A mathematics lesson, be it in kindergarten or in high school, should be an opportunity to develop mathematical thinking and logical reasoning. Over time, students may forget theorems, procedures, and definitions (especially if they don’t pursue mathematics-intensive careers) but they will benefit from the higher order thinking and gymnastics of the mind cultivated in mathematics. Below are five pointers I share with teachers, in my sessions, and in my books. I hope they will help you orchestrate rich exchanges.
Believing:
No strategies, routines, or activities will work without teachers’ belief that all students, regardless of color, creed, age or gender are capable of sophisticated mathematical thinking and that their thinking is worthy of attention. That is my fundamental premise.
Starting:
Whether teaching addition, fractions, rates of change, or volumes of revolution, start the lesson by inquiring about students’ prior knowledge. Students are not blank slates; they have ideas. List them on the board, refer to them, and build on them. Qualify strategies using student names. Students will have a real sense of participation in the lesson development.
Revoicing:
We often respond to students’ answers with “Yes!”, “Not quite!”, a smile, a frown, etc. Revoicing a response with neutrality and without injecting our own thinking, positions students in relation to one another, facilitating debate and fostering argumentation. Add a verification such as “Is that what I heard?” or “Is that what you mean?” then invite others to react and discuss.
Probing:
Probe students’ reasoning behind correct answers, not only incorrect ones. It sends the message that cultivating correct mathematical thinking is as important as getting the right answer, if not more so! A right number is not transferable to another problem but a sound strategy is a powerful tool to be used repeatedly.
U-turning:
Notice your reaction to a student’s question. Does it often lead to a dialogue, between you and him/her, while others grab the chance to talk? Try u-turning questions back to the class, inviting others to engage: “What do you think?”, “Who can enlighten us?”, “How could we find out?” It prolongs the productive struggle a bit more!
