The Standards of Mathematical Practice describe the “processes and proficiencies” that maximize students’ deep and lasting conceptual understanding in mathematics.
The first listed Standard of Mathematical Practice is “Make sense of problems and persevere in solving them.” The process of making sense of anything involves (a) evaluating it yourself first; (b) sharing your thinking with others; and (c) reflecting on your interactions with others to refine your thinking. Encouraging students to habitually think, share, and reflect serves them as both budding mathematicians and as problem solvers. The most effective strategy for successful implementation of this standard is to present ample opportunities for students to talk, talk, talk in your classroom. Discourse, particularly in small groups or with a partner, builds confidence and provides different mathematical views.
1. After presenting a problem and having students briefly think about it themselves, they discuss their solution pathway and accompanying reasoning with a partner. Their ideas may be validated or tweaked, but are always recognized.
2. As students solve the problem, allow them to seek advice and help from their partner. This builds a sense of confidence and teamwork.
3. After solving the problem, invite students to share their results and reasoning in small groups. This reflective practice allows students to revisit and justify their thinking, learn the approaches of others, and identify relationships between different solution pathways.
The mathematical practices are not standards taught in isolation. Think of them as the sauces that blend into every content “dish,” adding flavor, interest, and relevance.