anchors at 0 and 5.)

I then asked the computer to pick another number. But the catch was that each next student could not answer with a number that a previous student had already chosen. So gradually we started to cover the line with solutions to the inequality. Pretty soon, with a little questioning and prodding from me, my students in 1st block picked up on the fact that the solutions were z <= 4 and they could articulate WHY solutions were not going to be bigger than 4.

Then I changed it up. I wrote

x + 2 < 10

on the board and placed new anchors at 0 and 10.

I told the students they were now going to work in groups and the game was to get as close to 10 without going over. The team that was closest would get extra credit. They really got into this and were very loud talking with each other about possible solutions. In first block I made it a race, but this was a bad idea. In second block I just let everyone go up at once. I told them they needed to carefully consider what they thought other groups were going to write.

And wow I got some awesome answers from 1st block.

I got: 5, 7, 7.5, 7.9, 7.9 repeating, and 9.9 repeating.

The repeating groups really surprised me, but we got some awesome discussion out of it. I had to convince them that .9 repeating meant that they had effectively answered 8 and 10. I don’t know if I convinced any of them with my very, VERY informal real analysis argument (“If two numbers are the same, then the distance between them is zero, right? Well, if we take…”) I am going to have them discuss this link¬†with a bunch of proofs tomorrow and I am excited about it. Probably as the Warm Up so I can have an excuse to make the other classes talk about it too.

So that got us “off-topic” for a while, but then once we got back to the number-line I prodded the class until they were telling me that they could just keep adding 9s to the end of 7.9 to get closer and closer to 8 AND that x couldn’t be exactly 8 because then we would have 10<10. I am certain that not everyone got it, but overall I was really pleased with how the discussion went and we will return to it.

This went really well in both blocks, but I want to refine the activity so the students can really see that solutions are covering all of the number line up to 8 but stopping there. I will have to think some more on how to make this covering with the paper hangers more obvious. I might try to make the students come up with 10 solutions as a group and so we can get a whole bunch on the line all at once. I did this activity on the fly today since I came up with it yesterday during football. Next time I might have a sheet ready with some prompts to push them towards giving non-integer answers to help cover up more of the line. They were actually pretty good at giving positive and negative answers already.

After the clothesline math activity I gave direct instruction on how to solve one-step equations and then we practiced in-class. I really think this lesson went well. We will see how much they picked up tomorrow when I introduce two-step inequalities.

As for Geometry, they are still struggling with proof writing, which makes sense, but it was really like pulling teeth today to get them to answer my questions about the proof. We will continue tomorrow. I repeated to them that I know that writing proofs is difficult and it takes a while to learn.

Overall I was really happy with how classes went today, and I was especially pleased with the math I got out of the students when using the clothesline.

Thanks reading.


Second Breakfast: Day 32 Or Compliance

Earlier today while teaching Foundations I had an idea and I thought “Oh, I should include that in my daily blog post.”

Well, I don’t remember what it was now. I’m sorry.


Okay, so I know I’m doing that annoying stream-of-consciousness thing right now but I was hoping writing the above sentences would help me remember, and it worked.

So I remember what the thing was now.

Here we go. (And it’s gonna seem weird because now that I remember I’m gonna go back up and change the title so it would seem at first glance that I never really forgot what I was going to say, but I did, I promise. It’s weird how writing can compress and obscure time right? Maybe it took me an hour to write this much but you read it in a few minutes. And maybe I didn’t write it in the order that you are reading it. (I did, but you can’t tell.) Except for the title, but we’ve already covered that. Alright stopping now.

Here we go for real:


As an undergraduate, I very much agreed with the idea espoused by the many SBG (Standards Based Grading) bloggers and other folks in the #mtbos about how grades should never reflect compliance, but only understanding. That struck me as making a lot of sense, your grade in your class should only reflect what you know and nothing else.

I still really like that ideal and believe that if I am going to assign grades at all (a perfect world being where I assign no grades) then that is probably the best system for grading.

