**Warm Up**: I want these to be open-ended tasks that encourage students to talk and think about math. I want them to set the tone for the class, which means I don’t want to be harping on students or make them too hard that they feel lost. Every Wednesday the warm up is a Which One Doesn’t Belong and every Friday the Warm Up is a written reflection on the past week of math class.**Homework Questions**: I consider homework to be practice and I don’t want to grade practice. But I am expected to give credit for homework at the school. Luckily as a department we didn’t want to give too much credit for homework, so the department chose 3 points. I would have preferred 5 points but that’s a personal preference so the grade divides into 100 evenly, not a pedagogically sound preference. I give 3/3 if the kids turn something in and 0/3 if they don’t. I don’t check for accuracy, only attempt. However, I give homework quizzes each Monday (over the previous week’s homework) so I start every class after the bellringer with some time for homework questions. The diligent students know that I will be taking a problem from the assignment and making it the homework quiz. It’s the exact same questions, but not all of them. This is how I hold them accountable for homework even though it is graded for completion.**Skills Check**. This is a quiz, but I don’t tell them it’s a quiz and I don’t grade it. I have them write it in their notebooks and label it with “Skills Check” and the date. I do tell them explicitly it is meant to help them (and me) figure out where they are at with the current material. In this way I can quiz my students every day at the beginning of class and assess where they are at without them freaking out about daily quizzes. Last year I used the Warm Up for this purpose sometimes along with exploring problems and I didn’t like the tone it set. I like it much better now that I have two separate things. I start every class with these three activities and it gives the students a nice sense of routine and pacing to start the class.**Activities**: This might be notes, or some activity that I wrote, or a game, or completing a worksheet, or a quiz. If notes, I will always follow with individual practice. If an activity, I follow up with notes so that we can summarize what we did as a class. The order of these depends on the topic and whether I think the students would benefit from discovering or exploring first or if I need to set the stage before they try a new concept. The activities stage could be anywhere from 1-4 different things in a variety of formats from individual, group, or whole class and I try to keep the pace moving quickly so they don’t get off track.**Closing**: This is the last few minutes of class. I repeat the homework assignment and then pace the room, pointing out trash, asking them to put away markers, erasers, and calculators, and ask them to fix or straighten desks. If I don’t ask then they don’t do it and my room is left a mess.

This has been working really well for me. Sometimes some of my students still struggle with transitions or staying on task, but I keep on them.

Thanks for reading.

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So I drew a box (I love me some box analogies) and labeled it AND. Then I drew two openings on the left and one opening on the right. I wrote T in front of both openings with arrows going into the box and then an arrow coming out of the other side and wrote a last T. Then I gave an example of some AND statement like “My name is Mr. Belcher and I teach math.”

I then repeated with all of the possibilities for True and False and then did it all over again with an OR box.

I was really proud of one student who raised her hand and said, “So, if there is at least one False, then AND will be False. And if there’s at least one True, then OR will be True.” I had not said that explicitly out loud so I was blown away when she said that. She gave that summary very quickly after I had introduced the box analogy and I heaped praise on her.

EDIT: I forgot that in second block another student said “So for the AND box it’s T-way or the highway” which was not only correct but cracked me up.

The students seemed to understand this what goes in and out of the box analogy very well and were able to complete the pattern without me giving it to them, which I was also pleased about.

And it really paid off. When we transitioned to compound inequalities, they did much better with “False AND True is False” or “True or False is True” than they did with union and intersection understandings. I will keep pushing union and intersection as well, but I am very happy about how well the box/CS function analogy went over.

I forgot to finish writing this yesterday so I am writing it this morning before work instead and this is all I have time to write.

Thanks for reading.

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For Foundations, I introduced compound inequalities. I began by reminding students about the definition of a set (which they learned in the first unit) and then I introduced union and intersection. I didn’t spend as much time actually giving examples of inequality problems as trying to help them understand AND and OR. Last year this was the biggest obstacle to my students solving compound inequalities and I don’t know how much of an improvement I made this year. I ended up cutting notes short because of how long the AND and OR explanation went. Tomorrow I will follow up with more complicated examples and how to connect multi-step inequalities to compound inequalities.

I would really like to do some integrated computer science lesson to help students see how AND and OR work in a programming language, but I tried this last year and the CS got in the way. I either need a better way to introduce the concept using CS or I need to have CS integrated in the course from the beginning. (Something I am interested in for sure. I have been kicking around the idea of a curriculum that using programming to teach algebra I for a while, but I don’t yet know enough about programming to make it a reality. And even when/if I do come up with such a curriculum, it wouldn’t be a perfect fit for the current course that I am teaching. So I’ll have to table it for now.)

