Process Standards for School Mathematics
MMSD has adopted the following five NCTM Process Standards for School Mathematics (PSSM, pp. 52, 56, 60, 64, 67) which align with Wisconsin Model Academic Standard A: Mathematical Processes, 1998 (p. 4):
Students in Wisconsin will draw on a broad body of mathematical knowledge and apply a variety of mathematical skills and strategies, including reasoning, oral and written communication, and the use of appropriate technology, when solving mathematical, real-world, and non-routine problems.
In order to participate fully as a citizen and a worker in our contemporary world, a person should be mathematically powerful. Mathematical power is the ability to explore, to conjecture, to reason logically, and to apply a wide repertoire of methods to solve problems. Because no one lives and works in isolation, it is also important to have the ability to communicate mathematical ideas clearly and effectively.
In grades 6-8 all MMSD students will develop and apply the following mathematical processes continuously through their development of content knowledge:
PROBLEM SOLVING—The student will develop problem-solving abilities (WMAS A.8.3)
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to build new mathematical knowledge;
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by analyzing problems that are routine and non-routine;
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by applying and adapting a variety of appropriate strategies (illustrating, guessing, simplifying, generalizing, shifting to another point of view, etc.);
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by monitoring and reflecting on the process of mathematical problem solving.
REASONING AND PROOF—The student will develop reasoning abilities
(WMAS A.8.1, A.8.2)
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to make and investigate mathematical conjectures and proofs;
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to evaluate information, mathematical arguments and proofs;
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to perceive patterns;
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to identify relationships;
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to formulate questions for further exploration;
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to evaluate strategies;
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to justify statements and defend work;
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to assess reasonableness of results.
COMMUNICATION—The student will develop written and oral communication skills
(WMAS A.8.2, A.8.4, A.8.5)
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to organize and consolidate mathematical thinking;
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to explain mathematical thinking coherently and clearly to peers, teachers, and others;
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to analyze and evaluate the mathematical thinking and strategies of others;
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to use the language and conventions of mathematical discourse (e.g., symbols, definitions, labeled drawings, and labeled answers) to express mathematical ideas precisely;
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to formulate logical arguments that clearly show why a result makes sense.
CONNECTIONS—The student will develop connections
(WMAS A.8.6)
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between prior knowledge and new knowledge;
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between and among mathematical ideas;
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to understand how mathematical ideas interconnect and build on one another to produce a coherent whole;
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to recognize and apply mathematics in contexts outside of mathematics.
REPRESENTATIONS—The student will create and use mathematical representations
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using technology;
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including tables, graphs, equations, drawings, charts, physical models, symbolic representations, and verbal descriptions;
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working fluently among tables, graphs, equations, drawings, charts, physical objects, symbols, and verbal descriptions;
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to organize, record, and communicate mathematical ideas;
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to model and interpret physical, social, and mathematical phenomena.
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