Well, today I was giving grades for compliance. I set up the Point Collector Activity on Desmos. It’s a beautiful activity. My students just plain old weren’t doing it. They were confused. For some reason, they just don’t read the directions. Or they read them and don’t understand them. Or they don’t try to understand them because they’d rather talk. I don’t know. I was frustrated because instead of a worksheet I was trying to give them an interactive assignment that still taught them about inequalities, but they just weren’t into it.

I thought maybe that I needed to scaffold the activity some more, so in 2nd block, I turned on teacher pacing and had them all do screens 1 and 2 with me. This took way more time than I wanted it to. And then when I released them to try the rest on their own, I did get more engagement than 1st block, but still not a lot. And I still couldn’t tell if it was because the activity was too hard or if they just weren’t trying.

I’ve been feeling discouraged this week because, as I wrote earlier, good classroom management doesn’t produce motivation. It’s just good classroom management. And I don’t have completely good classroom management yet, I just have better classroom management than last year. (And just about anything is an improvement from last year, let me tell you. It kinda sucks how in teaching you essentially have already hit rock bottom and then you climb up from there. Or maybe it doesn’t, I don’t know. What I’m saying is, the first year is hard.)

Some teachers on Twitter would tell you that the lesson has to be motivating and that good lesson design is the best classroom management. I agree to extent, but I think that only goes so far and it’s a little frustrating to hear. Sometimes a good lesson plan isn’t good enough either. Teaching students that have to be constantly motivated is extremely draining.

So I made the Point Collector assignment worth 1 point for each screen completed. I hate using grades as a punishment (“Do this or you will get a bad grade”) but honestly that’s the only thing that seems to work for the context that I exist in as a teacher. (And sometimes it doesn’t work even then!)

For the college classes I teach online, my grading looks like this:

50% quizzes (They’re standards aligned using an SBG system)

40% tests

10% discussion board and miscellaneous (so participation)

This is much closer to what I want for grading ideologically. 95% of my students’ grades is completely based on whether they have mastered content. They could ignore my “How’s the class going for you?” 10 point check-ins and still get an A if they understand calculus. But those students either learn and pass my class or they waste their money and time. I don’t have to motivate them. I couldn’t even if I wanted to, it’s an online class.

But my freshman and sophomores? The ones that I find myself saying sentences to that I also say to my 2 year old son?

“Don’t touch that”

“No, don’t throw that”

“Hey, sit down”

“Please be patient”

“Hey. Please don’t yell at them”

Sometimes the only thing I can do to get them to even begin to try to think about a question is “This is for a grade”.

And maybe you’re reading this thinking “But what if you just tried…” and honestly right now I’m feeling as though whatever you’re gonna say isn’t going to help. Maybe it’s because it’s Friday and it’s been a long week, or that my Geometry class was crazy and I had to ask a student to leave after she said “I am f*cking pissed” after I moved her seat because she kept talking and then she turned around and denied she said it 2 seconds later when I addressed it. I don’t know.

I don’t want this whole post to sound negative because I’m not actually as despondent as this is probably reading, I’m just trying to justify using grades for compliance to myself.

Is it helping you? It’s helping me right now.

Okay, positives:

  • I have gotten way better at estimating how long it will take a class to do an assignment (Thanks, EdRealist.)
  • I am pretty good at coming up with assignments from scratch to help students work through an idea
  • My classroom management is better (Geometry got WAY wild today and I still got them wrangled back down after some serious seat shuffling and then the removal from class)
  • My Foundations students are doing well content wise (even if they were lost during the point collector activity. I still don’t know why that threw them for a loop, but the actual content itself they are doing okay with.)
  • I have gotten much better at staying cool on the outside even when I am frustrated inwardly with students. 32 days in I haven’t yelled in anger at a class. Only spoken firmly or quietly and seriously.
  • I feel more organized and on top of my “extra” duties this year

That’s all I can think of for now. I will probably blog about the topics of grading for compliance and classroom management versus motivation again. They have been on my mind a lot this year.

Thanks for reading.


Second Breakfast: Day 31

TMI Warning

I woke up last night coughing and threw up a whole bunch. It wasn’t a stomach virus, I had a whole bunch of phlegm in my sinuses, and my lungs, and apparently in my stomach. I don’t know if it was allergies or a sickness or what. But there was waaay to much phlegm in my system. I popped an off-brand mucinex and went to bed.

