July 5, 2016

Teaching Secondary Mathematics

I signed up for a grad course through Teacher Step (online courses at your own pace and you can get a free kindle!) and completed it over the past four days. The essays I wrote are about videos embedded in the course so those wouldn't be so interesting for you to read, but I also took some notes on the book Teaching Secondary Mathematics that I'd like to process, so you get to read them if you'd like to! The book is written for preservice teachers but it wasn't bad. I didn't yell at it and I snapchatted a couple references (teachers as professionals and a funny section about Gauss, I think, snapchats disappear which is both nice and annoying).

My first three notes say: plan, reflect, reflect more

Last year I did a nice job of making unit plans. I'd open a new document at the beginning of each unit and then make a list of topics and lesson ideas for the unit. As I progressed through the unit the ideas got sorted into numbered lessons. After I taught a lesson I sometimes wrote a note about a change to make the next time. These unit plans were quite lovely starting places this year. I wish that I had reflected (last year as well as this year) on lessons that went well in addition to noting changes to make. Question phrasing, timing, small things that are easy to remember from class to class over a few days but absolutely not within my ability to recall a year later.

"Direct instruction is defined as the teacher placing the highest priority on the assignment and completion of academic activities." (p. 7)

I thought that was a weird definition of direct instruction. There were others in the book but this one jumped out at me as a reminder - in education we don't have a clear, common language. When I say direct instruction and someone else thinks this is what I mean we're not even having the same conversation!

"Students should become aware of their own thinking process, strategies, and critical-thinking abilities." (p. 22)

Towards the end of the year I asked students to journal on "What do you know about how people learn?" and their responses were so uninspired I couldn't even share them. It made me realize that we don't spend enough time [in my district] talking to students about how they learn. I talk about strategies for learning particular things, but I would like to spend more time talking about learning in general. I think it would increase students' growth mindsets, increase their perception of math and help them learn. I did quarterly math practice portfolios last year, this year I'd like to include a survey on their attitudes about math (class) and a reflection on the quarter. It would be great to track growth throughout the year. (There's also a quote on p. 46 about journaling on attitudes toward math that contributed to this plan.)

Representatives from industry listed "mathematical expectations from the perspective of an employer and say employers want people who:

  • Are capable of setting problems up, not just following formulas. 
  • Know how to interpret the numbers or answers they get. 
  • Are aware of a variety of approaches for solving problems. 
  • Understand the mathematical features of a problem and can work in groups to reach solutions. 
  • Recognize commonalities of mathematics in different problems. 
  • Can deal with problems that are not in the format often presented in the learning environment. 
  • Value mathematics as a useful learning and work tool." (p. 25)

This list aligns with the practice standards but it might be interesting to share it with students as a slightly different perspective.

My evaluator told me that his goal for me this year is to find ways to explicitly teach group work skills. He suggested having my co-teacher and I model, but that's only going to get us so far. On pages 39-40 in this book they describe a protocol called "Scored Discussion."  It is similar to a participation quiz but only one group is working at a time. I found when I did participation quizzes students were not very engaged in the notes on the board (during or after the group work). But I don't love the idea of only one group working at a time. Here's my idea for a modified version: once a week we do a group worthy task and I tell one group ahead of time that they'll be presenting. However, I'm not interested in them presenting their solution, I want them to present their questions and conversation. Ideally I'd just sit near the group and take notes but in practice the group members will be responsible for doing that recording. Then, once everyone in the class has had some time to think (but ideally before they have all finished solving) I will have everyone pause to hear the progress the group of the week has made. We will list all their good student skills as well as their math skills. If they're stuck then other groups can chime in. Otherwise everyone can get back to work with a nice reminder of how to be a good group member and a few hints if other groups hadn't done the same thing. I know this isn't going to be something I'll love doing - I want students to jump into the math and be great collaborators - but I do think it would be something worth doing. And it doesn't sound so different from my usual flow that I'll drop it at the first sign of time crunch.

Kindle made this, including the page number, for me automatically every time I pasted a quote! Technology is so cool.
Rock, David; Brumbaugh, Douglas K.. Teaching Secondary Mathematics. Taylor and Francis. Kindle Edition.


  1. Out of curiosity, are you at Professional Licensure, and if so, did the TeacherStep course give you PDPs? I'm also in MA and thinking about a TeacherStep course and I'm wondering how smoothly PDPs might work.

    1. Some of the courses from TeacherStep only offer PDP's while others offer grad credits. I'm at professional licensure but taking grad courses to get all the way across the pay scale.

    2. MA offers PDPs for grad courses as well (I think it's 15 or 22.5 per credit). I don't know how they feel about online courses based outside Massachusetts.