• Do I believe there is a spectrum of flexible predispositions which people hold with respect to further developing their math proficiency, their math self-identity, their math curiosity, etc.?
• Do I reinforce respectful listening and sharing in a safe environment?
• Do I have students set goals for themselves and self-monitor their progress?
• Do I avoid competition and timed tasks because I recognize that speed does not equate to fluency?

Math manipulatives are physical objects students can use to better understand abstract mathematical concepts. Students from all grade levels can benefit from the use of physical and virtual manipulatives in math instruction.

• Do I have students share their understanding of a concept before I share mine?
• Do I use my students’ responses to determine future lessons, strategies and content presented?
• Do I plan activities that allow students to experience contradictions to their current understandings and then discuss their new learning?
• Do I allow wait time when asking questions?
• Do I encourage students to show initiative and autonomy in their work?

• Do I model learning from errors?
• Do I demonstrate confidence and respect in my students’ abilities?
• Do I avoid praising a correct solution or displaying excitement over an interesting idea?
• Do I expect students to persevere to solve mathematical problems?
• Do I provide hints but not solutions?
• Do my responses encourage the students to keep thinking?
• Do I focus on the process, using a “wrong answer” as an opportunity to learn?

Peter Liljedahl’s research² and work with thinking classrooms promotes active student participation and engagement while working collaboratively on well-designed tasks that include a productive struggle. The teacher’s role is to establish a positive environment where students are encouraged to engage in struggle and collaborate, and creativity is both celebrated and required.

Interactions between students and teachers can impact student achievement. Meaningful feedback, mathematical mindset messages and positive relationships contribute to the success a child will experience. When these relationships include an opportunity to fail, an opportunity to struggle, an opportunity to contemplate, and an opportunity to celebrate success, a student can develop important skills in math including problem solving, collaboration, creativity, and persistence, among other important traits and behaviours.

“Respect is more than tolerance and inclusion – it requires dialogue and collaboration.” 8 Ways: Aboriginal pedagogy from Western New South Wales. Dubbo, NSW, Australia: The Bangamalanha Centre (2012)

• Do I ask open-ended questions?
• Do I encourage students to ask questions of each other?
• Do I expect students to explain all their answers, regardless of whether the answer is correct?
• Do I model listening attentively to all answers?
• Do I use group or whole class discussions to determine whether an answer is correct (rather than being the authority)?
• Do I model respect for multiple strategies for solving a problem?