First, I want to thank everyone for their kind words here and on Twitter about my last post. It made me feel like I am doing at least a few things right in my classroom this year.
This week, I was working with 7th graders on scale drawings, and I spent quite a bit of classtime working on a problem where we first scaled the sides and then found the area of the room and then we found the area of the unscaled room and then scaled and we found different answers (although we eventually found that if you square the scale and then scale the unscaled area, you end up with the same answer). I thought we had a good talk about this, but then a student asked me if their answer was right to another problem, and they had just multiplied the area and the used the scale, which we had literally just proven not to work. I was a good opportunity, though, to let her table partner explain why that didn’t work.
I also have recently realized that I have planned a lot of interesting problem based activities for my 6th and 7th graders, but ever since we started graphing in Algebra, I have found it hard to find good activities. I have also gotten some pushback, from students and parents, when we try thinking activities that I “haven’t been teaching them anything,” which I have tried to explain to both parties, but I can’t always get them to understand that my class will be a little different than what they have had previously. Because we were moving away from graphing for a little bit and into solving systems of equations, I thought it would be fun for them to explore finding the intersections of systems of equations. But that ended up more like pulling teeth. When I asked them how we might find where they had the same output and input, one student suggested making a function table and looking at the values. We had some good thoughts about what numbers to plug in (always start with 0 and see if the outputs are getting closer or further away) but when we realized that the answer to the first pair of equations was a fraction, the class got derailed again. We talked about graphing both lines, which would be a good suggestion if we could perfectly tell from a graph what fraction this might be, but unfortunately that wouldn’t work either. It took quite a bit of prompting to get them to think about setting equations equal to one another from slope intercept form. And then it became apparent how many of them we just not paying attention when I asked them to explore 5 pairs of problems for homework and I got comments that ranged from “what were the answers to the ones we worked” (I had already erased them) and “what do I do with the equations to find the answers” (which I refused to answer since we had spent a good 30-40 minutes working on just that). I also worry that there wont’ be actual thinking about this on their part and it will come down to asking their parents, reading something in the book, or just googling it, but there’s no helping that at this point. Oh well. I guess we will try again on Tuesday.
6th grade on Friday was a good time, though. We played single-step equation Bingo. They showed some great strategies. They still struggle with solving singles-step problems with fractions, so when we had those, many would copy them down and use time when they had an easier problem (such as 8x=8) making sure they got the correct answer or checking their answer to fraction problems.
After a tough week I was pretty bummed on Saturday morning and I was cruising Twitter looking for some guidance and and motivation. I would like to thank @brennemania for linking to Emergent Math’s excellent Problem Based Learning Starter Kit and helping me find some of that guidance and motivation. Reading this (as well as Dan Meyer’s Unengagables article linked to in this post) helped me realize that I wasn’t the only person struggling and that I could do good things if I kept trying. I feel like I need to bookmark both of those and read them once every couple of weeks to keep myself motivated. This is the biggest thing that has helped me since finding the MTBoS is support to pick me up when I am feeling down and the inspiration to try new things and learn from my mistakes. Thank you to everyone who I have interacted with here or on Twitter for helping me stay positive and giving me feedback on my teaching!