I'm struggling to find time to write thoughtful posts. But I am taking pictures. Here's some fun shots of our Ball Drop experiment in Algebra 1.
This past summer, I was honored by the Colorado Council of Teachers of Mathematics as the 2017 Outstanding Secondary Mathematics Teacher for Region 2. One for each region of the State. I didn't post this in September when it happened, because, honestly, it felt really weird to have people congratulating me. And then life showed up and it got lost as it moved farther down the 'to do' list.
I spent some time this past week reflecting on 2017. While going through my journal I was reminded of this wonderful little event. Part of my desire for this next year is to celebrate more. This is my first attempt.
My school district even gave me a shout out on Twitter:
I'm very thankful to all of the wonderful educators I've worked sidebyside with over the years and those who I've had the pleasure of interacting with online through the #MTBoS. Thank you for your kind words, your wisdom, your patience, and your friendship. I'm so very humbled that I get to be on this journey with such quality people. Without a doubt, I'm a better teacher because of your encouragement to try new things and to fail early and often. You all are the best! I truly believe we are better together. Always. I spent some time searching for a card matching exercise for exponential functions. I found a couple but none that did exactly what I wanted them to do. Rather than spending an hour searching for what I wanted, I spent an hour and made it. Although, to be real, I'm not sure what I made is what I wanted either. I plan to use it early next week. Students match percent growth and percent decay equations, graphs, descriptions, and tables. Not every function has a description or a table. I thought I'd cut down on the process of elimination solution method. I also included some function forms students would probably not be familiar with yet but I would like them to take a stab at looking at the form of the function and guessing what the matching graph might be like. I've included the files as both a pdf and word doc.
Update: I added an extra page with recursive definitions of most of the functions... just in case you want to add the extra step of complexity!
With systems of equations, I tried something new for review. Instead of doing the normal routine of making a review assignment and then having students solve it, and then having the students who don't do the assignment be the ones who need to do it the mostI had students make their own review assignment. Hey, why not? Here are the directions I gave to the class (link to Google Doc here):
Here are the sections we covered this chapter: 61: Graphing Systems of Equations 62: Substitution 63: Elimination using Addition and Subtraction 64: Elimination using multiplication 65: Applying systems of Linear Equations 66: Systems of Inequalities At first, there where the obligatory moans from the classroom when I introduced the assignment. But, when I told them they only had to create 6 problemone from each of the sections for the chapterthe mood changed. Don't get me wrong, they didn't cheer or anything, but I did have buyin from most of the class. When students asked me what a certain section was about, I directed them back to their textbook. I have both an inclass set and we have online pdf's so access should be an issue. Students checked their 'correct' solutions using Desmos. I appreciated how much this pushed students to understand the mechanics of solving systems of equations on a deeper level. It's one thing to use an algorithm. It's another to intentionally break the algorithm and see what you get when you break it. Sadly, this assignment didn't fix the problem of students who really really need to work on the assignment not doing the assignment. I guess if I had the magic fairy dust to fix that, I would be a very rich man. If I had to change one thing about this task next year, it would be that students didn't really know what I expected of them; there was some confusion as to what the end product might look like. So, I took pictures of this year's work to show to next year's students. I can usually go through the pictures without saying a word. Students start to get a pretty good intuition about what 'good work' versus 'bad work' feels like. This looks nice. This... doesn't look as nice. Here's some examples of studentcreated practice tests. I've included four different levels: the "Oh my goodness, can I frame this?" the "Good attempt but struggles with organization" the "I appreciate how much effort you put into this but it took me some time to figure it out", and the "Can you walk me through this, please?" Excellent Work: Good attempt but can use a little more organization to help the reader understand what's happening: Solid Effort: Can you walk me through this, please?: Thanks to Dan Greenberg for the idea!
I'm starting my second real book on formative assessment. I finished Embedding Formative Assessment by Wiliam and Leahy. Now I'm starting The Formative 5 by Fennel, Kobett, and Wray. Something I've noticed about both books: neither one suggests using warmups as a researchbacked strategy in the classroom.
I'm thinking about dropping them. Granted, I've only done them for like 3 months but I'm frustrated. My actual problem is that I can't fit everything into a lesson I want to fit in. I want to: i) have a discussion about a warmup ii) check and go over questions on the previous night's practice work/homework (quick stat: 8090% of my students do the homework on any given assignment) iii) teach an interesting lesson/investigation/experiment/whatever iv) and to top it all off, have students complete an exit ticket As it turns out, that's too much to pack into one day. I talked this out with one of our district middle school math coaches (Dan Greenberg) yesterday. He's like a ninjamatheducationguru. It's awesome. After turning my questions back on themselves several times, he helped me figure out that warmups are the least productive of the options I want to pursue. Rather than trying to spiral in old ideas, or bring up Visual Patterns, or Which Ones Don't Belong, or whatever other good 'extra' things I want to do in a day, maybe I could use problems from the previous night's homework as a launch for group discussions. It would help students see the value in doing the homework. It would be a natural tie in of the previous day's work to what we would be looking at today. And it would help me better understand what my students do and don't understand about what I'm attempting to teach. Those other things are totally cool, I simply need to plan time for them rather than trying to shove them into an already full plan for a day. So, I'm thinking about letting something good go. I spent days pulling together what I believe is an allstar cast of warmups to use in Algebra 1 this year. It's hard. This is my second attempt at a D.I.Y. iPad document camera stand. The height is adjustable via the screw at the back of the post. The leg towards the bottom of the picture is extended from the post to allow the iPad camera to center over the object better. I created a swivel to allow it to turn into an iPad tripod. I use it to take video in my classroom. Mostly, this ends up with me taking video of an experiment so my students can get better measurements. Here, my students are taking video of the experiment. Did Barbie hit the ground or not?! Instant replay. Here's a screenshot of the iPad video. Not too shabby. And, it's collapsible! I've added to a previous post to create some detailed instructions here, if you're interested.
