The authors of Teaching Numeracy: 9 Critical Habits to Ignite Mathematical Thinking write:
"Playing Clue or Twenty Questions, reading Nancy Drew, and watching Scooby-Doo were a big part of our childhood memories. Why? Because we became part of the mystery. We collected all the clues, made our predictions, inferred from the implications, and became part of the action. We were reading the situation and actively reading the world." (pg. 53)
This description resonates with me and describes how I want my math class to flow. How awesome would it be if students could become part of the "story" in each class, uncovering clues, putting ideas together, and celebrating the ending with a mystery solved. I am pondering how to create this vibe, this environment, this structure!
Predicting, inferring, generating and testing hypotheses are all very closely related. Recognizing trends and using patterns are also related. And all of these activities are very much a part of the secondary classroom.
Always, Sometimes, Never are statements that allow students to justify thinking using prediction, inference, and testing hypotheses. Just this week I launched a
new website curating statements to be used for this purpose. They will make good classroom warm-ups, discussion starters, or assessment opportunities. Check out
the website, and please, help add statements. It is definitely a work in progress!
Collecting data to examine patterns is a great way to illustrate the relationship between the circumference and the diameter of a circle (pi), the relationship between the legs of a right triangle and its hypotenuse, or the values of a quadratic and the discriminant. I use this activity borrowed from a Holt textbook before introducing the discriminant:
Students graph the functions and complete the table. They talk together with partners about patterns they see and make conjectures. We discuss their ideas as a class, and then hopefully, explanations of the discriminant make more sense to them as we apply it to problem solving.
Several sites provide support for teachers wanting to develop this habit:
- Estimation 180: great for working on number sense. Students guess - make a prediction. The value comes in the discussion as students explain the evidence they use to support their inferences.
- Visual Patterns: the place to go for building understanding of patterning, for developing and testing hypotheses.
- Which One Doesn't Belong: perfect for examining patterns, making inferences.
- Graph of the Week: Awesome site for analyzing graphs, making inferences, recognizing trends!
Do you have a structure or routine to promote inferring, patterning, testing hypotheses in your classroom?
I started delving into Teaching Numeracy: 9 Critical Habits to Ignite Mathematical Thinking recently. The introduction caught my attention because I spent a chunk of my career in elementary school. There, much attention is given to teaching reading strategies to students like fix up strategies, thinking strategies, making connections and more. Authors Pearse and Walton take those ideas and apply them to math.
Yes, the book is written primarily for K-8 teachers. But strategies can often be applied to a wide range of audiences and I want to make connections from the book to my high school class!
Pearse, M., & Walton, K. (2011). Habit 1: Monitor and Repair Understanding. In Teaching numeracy: 9 critical habits to ignite mathematical thinking. Thousand Oaks, Calif.: Corwin Press. 
