Criterion

Limited (1)

Developing (2)

Proficient (3)

Exemplary (4)

2a) Use problem solving to develop conceptual understanding, make sense of a wide variety of problems and persevere in solving them, apply and adapt a variety of strategies in solving problems confronted within the field of mathematics and other contexts, and formulate and test conjectures in order to frame generalizations.

Lesson does not clearly engage students in problem solving to develop conceptual understanding, to make sense of a wide variety of problems and persevere in solving them, to apply and adapt a variety of strategies in solving problems confronted within the field of mathematics and other contexts, and to formulate and test conjectures to frame generalizations.

Lesson inconsistently engages students in problem solving to develop conceptual understanding, to make sense of a wide variety of problems and persevere in solving them, to apply and adapt a variety of strategies in solving problems confronted within the field of mathematics and other contexts, and to formulate and test conjectures to frame generalizations.

Lesson consistently engages students in problem solving to develop conceptual understanding, to make sense of a wide variety of problems and persevere in solving them, to apply and adapt a variety of strategies in solving problems confronted within the field of mathematics and other contexts, and to formulate and test conjectures to frame generalizations.

Problem solving for develop conceptual understanding, for making sense of a wide variety of problems and persevering in solving them, for applying and adapting a variety of strategies in solving problems confronted within the field of mathematics and other contexts, and for formulating and testing conjectures to frame generalizations is abundantly evident.

2b.1) The teacher develops and implements supports for literacy development across content areas and for utilizing appropriate mathematical vocabulary and symbols to communicate mathematical ideas to others.

Development and implementation supports for literacy development across content areas and for utilizing appropriate mathematical vocabulary and symbols to communicate mathematical ideas to others is not evident.

Development and implementation supports for literacy development across content areas and for utilizing appropriate mathematical vocabulary and symbols to communicate mathematical ideas to others is somewhat evident.

Development and implementation supports for literacy development across content areas and for utilizing appropriate mathematical vocabulary and symbols to communicate mathematical ideas to others is sufficiently evident.

Development and implementation supports for literacy development across content areas and for utilizing appropriate mathematical vocabulary and symbols to communicate mathematical ideas to others is abundantly evident.

2b.2) The teacher engages learners in abstract, quantitative, and reflective reasoning with attention to units.

Engagement of learners in abstract, quantitative, and reflective reasoning with attention to units is not evident.

Engagement of learners in abstract, quantitative, and reflective reasoning with attention to units is somewhat evident.

Engagement of learners in abstract, quantitative, and reflective reasoning with attention to units is sufficiently evident.

Engagement of learners in abstract, quantitative, and reflective reasoning with attention to units is abundantly evident.

2b.3) The teacher facilitates learnersÕ ability to construct viable arguments and proofs and critique the reasoning of others.

Plans to facilitate learnersÕ ability to construct viable arguments and proofs and critique the reasoning of others are not evident.

Plans to facilitate learnersÕ ability to construct viable arguments and proofs and critique the reasoning of others are somewhat evident.

Plans to facilitate learnersÕ ability to construct viable arguments and proofs and critique the reasoning of others are sufficiently evident.

Plans to facilitate learnersÕ ability to construct viable arguments and proofs and critique the reasoning of others are abundantly evident.

2b.4) The teacher facilitates learnersÕ ability to represent and model generalizations using mathematics, to recognize structure, and to express regularity in patterns of mathematical reasoning.

Plans to facilitate learnersÕ ability to represent and model generalizations using mathematics, to recognize structure, and to express regularity in patterns of mathematical reasoning are not evident.

Plans to facilitate learnersÕ ability to represent and model generalizations using mathematics, to recognize structure, and to express regularity in patterns of mathematical reasoning are somewhat evident.

Plans to facilitate learnersÕ ability to represent and model generalizations using mathematics, to recognize structure, and to express regularity in patterns of mathematical reasoning are sufficiently evident.

Plans to facilitate learnersÕ ability to represent and model generalizations using mathematics, to recognize structure, and to express regularity in patterns of mathematical reasoning are abundantly evident.

2b.5) The teacher facilitates learnersÕ ability to use multiple representations to model and describe mathematics.

Plans to facilitate learnersÕ ability to use multiple representations to model and describe mathematics are not evident.

Plans to facilitate learnersÕ ability to use multiple representations to model and describe mathematics are somewhat evident.

Plans to facilitate learnersÕ ability to use multiple representations to model and describe mathematics are sufficiently evident.

Plans to facilitate learnersÕ ability to use multiple representations to model and describe mathematics are abundantly evident.

2c) Formulate, represent, analyze, and interpret mathematical models derived from real-world contexts or mathematical problems.

