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.
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- 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 5: Predict, Infer, Recognize Trends, Use Patterns
What I liked most about this chapter (and actually the one that follows) is that it conjures up the image of a classroom of thinkers. The quote above (p 55) sums up a major issue with mathematics instruction in the United States–we don’t allow students to struggle.
Some of the most powerful research I have read relates to the cultural differences in the way we teach math in the United States compared with Japan and Germany. In 1995, as part of the Third International Mathematics and Science Study (TIMSS), Dr. James Stigler studied the instructional techniques of teachers in Japan, Germany, and the United States and documented the findings in his book, The Teaching Gap. He found that teachers in Japan expected their students to be confused and struggle, while teachers in the United States felt that if their students were confused then they hadn’t been clear in their explanations. In other words, struggle is not part of our teaching culture in the United States. I recently heard Dr. Yeap Ban Har speak about math instruction in Singapore, and one piece of information he shared drew gasps from the room. In Singapore, 20% of their standardized assessments are problems of a type students have never experienced before. Now THAT’S problem-solving!
The authors make a great point on page 56 about how important it is that learning is relevant to students. Something as simple as using students’ names in story problems can help draw them into the learning. It’s not that difficult to rewrite word problems using the students’ interests and names, but it can have a big impact. I watched a masterful teacher in my school last year do a Problem of the Day written about one of her students at batting practice (she hit 90 balls, 27 went over the fence and the rest stayed in the field). The students were so engaged and the little girl felt like a star! Not only was it a great math problem, but this teacher also exposed her students to an activity (batting practice) that many were not familiar with.
I was reminded that the purpose of the book is to “ignite mathematical thinking” when I read the passage on page 62 about modeling metacognitive self-talk. It’s so important that we model this type of behavior for students, because it is a learned behavior. Just as reading teachers “think aloud” when they are modeling what good readers do, we should be consistently doing the same in math.
Habit 6: Question for Understanding
“To maximize problem-solving, application, and the development of a variety of thinking skills, it is vital that we pay more attention to improving our questioning in mathematics lessons.”
The research could not be any more clear on the topic of questioning in mathematics, and the authors did a great job of listing and categorizing it (p 69-71). I always appreciate it when a book connects and spirals ideas, so here we see how questioning supports the previously discussed skills of monitoring and repairing and metacognition. The questioning ideas on pages 71-73 are gold! I, for one, will definitely be copying this page and keeping it close by. Dr. Yeap modeled a couple of very powerful questioning techniques that I would like to add to the list. The first technique was asking, “Your friend says that 8 + 6 = 14, because it’s like 10 + 4. Do you agree?”. The other was so simple, yet so effective. After giving him a solution he asked, “Are you sure?”. Right or wrong, he asked the question over and over. Even as an adult who was, I should say, pretty confident with my answers, I immediately looked back and checked over my work. And isn’t that what we want our students to do? I’m anxious to see if it works for them as well as it did on me! Finally, I loved the I Learned/I Wonder two-column notes idea on page 77. What a great way for students to summarize their thinking in their math journals!
So there’s my recap of the two chapters. What spoke to you?