Beliefs about Teaching and Learning Mathematics: Unproductive Productive Beliefs Current Beliefs Action to Take Beliefs Mathematics learning Mathematics learning should focus on should focus on practicing procedures developing and memorizing basic understanding of number combinations. concepts and procedures through problem solving, reasoning, and discourse. Students need only to All students need to learn and use the same have a range of standard computational strategies and algorithms and the approaches from which same prescribed to choose in solving methods to solve problems, including, but algebraic problems. not limited to, general methods, standards algorithms, and procedures. Students can to Students can learn apply mathematics only mathematics through after they have exploring and solving mastered the basic contextual and skills. mathematical problems. The role of the teacher The role of the teacher is to tell students is to engage students in exactly what tasks that promote definitions, formulas, reasoning and problem and rules they should solving and facilitate know and demonstrate discourse that moves how to use this students toward shared information to solve understanding of mathematics problems. mathematics. The role of the student The role of the student is to memorize is to be actively information that is involved in making presented and then use sense of mathematics it to solve routine tasks by using varied problems on strategies and homework, quizzes, and representations, tests. justifying solutions, making connections to
Beliefs about Teaching and Learning Mathematics: Unproductive Beliefs Productive Beliefs Current Beliefs Action to Take Mathematics learning should focus on practicing procedures and memorizing basic number combinations. Mathematics learning should focus on developing understanding of concepts and procedures through problem solving, reasoning, and discourse. Students need only to learn and use the same standard computational algorithms and the same prescribed methods to solve algebraic problems. All students need to have a range of strategies and approaches from which to choose in solving problems, including, but not limited to, general methods, standards algorithms, and procedures. Students can to apply mathematics only after they have mastered the basic skills. Students can learn mathematics through exploring and solving contextual and mathematical problems. The role of the teacher is to tell students exactly what definitions, formulas, and rules they should know and demonstrate how to use this information to solve mathematics problems. The role of the teacher is to engage students in tasks that promote reasoning and problem solving and facilitate discourse that moves students toward shared understanding of mathematics. The role of the student is to memorize information that is presented and then use it to solve routine problems on homework, quizzes, and tests. The role of the student is to be actively involved in making sense of mathematics tasks by using varied strategies and representations, justifying solutions, making connections to
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