NCTM CAEP Mathematics Content for Secondary. - Apply knowledge of major concepts, algorithms, procedures, applications in varied contexts, and connections within and among mathematical domains as outlined in the NCTM CAEP Mathematics Content for Secondary. - Explain how concepts, algorithms, procedures, and applications have developed. - Apply knowledge of major concepts, algorithms, procedures, applications in varied contexts, and connections within and among mathematical domains as outlined in the NCTM CAEP Mathematics Content for Secondary. - Explain how concepts, algorithms, procedures, and applications have developed. - Apply knowledge of major concepts, algorithms, procedures, applications in varied contexts, and connections within and among mathematical domains as outlined in the NCTM CAEP Mathematics Content for Secondary. - Explain how concepts, algorithms, procedures, and applications have developed. - Apply conceptual and procedural knowledge of major concepts, algorithms, and applications in building new knowledge from prior knowledge and experiences. Standard 2: Mathematical Practices Standard 2: Effective teachers of secondary mathematics solve problems, represent mathematical ideas, reason, prove, use mathematical models, attend to precision, identify elements of structure, generalize, engage in mathematical communication, and make connections as essential mathematical practices. They understand that these practices intersect with mathematical content and that understanding relies on the ability to demonstrate these practices within and among mathematical domains and in their teaching. Program evidence of candidates’ attainment of Standard 2: Assessments, rubrics, and data charts are aligned with standard elements. Alignment to standard element(s) is provided within assessment rubrics per criterion. Data charts are aligned with assessment rubric and report candidate performance by the level (individually scored items) at which it is collected. Assessment rubrics contain discernible levels of performance. Assessments are required of all candidates. Decision Criteria: Attainment of Standard 2 is based on two considerations:
Reason abstractly, reflectively, and quantitatively with attention to units, constructing viable arguments and proofs, and critiquing the reasoning of others; represent and model generalizations using mathematics; recognize structure and express regularity in patterns of mathematical reasoning; use multiple representations to model and describe mathematics; and utilize appropriate mathematical vocabulary and symbols to communicate mathematical ideas to others. constructing viable arguments and proofs, and critiquing the reasoning of others. - Represent and model generalizations using mathematics. - Recognize structure and express regularity in patterns of mathematical reasoning. Use multiple representations to and describe mathematics. - Use appropriate mathematical vocabulary and symbols to communicate mathematical to others. constructing viable arguments and proofs, and critiquing the reasoning of others. - Represent and model generalizations using mathematics. - Recognize structure and express regularity in patterns of mathematical reasoning. Use multiple representations to model and describe mathematics. - Use appropriate mathematical vocabulary and symbols to communicate mathematical ideas to others. constructing viable arguments and proofs, and critiquing the reasoning of others. - Represent and model generalizations using mathematics. - Recognize structure and express regularity in patterns of mathematical reasoning. Use multiple representations to model and describe mathematics. - Use appropriate mathematical vocabulary and symbols to communicate mathematical ideas to others. - Demonstrate an appreciation for mathematical rigor and inquiry. Element 2c Formulate, represent, analyze, and interpret mathematical models derived from real-world contexts or mathematical problems. - Formulate, represent, analyze, and interpret mathematical models derived from contexts or mathematical problems. - Formulate, represent, analyze, and interpret mathematical models derived from contexts or mathematical problems. - Formulate, represent, analyze, interpret, and validate mathematical models derived from real-world contexts or mathematical problems. - Demonstrate flexibility in mathematical modeling when confronted with different purposes or contexts. Element 2d Organize mathematical thinking and use the language of mathematics to express - Organize mathematical thinking. - Use the language of mathematics to express ideas precisely, both orally and in writing to peers, teachers, or students. - Organize mathematical thinking. - Use the language of mathematics to express ideas precisely, both orally and in writing to peers, teachers, or students. - Organize mathematical thinking. - Use the language of mathematics to express ideas precisely, both orally and in writing to multiple audiences including peers, teachers, students,
progressions impact the teaching of secondary students at different developmental levels. Element 3b Analyze and consider research in planning for and leading students in rich mathematical learning experiences. - Analyze and consider research in planning for mathematics instruction. - Incorporate research-based methods when leading students in rich mathematical learning experiences. - Analyze and consider research in planning for mathematics instruction. - Incorporate research-based methods when leading students in rich mathematical learning experiences. - Analyze and consider research in planning for mathematics instruction. - Incorporate research-based methods when leading students in rich mathematical learning experiences. - Extend their repertoire of instructional methods that address students’ diverse learning needs through participation in leadership opportunities such as conferences, use of journals and resources, and engagement with professional organizations. Element 3c Plan lessons and units that incorporate a variety of strategies, differentiated instruction for diverse populations, and mathematics-specific and instructional technologies in building all students’ conceptual understanding and procedural proficiency. - Plan lessons and units that incorporate a variety of strategies. - Plan lessons and units addressing student differences and diverse populations and how these differences influence student learning of mathematics. - Include mathematics-specific and instructional technologies in planned lessons and units. - all students’ conceptual understanding and procedural proficiency in planned lessons and units. - Plan lessons and units that incorporate a variety of strategies. - Plan lessons and units addressing student differences and diverse populations and how these differences influence student learning of mathematics. - Include mathematics-specific and instructional technologies in planned lessons and units. - Build all students’ conceptual understanding and procedural proficiency in planned lessons and units. - Plan lessons and units that incorporate a variety of strategies. - Plan lessons and addressing student differences and diverse populations and how these differences influence student learning of mathematics. - Include mathematics-specific and instructional technologies in planned lessons and - Build all students’ conceptual understanding and procedural proficiency in planned lessons and units.
secondary mathematics by a university or college supervisor with secondary mathematics teaching experience or equivalent knowledge base. secondary mathematics by a university or college supervisor with secondary mathematics teaching experience or equivalent knowledge base. secondary mathematics by a university or college supervisor with secondary mathematics teaching experience or equivalent knowledge base. - Use student performance data to inform instructional planning and delivery over time. NCTM Element Preservice teacher candidates: Unacceptable than two assessments or assessments provide little or no evidence that secondary candidates: Acceptable At least two assessments provide evidence that secondary candidates: Target At two assessments provide evidence that secondary candidates: Element 7c Develop knowledge, skills, and professional behaviors across both middle and high school settings; examine the nature of mathematics, how mathematics should be taught, and how students learn mathematics; and observe and analyze a range of approaches to mathematics teaching and learning, focusing on tasks, discourse, environment, and assessment. Demonstrate knowledge, skills, and professional behaviors at both middle and high school settings. Examine the nature of mathematics, how mathematics should be taught, and how students learn mathematics. Observe and analyze a range of approaches to mathematics teaching and learning, focusing on tasks, discourse, environment, and assessment. Demonstrate knowledge, skills, and professional behaviors at both middle and high school settings. Examine the nature of mathematics, how mathematics should be taught, and how students learn mathematics. Observe and analyze a range of approaches to mathematics teaching and learning, focusing on tasks, discourse, environment, and assessment. Demonstrate knowledge, skills, and professional behaviors at both middle and high school settings. Examine the nature of mathematics, how mathematics should be taught, and how students learn mathematics. Observe and analyze a range of approaches to mathematics teaching and learning, focusing on tasks, discourse, environment, and assessment. Participate in innovative or transformative initiatives, partnerships, or research projects related to the teaching of secondary mathematics.