Glad to see you’re back for more great math discussions!
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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.
- 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 7: Summarize, Determine Importance, Synthesize Using Note Taking and Journaling
“Writing shifts the responsibility for learning away from the teacher and toward the students by encouraging personal learning”
As the authors note early on in the chapter (p 79), the three skills discussed in this chapter–summarizing, determining importance, and synthesizing–have “the power to force students to own their mathematical thinking and be able to take it with them into the real world.” Of course, these are not skills that only support math learning. In fact, they might be more often thought of as language arts skills.
Although we don’t use textbooks for math instruction on my campus, I have used the textbook scavenger hunt idea with science texts in the past, and I think it’s a great way to introduce students to the features of a nonfiction text.
Likewise, because we are an elementary campus, we don’t do much note-taking. When I’ve seen it in the classroom, it has most often taken the form of the Interactive Cloze System described on page 86. The teacher prepares an anchor chart prior to the day’s mini-lesson, with blanks in place of keywords and phrases. Students have a printed copy of the same anchor chart. Students interact with the teacher during the mini-lesson to fill in the missing words. After the mini-lesson, students glue their completed work into their math journals. I’m curious to hear what other elementary teachers say about note-taking.
From note-taking, the chapter moved on to journaling. Journaling is huge, in my opinion, and should be an ongoing part of math instruction at every grade level. I particularly liked when the authors referred to the concrete, representational, abstract sequence of instruction (p 92) and the way that math journals can be used to move students from the concrete to the representational and abstract. It’s so important that those stages overlap, and journaling is the perfect way to connect them.
The authors addressed and dismissed the elephant in the room–the time required for journaling–by citing research that journaling can help reduce the need for review and reteaching (p 93). I think that underscores the fact that when students put their thoughts in writing, they “clarify their thinking, and as they write, they expand their knowledge of the math.” (p 92). In other words, learn it deeply the first time around and you won’t need to review and reteach.
I loved the sentence starters on page 96, because students often just don’t know where to start to put their thoughts in writing. And, I think, teachers can fall into a routine and overuse certain prompts. I knew Margie wouldn’t mind, so I took the liberty of creating a poster with some of the prompts. Like the Math Fix-Up Tools from Habit 1, I also made a smaller, B&W version students can glue in their journals. Grab the writing prompts poster here.
If you are not using exit tickets in your classroom, be sure to read pages 96-97 and give them a try. They are a quick, easy, and extremely powerful formative assessment tool. Once you have the stack of exit tickets, you can easily sort them to create your small groups for the next day’s instruction. You don’t need fancy forms for the exit tickets–plain index cards work great.
While there were many practical activity suggestions offered on pages 98-101, my favorites were the 3-2-1 Journal Entry (p 98) and having students Compose Problems (p 99).
I have used the 3-2-1 format with adult learners in professional development sessions, but I like the idea of using it with students. I also like the suggestion provided for changing up how to use the 3, 2, and 1 (examples of learning, nonexamples, ways to tell the difference).
An activity I have used extensively is what I call You Write the Story, which is a fancy name for having students compose problems. You give the students an equation, such as 24 x 6 = ?, and they must write a story problem that can be solved using the equation. This is a VERY difficult activity for some students and takes a great deal of modeling, but it really does shine a spotlight on their understanding of the operations. You can easily differentiate the activity by using larger or smaller numbers; different structures, such as 68 + ? = 133; and even two-step equations, such as (24 x 6) – 32 = ?.
Check out this post from Mr. Elementary Math for some great question prompts!