This week we finish up the final two critical habits.
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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 8: Develop Vocabulary
“Understanding the language of math gives students the proficiency they need to think about, confer, and integrate new math concepts as they are presented.”
Academic vocabulary is difficult for all students, and it is particularly hard for ELL students, making this an important chapter. I liked the idea of helping students form Vocabulary Habits (p 103), because our goal is for students to become more independent learners. Unfortunately, many students don’t get past the first habit–identifying when understanding has broken down and realizing they have to do something to move on. The authors made a great point that teachers need to plan think-alouds to show students what the habits look and sound like in practice. The whole idea of teacher think-alouds in math instruction has been a recurring theme throughout this book. I think this practice is so much more common in reading instruction, and math teachers have yet to tap the power of this instructional practice. If we want students to develop their own vocabulary habits, we need to model and teach the habits.
The second bullet on page 105, about words that have different meanings in math than in regular conversation, caught my attention. I attended a vocabulary session with Christine Moynihan, author of Math Sense, at CAMT, and she talked about this very thing. Words such as right, plane, and reflection have more familiar meanings unrelated to math. She also pointed out that even within a math context, some words have multiple meanings. Words such as round, square, and second. The list under Be innovative in your vocabulary instruction on page 107 is extremely comprehensive and will be a valuable planning tool. The second bullet, Use the words in your own speech, requires teachers to develop habits of their own! First and foremost, we need to be precise in our own mathematical language. It is a sum or a product, not an “answer”. Consider having someone videotape one of your math lessons and analyze your use of language as you view the video. Videotaping can seem very awkward at first, but it is a great reflective tool and no one needs to see the video but you!
Habit 9: Collaborate to Learn
“When collaborative moments are built into your lessons, your students will learn to appreciate each other’s thinking.”
For me, the true gold in this chapter came on page 118 with the statement, “True collaboration is not what some consider to be ‘group work'”. Amen! You can probably put this into the context of your own work experiences. Many teams do team planning, yet not all team planning would be described as truly collaborative. As the authors point out, true collaboration requires planning, the establishment of community and group norms, and an equal commitment from all members. True collaboration is difficult for adults, so I’m sure we realize how much support students will need to effectively collaborate.
If you are not sure if your instructional style is fully supporting student collaboration, you might use the list of key ideas on pages 121 and 122 as a reflective tool by turning each statement into a question and rating your answer using a scale. For example:
- Have I arranged my desks so that students can easily talk and listen to each other?
- Do I encourage students to generate questions and direct their questions to the rest of the class, not simply to the teacher?
- Do I maintain an atmosphere of acceptance and freedom?
You will probably find that you are already doing many things to foster collaboration in your classroom, but you might find a couple of new ideas as well.
And Now for Something Completely Awesome and FREE!
Greg Coleman, aka Mr. Elementary Math, was inspired by the question prompts in Habit 6, and he created this amazing set of questioning prompts. Click here to head over to his blog and download them! Thanks so much, Greg. You are one talented dude!
Please add your thoughts about these two chapters in the comments!