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1. Knowledge of Mathematical Problem Solving. Candidates know, understand, and apply the process of mathematical problem solving. Indicators 1. Apply and adapt a variety of appropriate strategies to solve problems. 2. Solve problems that arise in mathematics and those involving mathematics in other contexts. 3. Build new mathematical knowledge through problem solving. 4. Monitor and reflect on the process of mathematical problem solving.
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2. Knowledge of Reasoning and Proof. Candidates reason, construct, and evaluate mathematical arguments and develop an appreciation for mathematical rigor and inquiry. Indicators 1. Recognize reasoning and proof as fundamental aspects of mathematics. 2. Make and investigate mathematical conjectures. 3. Develop and evaluate mathematical arguments and proofs. 4. Select and use various types of reasoning and methods of proof.
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3. Knowledge of Mathematical Communication. Candidates communicate their mathematical thinking orally and in writing to peers, faculty, and others. Indicators 1. Communicate their mathematical thinking coherently and clearly to peers, faculty, and others. 2. Use the language of mathematics to express ideas precisely. 3. Organize mathematical thinking through communication. 4. Analyze and evaluate the mathematical thinking and strategies of others.
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4. Knowledge of Mathematical Connections. Candidates recognize, use, and make connections between and among mathematical ideas and in contexts outside mathematics to build mathematical understanding. Indicators 1. Recognize and use connections among mathematical ideas. 2. Recognize and apply mathematics in contexts outside of mathematics. 3. Demonstrate how mathematical ideas interconnect and build on one another to produce a coherent whole.
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5. Knowledge of Mathematical Representation. Candidates use varied representations of mathematical ides to support and deepen students’ mathematical understanding Indicators 1. Use representations to model and interpret physical, social, and mathematical phenomena. 2. Create and use representations to organize, record, and communicate mathematical ideas. 3. Select, apply, and translate among mathematical representations to solve problems.
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6. Knowledge of Technology. Candidates embrace technology as an essential tool for teaching and learning. Indicator 1. Use knowledge of mathematics to select and use appropriate technological tools, such as but not limited to spreadsheets, dynamic graphing tools, computer algebra systems, dynamic statistical packages, graphing calculators, data-collection devices, and presentation software.
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7. Dispositions. Candidates support a positive disposition toward mathematical processes and mathematical learning. Indicators 1. Attention to equity 2. Use of stimulating curricula 3. Effective teaching 4. Commitment to learning and understanding 5. Use of various assessments 6. Use of various teaching tools including technology
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8. PEDEGOGY – Knowledge of Mathematics. Candidates possess a deep understanding of how students learn mathematics and of the pedagogical knowledge specific to mathematics teaching and learning. Indicators 1. Selects, uses, and determines suitability of the wide variety of available mathematics curricula and teaching materials for all students including those with special needs such as the gifted, challenged and speakers of other languages. 2. Selects and uses appropriate concrete materials for learning mathematics. 3. Uses multiple strategies, including listening to and understanding the ways students think about mathematics, to assess students’ mathematical knowledge. 4. Plans lessons, units and courses that address appropriate learning goals, including those that address local, state, and national mathematics standards and legislative mandates. 5. Participates in professional mathematics organizations and uses their print and on-line resources. 6. Demonstrates knowledge of research results in the teaching and learning of mathematics. 7. Uses knowledge of different types of instructional strategies in planning mathematics lessons. 8. Demonstrates the ability to lead classes in mathematical problem solving and in developing in-depth conceptual understanding, and to help students develop and test generalizations. 9. Develops lessons that use technology’s potential for building understanding of mathematical concepts and developing important mathematical ideas.
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