I am really pleased with how well my first block class is doing. Although I have a few disengaged students that I will keep trying to reach, I have won that class over. They trust me and they try the activities that I give them.

My second block is sometimes still a little wary of my activities, but they still do well. What’s frustrating is that it’s hard to tell when they are going to have a good day, but on the bright side, I have gotten better at ensuring that a good or bad day for the kids doesn’t determine whether or not learning happens. That was a big weakness of mine as a first year teacher. If the students weren’t feeling it, nothing got done. This year, it doesn’t matter if they are feeling it or not, the students who want to learn are going to be allowed to learn. I have definitely seen improvement there.

During lunch, I got our entire lunch group arguing vigorously about whether the proposed solution to the Monty Hall problem was correct and it was hilarious. (Ha, you thought I was going to write more about that but even though this really did happen today, I needed a throw-away title because I had nothing better. YOU’VE BEEN CLICK-BAITED SUCKERS!)

My geometry class also went better today. I still feel what I wrote yesterday is true, I am afraid my class can be boring. But maybe yesterday it was extra bad because we were just reviewing for the test. They did well today and we played grudgeball. I modified my grudgeball rules to fit more closely with my colleagues version and I like his rules much better. I will write them up some other time, maybe when I have Foundations play grudgeball next week.

I have got an insane amount of grading to do and we are having people over for dinner tonight so I need to get home and make a meatloaf, which means this is all I am going to write for now.

Thanks for reading.

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I can tell it’s boring.

I don’t know what to do about it.

They’re bored.

I’m bored.

It’s over 90 minutes of boring.

I love Geometry.

It’s super fun when you try to solve puzzles and draw stuff.

School geometry is boring.

I don’t know how to make it not boring.

Help.

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I reach the end of 6th bell, my last students for the day leave, and I’m just tired.

If I don’t write my blog immediately, I get distracted. And then I’m at the bar with some work colleagues, and then I’m at home eating dinner with my family, and then I’m passing out in my bed next to my wife.

And then it’s Sunday evening and I haven’t written a reflection for Friday.

I think I’m starting to hit a slump. The adrenaline of starting my second year is wearing off and I’m getting tired as we stretch into October and near the end of the 1st Quarter. I find myself thinking about what going back to graduate school or another job would be like. I’m tired.

Thanks for reading.

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Of 45 Algebra students, I received 13 submissions on the Google Form. I gave everyone else who did not submit a 0.

I’m not just frustrated that they didn’t follow directions, I’m frustrated because I watched most of them do the work I asked them to do. Of the 24 matching problems, I would estimate just from walking around and helping that almost every student completed at least 15 or so. And they didn’t turn them in. More than half turned nothing. I gave the directions at the beginning of class, during class, AND at the end of class.

My middle block was the quietest and hardest working they have ever been. And still most of them didn’t turn in their work.

IS ANYONE EVEN LISTENING TO ME?

So today was good and not-so-good. It seemed as though most of my students are getting the hang of solving inequalities, but it also seems as though most of them can’t follow directions or turn in the work that they did.

Teaching freshman is very discouraging sometimes.

My Geometry class went really well because they were still presenting projects to me. I gave them a packet of worksheets that was a mix of review from the previous section and work over the next two sections. I don’t think I am going to have to lecture on the final two sections of this unit much, but they are almost entirely algebra review. Most of my students finished those worksheets with “new” material today without asking me any questions at all.

While they were working on that, I had students presenting their projects. There were a lot of disappointing ones, but there were a few that were outstanding. This one in particular is my favorite and is now on top of my bookshelf in the classroom.

Not only was she the only student to choose a fold-out poster board instead of a boring powerpoint, she picked one of my favorite proofs of the Pythagorean theorem by one of my favorite Presidents. Overall I was super excited about it.

I’m going to allow my Foundations students to turn in their work tomorrow for partial credit and then have a talk with them about following directions. We’ll see how it goes.

Thanks for reading.

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Which was, you know, fun.

And by fun I mean very, very, verrrry boring.

Anyway. I only saw Geometry today. I gave them as in-class assignment to try while they presented their Pythagorean proofs to me. A few of them were very good, but mostly they seemed lost. I think I will probably take one or two proofs from list and use it as an activity so the project isn’t a total loss. Didn’t really do any teaching today so there’s not much to write about. All I can say is that if my job was to proctor standardized tests and nothing else, I would quit. Hoo-boy is that not fun.

Thanks for reading.

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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.

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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.

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

OH.

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:

Compliance.

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.

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