Wow! Are we off to a great start or what? What amazing comments you all contributed to our discussion of the Preface and Introduction last week! Each week, I’ll provide links to all previous posts, so any time you happen to wander across the book study you can jump right in.
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If you’re just joining us, we’re reading and discussing Teaching Numeracy, 9 Critical Habits to Ignite Mathematical Thinking, by Margie Pearse and K. M. Walton Let’s dive right in and look at the first two critical habits!
- Preface and Introduction
- Critical Habits 1 & 2
- Critical Habits 3 & 4
- Critical Habits 5 & 6
- Critical Habit 7
- Critical Habits 8 & 9
- Essential Components 1, 2, & 3
- Essential Components 4 & 5
Habit 1: Monitor and Repair Understanding
“When we monitor our comprehension in literacy, we pay attention to whether or not we are understanding what we are reading. The same must happen in a mathematics classroom.”Raise your hand if this is what you see happening in your mathematics classroom. What? I don’t see any hands raised, and it’s not just because I can’t actually see you Ha ha. How could something so simple and common sense have eluded mathematics instruction for so long? I know I hear language arts teachers reference “fix-it” strategies all the time, and anchor charts outlining them are a staple in language arts classrooms. When I saw the list of mathematics “fix-up tools” on pages 11 and 12, I immediately saw the power of teaching these strategies to our mathematicians. With Margie’s permission, I created a Math Fix-Up Tools poster you can download here. There are two versions–one that would be great for a poster and another, smaller B&W one students can glue in their math journals. Just remember it’s not enough to just put up a poster. You have to model, model, model!
Another thing I loved in this chapter was Margie’s narrative about the Working Answer Keys (p 15) and how she used them to improve the homework routine in her classroom. This past year I helped a 3rd-grade teacher implement a new homework process that allowed students to discuss their homework with another mathematician (student) in the class. The teacher then chose one mathematician to share his or her work on the document camera. The mathematical discussions the kiddos had were incredible! We also saw an improvement in the homework completion rate, because students who didn’t do their homework didn’t get to share in the mathematical discussions, and they did not like that at all. I could see that adding the Working Answer Keys would make the process even more effective.
Habit 2: Develop Schema and Activate Background Knowledge
“When a student feels that math is too hard or they can’t do it or they don’t understand it or everyone else gets it but them, you’ve lost him or her. Letting students consciously identify what they already know increases confidence and engagement.”
As soon as the authors made a connection between activating prior knowledge and making mathematics accessible to all students, they had me hooked, and I began looking at it from a whole new perspective. I know that in my own classroom, it was often “…a luxury to be considered only if time allows” (p 20) and not something that I consciously built into every lesson. So I guess I proved their point! Connecting the idea of developing background knowledge to something I’m already passionate about definitely made the learning more meaningful to me. I will be placing more emphasis on building background knowledge from here on out.
I noticed that the Key Ideas (p 20-22) included references to the concrete, representational, abstract (CRA) sequence of instruction, and I was positively giddy to see the authors state that manipulatives are for all grade levels, not just the primary grades. When we rush students through the concrete and pictorial stages, or skip them altogether, we do them a huge disservice. One argument for not using manipulatives more often is lack of time, but how much time does it take to remediate students with no conceptual understanding?
There are so many great ideas in these two chapters, and I can’t wait to read the rich discussion that is certain to take place. Remember, this is an interactive discussion! Feel free to participate either by posting your own response to the reading or by replying to the comments of others.