The formulation, representation, analysis, and interpretation of mathematical models derived from real-world contexts or mathematical problems are not evident or are minimally evident.

The formulation, representation, analysis, and interpretation of mathematical models derived from real-world contexts or mathematical problems are somewhat evident.

The formulation, representation, analysis, and interpretation of mathematical models derived from real-world contexts or mathematical problems are sufficiently evident.

The formulation, representation, analysis, and interpretation of mathematical models derived from real-world contexts or mathematical problems are abundantly evident.

2d) Organize mathematical thinking and use the language of mathematics to express ideas precisely, both orally and in writing to multiple audiences.

The organization of mathematical thinking and use of the language of mathematics to express ideas precisely, both orally and in writing to multiple audiences is not evident.

The organization of mathematical thinking and use of the language of mathematics to express ideas precisely, both orally and in writing to multiple audiences is somewhat evident.

The organization of mathematical thinking and use of the language of mathematics to express ideas precisely, both orally and in writing to multiple audiences is sufficiently evident.

The organization of mathematical thinking and use of the language of mathematics to express ideas precisely, both orally and in writing to multiple audiences is abundantly evident.

2e.1) Demonstrate the interconnectedness of mathematical ideas and how they build on one another and recognize and apply mathematical connections among mathematical ideas.

Few mathematical connections are made among mathematical ideas.

Some mathematical connections are made among mathematical ideas.

Sufficient mathematical connections are made among mathematical ideas.

In-Depth mathematical connections are made among mathematical ideas.

2e.2) Demonstrate the interconnectedness of mathematical ideas and how they build on one another and recognize and apply mathematical connections across various content areas and real-world contexts.

Few mathematical connections are made across various content areas and real-world contexts.

Some mathematical connections are made across various content areas and real-world contexts.

Sufficient mathematical connections are made across various content areas and real-world contexts.

In-Depth mathematical connections are made across various content areas and real-world contexts.

2f) Model how the development of mathematical understanding within and among mathematical domains intersects with the mathematical practices of problem solving, reasoning, communicating, connecting, and representing.

Modeling how the development of mathematical understanding within and among mathematical domains intersects with the mathematical practices of problem solving, reasoning, communicating, connecting, and representing is not evident.

Modeling how the development of mathematical understanding within and among mathematical domains intersects with the mathematical practices of problem solving, reasoning, communicating, connecting, and representing is somewhat evident.

Modeling how the development of mathematical understanding within and among mathematical domains intersects with the mathematical practices of problem solving, reasoning, communicating, connecting, and representing is sufficiently evident.

Modeling how the development of mathematical understanding within and among mathematical domains intersects with the mathematical practices of problem solving, reasoning, communicating, connecting, and representing is abundantly evident.

3a) Apply knowledge of curriculum standards for secondary mathematics and their relationship to student learning within and across mathematical domains.

The application of knowledge of curriculum standards for secondary mathematics and their relationship to student learning within and across mathematical domains is not evident or is minimally evident.

The application of knowledge of curriculum standards for secondary mathematics and their relationship to student learning within and across mathematical domains is somewhat evident.

The application of knowledge of curriculum standards for secondary mathematics and their relationship to student learning within and across mathematical domains is sufficiently evident.

The application of knowledge of curriculum standards for secondary mathematics and their relationship to student learning within and across mathematical domains is abundantly evident.

3b) Analyze and consider research in planning for and leading students in rich mathematical learning experiences.

The application of research in planning for and leading students in rich mathematical learning experiences is not evident.

The application of research in planning for and leading students in rich mathematical learning experiences is somewhat evident.

The application of research in planning for and leading students in rich mathematical learning experiences is sufficiently evident.

The application of research in planning for and leading students in rich mathematical learning experiences is abundantly evident.

3c.1) Plan lessons that incorporate a variety of strategies, differentiated instruction for diverse populations.

Lessons contain little to no strategy variation and differentiated instruction.

Lessons contain some strategy variation and differentiated instruction.

Lessons contain sufficient strategy variation and differentiated instruction.

Lessons contain an abundance of strategy variation and differentiated instruction.

3c.2) Plan lessons that incorporate mathematics-specific and instructional technologies in building all studentsÕ conceptual understanding and procedural proficiency.

Lessons incorporate little to no mathematics-specific and instructional technologies, or the technologies are not targeted for building all studentsÕ conceptual understanding and procedural fluency.

Lessons incorporate some mathematics-specific and instructional technologies targeted for building all studentsÕ conceptual understanding and procedural fluency.

Lessons incorporate sufficient mathematics-specific and instructional technologies targeted for building all studentsÕ conceptual understanding and procedural fluency.

