Rookie Year: Day 62 Or Goofy Line Names

Today was rough.

I really did not want to come in to work this morning. My son is sick and I had a little bit of that as well, but it is more than that. I am feeling tired and burnt out. I just didn’t have the energy to make my classes do what they needed to do. My lesson plan was pretty awful and did not go well in any of the blocks. I’m feeling a little bit like I did during my student teaching assignment where I was just existing the final few weeks. It’s not that bad but there are hints of it. I really hope it turns around because it makes the day difficult to get through.

The only positive was that while we were doing a class activity comparing the slopes of two lines. I was proud of all of my blocks for parts of this activity because I had neglected to label the two lines on the graph. Every single class wanted to call them something so that it was easier to talk about them and compare the slopes. Block 1 called them y1 and y2 which I was proud of them for but I loved what the middle block did. I asked them what they wanted to call the lines and I got “Albert and Deanna” which I thought was hilarious. So we calculated and compared the slopes of Albert and Deanna. In my final block, I got suggestions of y1 and y2 again but I then I asked if they wanted silly names like the middle block and I got Scooby and Shaggy, which was also fantastic. That activity was the one bright spot in the day where I wasn’t even treading water, my head went under a couple times.

I’m worried that if this cold gets any worse and I have to take a sick day I’ll not want to come back to work until after Christmas. I’m not sure what to do in order to turn my outlook around but I feel beat down. I’m really grateful that I am teaching blocks because I will get a fresh start with setting tone and classroom management in January. I really like the students that I have and I will see many of them again next semester, but I need a fresh start with new mixes of personalities and classroom dynamics. My current classes are really getting to me. I am already thinking about how I will do the “first day” activities at the beginning of the second semester and how I will set up and phrase things differently. But of course I still have plenty of instructional time left with my current classes and I am in no way giving up on them. I am just worn out, that’s all.

Thanks for reading.

 

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Rookie Year: Day 61

Today was the first day back from Thanksgiving break. I planned everything that I did in class today this morning because I was completely unmotivated to do any schoolwork over the last week. But I think I had a pretty good lesson plan put together. Last night Lauren, Ben, and I went to meet my in-laws at the Columbia Zoo for the light festival. One of the concession stands was selling hot chocolate. I snapped a picture because I immediately knew this would work as a nice linear equations lesson.

hotchocolate

I created a few questions and had the students compare prices for different numbers of cups purchased and at what levels it would be better to buy the regular hot chocolate or the souvenir hot chocolate.

Even as I type this I think if I do this lesson again I will just throw the image up on the screen and ask the class which one they would buy and why AND THEN have them do all the questions they prepared. I think maybe I kinda mathed it up too much and took away the natural curiosity that would have been helpful to the lesson.

But overall it went well and there was even one student who was grasping at very elementary ideas of limits without knowing it when I asked about cost per cup. We had made a chart of number of cups, total cost, and cost per cup and were considering how the cost per cup changed as we purchased more and more refills. I asked the class if we could ever get the cost per cup below a dollar and he asserted “Yeah, if we went out far enough” which I thought was a great way to phrase it. So I had the class calculate the cost per cup if we bought 1,000 cups of hot chocolate and then I asked them about how they thought the zoo made money off the hot chocolate. I got some great responses out of that from a few students as well, but not all of them.

I could tell that some of my students were tired coming back from Thanksgiving Break. It was the Monday following 5 days off after all. My voice started to go because this was the most I had talked in 9 days. The break was also why I did a lot of review for our Monday notetaking rather than trying to cover new material. I wanted to refresh their memories from last week. (And they needed more practice on the formula for slope.)

Tomorrow I am going to retry that activity about comparing slopes that I attempted last week but ruined by having too many lines. This time there will only be 2 lines to compare. I can really sense the tiredness of the class and my own tiredness. There are only 14 days left until Christmas break and we have exams after that so I need to push through to the end. I am worried we will not make it to the final subject of the course, which is arithmetic sequences. But I think if I err on the side of spending “too much” time on linear equations it will not be the end of the world.

Thanks for reading.

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Rookie Year: Day 60

This post is very late. It was a long week trying to get to this Thanksgiving Break and then my Saturday went differently than I had expected.

I lot of what I wanted to write about Friday I ended up talking with some #mtbos educators on Twitter like Kent Haines, Aran Glancy, Becca Phillips, and a few others. It started with this tweet. 

I tried to help the concept of slope connect with the intuition that my students have about steepness. I made a graph with lines of various slopes that all passed through the origin and had them compare slopes and how quickly the lines reached a certain y-value. They struggled. I once again made the mistake of trying to do too much. I needed to simplify the activity and only have two lines to compare. I keep making that mistake.

I will try again when I return after Thanksgiving. We still have plenty of activities and instructional time with linear equations.

Thanks for reading.

