# Standards of the P-6 Mathematics Specialist Endorsement

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1 Standards of the P-6 Mathematics Specialist Endorsement I. Mathematical Content Knowledge and Knowledge of Curriculum Candidates have deep understanding of mathematical content and knowledge of mathematical curricula appropriate to grade levels P 8. As a result, candidates: 1.1. Understand numbers and operations both broadly enough and deeply enough to teach arithmetic for understanding and to develop strategies for building conceptual understanding of number Use arithmetic to build algebraic concepts, appropriately apply algebraic reasoning and use algebraic notation and language correctly Are able to develop visualization and reasoning skills through use of technology and manipulatives Demonstrate expertise in selecting appropriate units and tools for the attribute being measured. a. Discriminate between and provide examples of procedural and conceptual knowledge. b. Utilize an extensive repertoire of interpretations of arithmetic operations using whole numbers, integers, fractions, rational numbers, and decimals. c. Use place value to represent whole numbers and finite decimals through various representations. d. Apply standard algorithms and mental math for calculations and interpret non-standard methods commonly created by students. e. Provide examples of various representations of integers and rational numbers and explore their relationships. f. Coach inservice teachers to build deep understanding of number and operations through different approaches. a. Use a variety of representations, including algebraic notation, to represent, generalize, and justify arithmetic claims. b. Use and critique different forms of mathematical and deductive arguments. c. Develop and use mathematical models to represent and solve real-world problems. d. Move from concrete experiences to important generalizations foundational to understanding major mathematical concepts. e. Recognize and explain properties of real numbers such as commutative property, associative property, distributive property, identities, and inverses, and how these properties affect the arithmetic of real numbers. f. Represent and analyze patterns and functions using words, tables, graphs, and algebraic notation. g. Coach inservice teachers in developing algebraic reasoning through knowledge of numbers and operations. a. Draw, decompose, and re-construct two- and three-dimensional shapes. b. Classify two- and three-dimensional shapes according to their properties and develop definitions of classes of shapes. c. Apply transformations and use symmetry to analyze mathematical situations. d. Communicate inductive and deductive geometric arguments, using correct technical vocabulary. e. Coach in service teachers in connections between geometric and algebraic concepts through use of technology. a. Compare units and convert measurements from one unit to another. b. Devise area formulas for basic shapes and estimate areas of irregular shapes. c. Recognize the behavior of measure (length, area, and volume) under uniform dilations. d. Coach inservice teachers in identifying and selecting the appropriate unit and tool for measuring various shapes. 5/19/101:36 PM 1

3 2.3 Know and are able to apply and model a variety of intervention strategies for meeting diverse student needs. 2.4 Respect all students and support student differences. d. Provide instructional options to meet developmental needs. e. Support classroom teachers in using a wide range of suitable instructional practices. a. Relate student characteristics to instructional decision-making. b. Articulate how differences in student characteristics can affect mathematics learning. c. Employ critical analysis and synthesis to identify, evaluate, and modify practice to meet the needs of a diverse student population. d. Adapt instruction and assessment to meet the individual needs of students. e. Support classroom teachers in using a wide range of instructional practices to meet diverse student needs. a. Provide evidence of self-efficacy for meeting the needs of diverse learners. b. Model practice that supports respect for student differences. III. Instructional strategies and the use of materials and technology Candidates have knowledge of developmentally appropriate instructional practices, approaches, methods, materials, technology, and reflective skills to support mathematics instruction. As a result, candidates: 3.1 Use a wide range of instructional practices that promote mathematics for learners at differing stages of development. 3.2 Evaluate curriculum materials; plan and use appropriate materials, including technology-based, for effective mathematics instruction for learners at various stages of development. 3.3 Encourage reflection on, and the discussion of what is effective, what is not effective, and how to make improvements. a. Acquaint teachers with successful and innovative strategies, including translating research findings into practice. b. Assist other teachers in developing significant mathematical tasks and leading classroom discourse that promote mathematical thinking. c. Support classroom teachers in developing a climate of inquiry, incorporating the process standards (problem solving, reasoning and proof, communication, connections, and representation) in their classrooms. d. Assist other teachers in implementing early intervention strategies with lowperforming students, including differentiation of time and teaching strategies. e. Coach teachers in a variety of instructional grouping options and methods to promote a positive learning environment. f. Assist other teachers by modeling effective instructional strategies a. Assist the building or district by recommending and aiding in the selection of instructional materials. b. Oversee the implementation of instructional materials and evaluate their effectiveness. c. Recommend appropriate technology to support mathematics instruction. d. Coach teachers in effectively implementing the use of a wide variety of technology in their classrooms (from low tech options to computer software). a. Use a variety of professional development models (e.g., peer coaching, lesson study, and action research). b. Assist other teachers to make instructional decisions based on student data. c. Analyze results of statewide and other standardized testing to make professional development decisions for teachers in the district. d. Conduct and analyze longitudinal assessment studies to determine program effectiveness and recommend changes for improvement. IV. Assessment, Diagnosis, and Evaluation Candidates use a variety of tools and practices to plan, implement, and revise classroom instruction to best meet the needs of all students. As a result, candidates can: 4.1 Critique and use a wide range of assessment tools and practices including individual and group, a. Determine the appropriateness of various assessment instruments. b. Use diagnostic, formative, and summative methods to determine students understanding of mathematics. 5/19/101:36 PM 3

6 successfully with teachers, administrators, families, and others to bring about positive change in the teaching and learning of mathematics. 6.5 Display positive dispositions to mathematics and the teaching of mathematics. facilitating professional development sessions or modeling classroom instruction. c. Establish positive rapport with all stakeholders. d. Encourage positive school culture that adapts to reform in mathematics education. a. Articulate the theories and research related to the connections between teacher dispositions and student achievement. b. Demonstrate and model a personal commitment to life-long learning in the areas of mathematics and mathematics education. c. Demonstrate the value of mathematics as a way of thinking and its application in other disciplines and in society. d. Promote teachers confidence, flexibility, perseverance, curiosity, and inventiveness in doing mathematics by engaging teachers in appropriate tasks and professional discourse about mathematics and mathematics teaching. 5/19/101:36 PM 6

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