Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. They monitor and evaluate their progress and change course if necessary. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They analyze givens, constraints, relationships, and goals.

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. The second are the strands of mathematical proficiency specified in the National Research CouncilвЂ™s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and oneвЂ™s own efficacy).Д¬8 1 Make sense of problems and persevere in solving them.

The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. These practices rest on important вЂњprocesses and proficienciesвЂќ with longstanding importance in mathematics education. The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students.

Standards for Mathematical Practice Print this page

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