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Rookie Year: Day 59

I felt really tired today and was not at my best. One of my classes did not start out on the right foot because I came in from greeting students in the hall to people out of their seats and some of the extra books thrown onto the floor. And then a few students would not sit down when I asked. I raised my voice. This is the class that has been giving me some difficulty for a while.

But I was tired before the class came in anyway so I blame myself more than them. The entire lesson was individual practice using Go Formative, Desmos Labs, and IXL. Many of them did not finish all of the assignments but others finished very early. I kind of split the difference between them working at their own pace and everyone all being forced to work together. I had deadlines and timers but I also allowed them to work ahead. I had a lot of students who kept getting off task. I had to clamp down on one block and stopped allowing them to talk to one another.

I also stayed an hour later today and tutored for someone else so that they could cover me next Monday while I am away.

But on the bright side:

  1. I get all of next week off for Thanksgiving because I took two personal days
  2. I think I have an idea for how to help my students build some more intuition on slope. I’ll try my idea when I return from Thanksgiving.

Thanks for reading.

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Rookie Year: Day 58 Or The Slopes of Mt. Doom

My brain is so fuzzy today. I’m struggling to type this because I just can’t think straight and I’m not sure why. Just one of those days I guess.

I introduced the concept of slope of linear equations today.

I began by pairing my students and giving them the silly drawing below.

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I totally made up the elevation of Mt. Doom this morning and I realize it’s unrealistic so save it, LOTR and earth science pedants.

As you can see, my Mt. Doom as the Eye of Sauron at the top of his tower, Frodo and Sam at the top, and a few eucatastrophe eagles on the way. Yes it is terrible. My middle block let me know as much.

I then asked the students to identify which portion of the path up the mountain, notated by the dots and lines, they thought was the steepest and then be prepared to defend their choice. I did not give them any tools or definitions to do this.

Some students goofed off instead of trying but many of them circled a part of the path they thought was the steepest. However, no one was able to defend their choice other than to say “This part looks the steepest”. Some coaxing did get phrases such as “most vertical” or “least horizontal” but they were missing the vocabulary to really say anything other than that. And honestly I was really happy with their answers. I wanted some more discussion and I definitely need to improve my skills in leading a guided discussion, but overall it went well in all of my classes and I felt it was a good way to introduce the idea of comparing relative steepness of lines. Of course, I am borrowing heavily from Dan Meyer again here with the example he mentions in that famous video “Math Class Needs a Makeover” where he has the ski slopes. However, he does a much better of job of showing the layers of abstraction than I did today. BUT, tomorrow we will look at the same picture in Desmos with some grid overlay so find the true answer.

After we did this, I drew two lines on the board and had the students compare the steepness to continue the discussion. I purposefully drew the first line to be very shallow but rise higher than the second line which was very short and very steep. I asked them to compare the steepness of the two lines. I told my students to pretend they were lazy like me and asked them which one they would rather walk up. This worked well in all of my blocks, but it worked especially well in my final block where some groups of students got very heated about the definitions of steepness and which one was steeper. But it still wasn’t the way I wanted it to be in terms of student conversations.

My biggest struggle I think with student conversations is that if I break them into smaller groups, I cannot be in all of the groups at once, pushing them to start arguing. (Once they get going they don’t need me) and they get off task. But if I do a whole class discussion like I did today, most of the students don’t get to talk or argue about the math. I need to get better at designing tasks that need less guidance from me so that the students can get started without me and classroom management so that everyone is working and also setting expectations early and modeling how small group discussion is supposed to work. I think there is a place for whole class discussion but my lesson today would have been served better if I could have had small groups working together. This has been my challenge all year.

After this discussion we moved to notes where I gave formal definitions of slope, talking about the ratio of change in y to change in x, teaching them the greek letter delta for change, and rise over run. I really emphasized that rise over run is just a way to remember the definition of slope and that change in y over change in x is more important to know. I’ve seen many students in later classes remember rise over run but have no idea what that means for calculating slope and I would rather not perpetuate this. I really wanted to help them get a more intuitive grasp of slope, but I realized today that I don’t know what kind of tasks and lines of questioning really help build this intuition. This is a very glaring gap in my content knowledge. I’m not saying I don’t know how to explain slope, I do, and well I think, but I don’t really want to explain it. I want to help them build understanding. My brain is too fuzzy right now to think on this. The words are coming to me faster than I can type and it kind of hurts. Blargh. The best I could do for building intuition today was to keep relating slope back to our idea of steepness and saying “How far does the line go up or down and how long does it take the line to go up or down? That’s slope. That’s change in y divided by change in x.”

The rest of the notes today after giving the definition of slope and talking positive, negative, zero, and undefined was working examples as a class. Then I set them on their own work. The notes took longer than I thought because of the discussion (and presentations at the beginning of class) so they did not have enough time to finish practicing in class. I will allow them to work on it again tomorrow and try some more ideas for building intuition.

I need to stop typing though, I keep making mistakes and my head is too fuzzy to think straight it is starting to give me a headache.

Thanks for reading.

