Minds on Mathematics - Ch2, Tools {Book Study}

Speaking of tools, I'm super duper excited about my new pencil sharpener! 

Maybe you've seen the Classroom Friendly Pencil Sharpener! It's not quiet like I've seen some sites suggest, but it definitely gives the sharpest point on a pencil that I have ever seen! I lucked up and found this baby on a teacher swap site for 10 bucks! 

Once I bought it, I knew I had to make cans for sharp and dull pencils. I got the labels from Donna @ Peace, Love and Learning and the polka dot pails from the clearance aisle at Walmart.

Okay, on to the tools referenced by Wendy Hoffer in Chapter 2 of Minds on Mathematics

These tools are "practices, skills, and strategies best suited for support learners" (Hoffer, p.21). And we, as teachers, must "explicitly offer instruction on these processes with the context of content learning" (p. 21).  More specifically, these tools are:
  • Common Core Standards of Mathematical Practice
  • 21st Century Skills
  • Thinking Strategies

Hoffer opens the chapter with asking a student how he approaches a word that is unfamiliar when reading. The students offers a slew of strategies to figure out the unknown word. When presented the same question in a math problem, the student only knows to start over. Hoffer sass we have to teach students strategies that are transferrable to new situations...encouraging students to develop understanding. 

In the next few pages, Hoffer shows what teaching the processes may look like in the context of the minilesson, work time, and reflection. Using the process standards from the Common Core, there are explicit examples of how to teach students to think. While it is plainly spelled out, we still have to figure out what that looks like for us. I teach in Texas, one of the few states that has not adopted Common Core, but I still found pages 22-23 helpful and I think many of the examples provided are great ways to teach students to think and process material. I can see how creating opportunities for discourse, scaffolding students' independence, allowing ample work time, modeling precision, and welcoming many approaches (just to name a few) can encourage thinking and problem solving.

Still...I see these words and I think I know what they mean in the context of a math lesson, but it really takes planning. While thinking comes naturally for me, it may not for my students. It is hard for studnets to know the thinking that goes into solving a problem unless I explicitly tell them. It's hard to do this "think-aloud" strategy, but it is crucial for students to hear the process going on in my mind. Otherwise, I am just solving a problem and students know none of what went into it other than the steps they see on the paper.

I appreciated the next section on thinking strategies, which really paired down on the plethora of examples provided in relation to Common Core and 21st century skills. Thinking strategies have come from reading research and proven to be helpful across content areas when students are trying to make sense of new information. These thinking strategies are:
  • asking questions
  • determining importance
  • drawing on background knowledge
  • inferring
  • making mental models
  • monitoring for meaning
  • synthesizing
On page 27 is a great chart with definitions of each and what students and teachers may say that would use the particular thinking strategies.
...if we take seriously the imperative that students need tools for independent problem solving, not just answers, these three lists [Common Core Standards of Mathematical Practice, 21st Century Skills, and Thinking Strategies] offer us a wonderful array of implements we can hand over to learners as tools to assist them in leveraging student understanding of content for themselves. (p. 29)
We have to teach students the strategies so that they can select and use them as needed. The lesson plan template I referred to making in my review of Chapter 1 has just expanded. Not only do I need to be thinking about what the teacher will do and what students will do, but now what thinking strategy I will offer and how that will be taught. I see this as a "yeah but" and Hoffer states that we don't have to do it all at once. Just consider one math standard at a time and one thinking strategy that can be paired with it when you teach it. Seems feasible to me...I need to not only teach the math concept, but a thinking process that students can use on their own as problem solvers.

Want to read what other teachers think about this book?
 Check out the book study link-up hosted by Sherrie @ Middle School Math Rocks!
Minds on Mathematics Book Study

1 comment

  1. I am really seeing that Minds-on Math workshop is really about purposefully planning out your lessons in advance. Think about teachers who just skim over the lesson and then attempt to teach it. We have Carnegie Learning as a curriculum and it was really important for me to work through all the problems in advance and see where the students would struggle (because if I struggled then they for sure would). We need to really front load our lessons with the skills and strategies we want to model for our students to make them better mathematicians. I am really enjoying the book and so glad you have yours now. Thanks for sharing your thoughts.