So when my alarm went off this morning I slept through it. Luckily Lauren woke me up, but I was not feeling great about going in to work. But it would have been too much extra work to set up a sub, and I wasn’t puking or coughing anymore, I was just very tired.

But work still went pretty well today. I was tired, but my students did alright. I wasn’t in top form for keeping them on task, but they did well with notes and we got some practice done. I am just tired and my stomach still feels a little queasy so I don’t really feel like writing much more about today than this.

I think the weekend will help.

Thanks for reading.


Second Breakfast: Day 30

One month into my sophomore year of teaching high school.

I didn’t really feel like teaching today and was kind of dreading students showing up. As I was walking into school, the though that popped into my mind was “I am getting tired of this job” which scared me that I had that thought. As I have processed that feeling throughout the day, I think I am tired of trying to be the motivation for all of my students. I managed to buck up this morning and tell myself that by worrying about it I was making it worse and it wouldn’t be that bad.

I was mostly right.

My Foundations did well today. We started into inequalities by using Desmos and Khan Academy. (I didn’t do a lot of direct instruction today, but the students responded well to the activities.) I changed up seating from groups of 4 to groups of 6. This seemed to open up the room a little bit because I went from 7 clusters of desks to 5 clusters.

My geometry did not go so well, but it wasn’t that bad either. I’ll have them back on track tomorrow.

Some realizations after one month:

  • I don’t know if I really like my choice of “Second Breakfast” to denote my second year teaching. Oh well. Too late now.
  • Classroom management can’t produce intrinsic motivation to learn, no matter how good the management is. I woke up thinking that on Tuesday morning. Apparently it was on my mind after feeling down on Monday.
  • I still have a long way to go in all areas: pedagogy, planning, time management, classroom management.
  • I’m not doing that badly. Comments from admin who did a walk-through today: “Collaborative classroom opportunities allowed students to work together. Mr. Belcher is very patient, positive and supportive,” which made me feel really good.
  • I am tired of the job, but I am also not tired of it. I think this morning was partially just some middle of the week exhaustion. Teaching is hard.

Thanks for reading.



Second Breakfast: Day 29 Or Happy To Be Wrong

Perhaps none of my students seemed concerned yesterday because they actually studied for the test. (Although I am still not sure why the review game was such slow going.)

Still, both of my Foundations of Algebra blocks did well on the Unit 2 test. Sure, it could have been better, but it wasn’t the massacre that I was fearing based on my experience last year. Here’s a histogram of most of the results:

Screenshot 2017-10-03 at 12.21.31 PM

So I’m feeling a lot better today. I am so happy to be wrong.

Now, I do have to finish grading the Geometry tests, but I’m optimistic.

Thanks for reading.


Second Breakfast: Day 28 Or Not Ready Yet

I was disappointed in how my Foundations classes went today.

On Friday I gave them a practice test. I am giving the real test tomorrow. I have been telling them that the real test is tomorrow for over a week. I have been telling them to study for over a week.

They had access to both the practice test AND the key the entire weekend.

Today we played a review game using the practice test.

We got through 5 of the problems.

Everyone seemed lost. No one had work written down. It was clear almost nobody in either block had studied last night or it seemed like any night.

I feel very discouraged about this because generally this year both of my classes have been responding positively to me. But it just doesn’t seem to bother them they they aren’t prepared for the unit test tomorrow.

I thought about moving the test back to review some more, but I have to stay on pace with the rest of the algebra teachers, so I really can’t. And honestly, I’m not even sure if I would. I am all for giving students the time they need to learn, but on the other hand, they actually have to be trying to learn. I’m not so convinced they currently are.

I gave a homework quiz to all three blocks today. Many, many students were lost and asking questions and then were upset when I wouldn’t help them on the quiz. Which told me that they didn’t actually do the homework that I have been giving them completion credit for. I ask “Does anyone have any homework questions?” every single day at the beginning of class after the warm up.

I think I am just tired and it’s Monday, but it’s hard to teach students who don’t show a lot of interest in learning. It starts to wear down on you.

I don’t know.

Thanks for reading.