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Rookie Year: Day 57

I’ve been feeling a little repetitive with my posts lately. I think I may have settled into a bit of a rut instructionally speaking. My 1st and 3rd blocks are about the same and my 2nd block where I have been struggling is marginally better. We are in the beginning of a brand new unit on what is arguably one of the starts of Algebra I: linear functions. I’m struggling with picking tasks for my students that really help them make connections.

Today we played a Kahoot to practice identifying linear and non-linear equations and graphs. I had mixed responses to the Kahoot. I try not to play it too often so that my students don’t get tired of it and I haven’t played it in a while, but I know that other teachers use it too. One class was excited, the other class groaned, and the third was ambivalent. The ambivalent class did the best however, sometimes asking me to stop and explain an answer. The Kahoot was too long. I searched the website and used one that another teacher had made. It had 32 questions and all of my students start to check out after around 20 or so. I’ll have to trim them for next time.

Next I had them come up with their own examples of linear and non-linear equations and tables. They wrote down their answer and then I had them share. I used traditional paper for this on little half-sheets. The half-sheets are nearly as nice for keeping kids accountable and taking a quick pulse of the room as Go Formative is, but I could tell that they were tired of that as well. This went the best in my final block, but all three were decent. I can tell that my students are just tired of learning math. No one is very enthusiastic or eager to share. They need the upcoming Thanksgiving break and so do I.

After the sort of think-pair-share minus the pair, I did use Go Formative to have them practice converting linear equations to standard form.

Finally I tried what I talked about in my post yesterday by trying to scaffold the activity of finding solutions to linear equations and then making the connection that the graph of a linear equation is the graph of the solutions. This final activity was not planned well enough (again) on my part. Argh. Two days in a row. I’ll get it.

Thanks for reading.

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Rookie Year: Day 56

Last week I had introduced the idea of linear equations for the first time. The day after introducing the concept we had tried a Desmos activity. The activity did not go well and many of the kids clearly did not understand how to identify linear equations just from looking at the equation. (They were perfectly clear on linear equations making straight lines, but recognizing what the equations looked like or grappling with the definition of linear was much harder for them.)

Today I essentially started over because I felt that they needed to try it again. After repeating the definition and listing the ways to recognize as a class, we practiced as a group. I threw a table on the screen and had them enter their thoughts on Go Formative. Engagement was rather low today. Even students were not actively disrupting they were simply not answering the questions. It is Monday but I think I need to change it up a little on my formative assessment formats. I am not sure. I do want to help them get into a routine so that they know what to expect, which means I only give “notes” on Monday’s and Wednesday and I try to use every other instructional activity that I can on the other days. (And also we don’t JUST do notes on Mondays and Wednesdays. The blocks are too long for that.)

I also wanted them to start to connect that solutions of linear equations lie on the graph of linear equations. So I wrote a linear equation on the board -2x+3y=21, put them in pairs, showed them what a solution looks like without giving them any (values for x and y that make the equation true), and then told them whoever found the most solutions got candy.

I was plotting solutions that they give me on the projector using Desmos, but it was not until the final block that I realized that I should also have the graph of the line on there so that they could see that their solutions showed up as points on the line. Oops. At least I improved throughout the day, haha. I had mixed success in every block. Some kids got really into it and found lots of solutions and others were not excited about the challenge at all.

I really like this activity (largely inspired by Dan Meyer’s Wolverine poem about teaching math class) because my students do what mathematicians do. They look for solutions to problems without any type of machinery to work with. I didn’t tell my students to pick a value for x and then solve for y. Or to look at the graph and pull off points. Or to use the slope of the line to just keep moving up and finding new values. But they did all those things. Or some of them did. A few. Most them guessed wildly and that’s okay. Because that’s what real mathematicians have to do sometimes. Just guess wildly.

Things I will do better next time:

Scaffold more. This activity could have taken up the whole block and been really useful if I built up to -2x + 3y = 21 by first having x + y = 21 and then extending so they aren’t just trying whole numbers and then having them do x-y = 21 and so on, building up difficulty so that finding solutions themselves aren’t as much of a challenge. (At first, anyway. Later I do want it to be a challenge.)

Wrapping up as a class more. I did a poor job helping the group summarize as a whole until last block and even last block was not perfect.

No matter though, I plan to repeat the activity tomorrow and do exactly those things.

On a non-curriculum side, I feel I need to be careful because I keep finding myself looking forward to next semester and my new set of classes. I think I’ve gotten so tired and run-down that I’m starting to feel I’ll do better when I get a fresh start with new classes and can start from the beginning on classroom management. But I need to make it through this semester first and there are still plenty of instructional days left were I need my students to be learning. I am really looking forward to Thanksgiving break, I need it. I requested to use 2 of my personal days so I have some extra time to travel and get to Indiana, where I go to Thanksgiving every year. I’m really hoping those get approved, but they are right before a holiday and I am low man on the totem pole.

Thanks for reading.

 

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