This is the second in a series of posts about formative assessment using some of the tools outlined in the book Embedded Formative Assessment by William and Leahy. The first post is here.
No Hands Up, Except to Ask a Question AND Rough Draft Thinking Every teacher intimately knows the problem of only 4 or 5 kids raising their hands to answer questions. This is meant to address that problem. I want to know what every student is thinking not just 4 or 5 of them. Rather than asking the entire class a question and then calling on students that raise their hands, I've moved to calling on students based on a set of cards for the class. Before every class I shuffle the cards. When I ask a question, students put their hands up but I remind them that I'm only calling on students with the cards. By no means is this a new idea in education. I tried it in my first couple years of teaching and it went very poorly. Students felt uncomfortable with me putting them on the spot let alone without knowing how to do the problem. Add on top of that my inexperience as a young teacher who still struggled with classroom management, along with my inability to foster a productive classroom conversation, and you had a recipe for disaster. This time things went incredibly well! What went differently? Rough draft thinking. Last year, as a school, we worked on writing across subjects. When I sat down with the English and History teachers and heard them talk about the significant revision process in their classrooms I was struck by how different the math classroom tends to be. We want our math students to try new ideas and embrace failure as part of the learning process but we only take their first answer as either right or wrong. Based on that conversation I attempted to shift classroom culture to embrace the revision process by talking about rough draft thinking. When I ask students to do something, I don’t expect them to do it correctly the first time. Nowhere else in life do we expect that. We expect that our initial attempt will be riddled with problems but at least it’s a starting place. It’s now part of the mantra in our classroom. I expect students to be kind and to be brave. Because I’m going to call on students using the cards, I need them to be brave. I’m expecting them to present their rough draft thinking. It’s nerve racking to present information when you feel very unsure of yourself and you know it’s probably incorrect. That’s okay. That’s the expectation. I expect you to present something that will be a starting point for our classroom conversation not the ending of it. For the rest of the class, I need you to be kind. There can be no laughing, or snickering, or giggling. At all. It doesn’t really matter whether it’s directed at the presenter or not. The presenter will feel like it is. We will honor each other’s ideas and critique them with care. If you're the one who yells out “That’s stupid!” I will ask you to leave without any questions asked. Can we agree on this together? Everyone nods their heads. This has gone incredibly well! The level of discourse in my classroom has been phenomenal. In late August, I had students taking chances and buying into my narrative of what a math classroom could look like that normally doesn’t happen until sometime in November. There has been zero push back on me calling on students who don’t know the answers. None. I can’t believe it. When a student doesn’t know what’s going on, I ask them to give a starting point for the conversation. How might they approach the problem? What information do they see that might be relevant? IDK isn’t an option if you’re called on. You have to help the class move forward somehow. I don't know who I borrowed the rough draft thinking idea from, but if it's you, thank you! I do know that Amanda Jansen (@MandyMathEd) is doing some great work in this area. We've officially been in school for one month. That means I'm one month into my push into formative assessment. My current resource is Embedding Formative Assessment by William and Leahy. I really appreciate the tone as well as the content of the book. Sometimes when you read education books by professionals it feels condescending or guilt ridden. That's not my experience so far. On a side note, I've not written in a book this much since grad school. I'll post my notes on the book sometime later. Because I have to start somewhere, I'm pulling most of my initial strategies from this book. I have a note in the margin of page 95 that says, "This pageandahalf could be my entire year of implementation".
My goal is to implement a couple of formative assessment strategies every month. This month I've tried to implement 3 of them. Well, 4, if you count attempting to be consistent in posting learning targets. I plan to split this up into separate posts, otherwise, I’ll never end up hitting ‘submit’. 1) WarmUps This really isn't much of a formative assessment strategy by itself. When I first started teaching, I used it to keep the kids busy while I took attendance and got myself ready to rock and roll. I never did much with the information I got back from the students. A couple of years (more than a decade) later, things have changed. Now, instead of trying to give myself a chance to breathe or stave off discipline problems, this is about attempting to fill in gaps in my students knowledge, keep major ideas and skills fresh, and generally push students towards deeper thinking regarding topics they’ve already seen. I could probably keep the list going for another paragraph or so. Quick little aside on this being selfserving: I'm hoping this will end my issues with students not knowing how to create a line from two points come the end of May when we spend almost 3 months on linearity at the beginning of the year. If I’m honest with myself about warmups right nowI hate them. I love what they look like in class but the amount of time warmups take is unreal. I need to figure out a way to do this quicker. Do I have a classroom conversation about the material or don't I? What's the point of having a problem in class if we don't interact over it? How do I know how well my students understand the material without having a conversation about it? But warmups always seems to take 10 minutes! That's 1/5th of my class. It'd work better if I only did warmups a couple of times a week but I don't know how to make it into a rhythm if it doesn't happen normally. Maybe I can pull back on it after another month or so. Breathe in. Breathe out. I keep reminding myselfI need to go slow to go fast. I just don’t know that I believe it every day. If you’re interested in what I’m working with, I stole a bunch of stuff from the #MTBoS and decided to compile them in different Google presentations. Whatever the slide deck I’m using for the day, when I create it, I copy a slide from one of the warmup files and put it in the daily presentation. Here’s my current treasure trove. 
Andrew Busch
I teach Math and Programming at Summit Middle School in Boulder, CO. Categories
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June 2018