Lessons incorporate an abundance of mathematics-specific and instructional technologies targeted for building all studentsÕ conceptual understanding and procedural fluency.

3d) Provide students with opportunities to communicate about mathematics and make connections among mathematics, other content areas, everyday life, and the workplace.

Opportunities for students to communicate about mathematics and make connections among mathematics, other content areas, everyday life, and the workplace are not evident.

Opportunities for students to communicate about mathematics and make connections among mathematics, other content areas, everyday life, and the workplace are somewhat evident.

Opportunities for students to communicate about mathematics and make connections among mathematics, other content areas, everyday life, and the workplace are sufficiently evident.

Opportunities for students to communicate about mathematics and make connections among mathematics, other content areas, everyday life, and the workplace are abundantly evident.

3e) Implement techniques related to student engagement and communication including selecting high quality tasks, guiding mathematical discussions, identifying key mathematical ideas, identifying and addressing student misconceptions, and employing a range of questioning strategies.

Implementation of techniques related to student engagement and communication including selecting high quality tasks, guiding mathematical discussions, identifying key mathematical ideas, identifying and addressing student misconceptions, and employing a range of questioning strategies is not evident.

Implementation of techniques related to student engagement and communication including selecting high quality tasks, guiding mathematical discussions, identifying key mathematical ideas, identifying and addressing student misconceptions, and employing a range of questioning strategies is somewhat evident.

Implementation of techniques related to student engagement and communication including selecting high quality tasks, guiding mathematical discussions, identifying key mathematical ideas, identifying and addressing student misconceptions, and employing a range of questioning strategies is sufficiently evident.

Implementation of techniques related to student engagement and communication including selecting high quality tasks, guiding mathematical discussions, identifying key mathematical ideas, identifying and addressing student misconceptions, and employing a range of questioning strategies is abundantly evident.

4a.1) Exhibit knowledge of adolescent learning, development, and behavior.

Knowledge of adolescent learning, development, and behavior is not evident.

Knowledge of adolescent learning, development, and behavior is somewhat evident.

Knowledge of adolescent learning, development, and behavior is sufficiently evident.

Knowledge of adolescent learning, development, and behavior is abundantly evident.

4a.2) Demonstrate a positive disposition toward mathematical processes and learning.

Positive disposition toward mathematical processes and learning is not evident.

Positive disposition toward mathematical processes and learning is somewhat evident.

Positive disposition toward mathematical processes and learning is sufficiently evident.

Positive disposition toward mathematical processes and learning is abundantly evident.

4b) Plan and create developmentally appropriate, sequential, and challenging learning opportunities grounded in mathematics education research in which students are actively engaged in building new knowledge from prior knowledge and experiences.

The planning and creating of developmentally appropriate, sequential, and challenging learning opportunities grounded in mathematics education research in which students are actively engaged in building new knowledge from prior knowledge and experiences is not evident.

The planning and creating of developmentally appropriate, sequential, and challenging learning opportunities grounded in mathematics education research in which students are actively engaged in building new knowledge from prior knowledge and experiences is somewhat evident.

The planning and creating of developmentally appropriate, sequential, and challenging learning opportunities grounded in mathematics education research in which students are actively engaged in building new knowledge from prior knowledge and experiences is sufficiently evident.

The planning and creating of developmentally appropriate, sequential, and challenging learning opportunities grounded in mathematics education research in which students are actively engaged in building new knowledge from prior knowledge and experiences is abundantly evident.

4c) Incorporate knowledge of individual differences and the cultural and language diversity that exists within classrooms and include culturally relevant perspectives as a means to motivate and engage students.

The incorporation of knowledge of individual differences and the cultural and language diversity that exists within classrooms and inclusion of culturally relevant perspectives as a means to motivate and engage students is not evident.

The incorporation of knowledge of individual differences and the cultural and language diversity that exists within classrooms and inclusion of culturally relevant perspectives as a means to motivate and engage students is somewhat evident.

The incorporation of knowledge of individual differences and the cultural and language diversity that exists within classrooms and inclusion of culturally relevant perspectives as a means to motivate and engage students is sufficiently evident.

The incorporation of knowledge of individual differences and the cultural and language diversity that exists within classrooms and inclusion of culturally relevant perspectives as a means to motivate and engage students is abundantly evident.

4d) Demonstrate equitable and ethical treatment of and high expectations for all students.

The equitable and ethical treatment of and high expectations for all students is not evident.

The equitable and ethical treatment of and high expectations for all students is somewhat evident.

The equitable and ethical treatment of and high expectations for all students is sufficiently evident.

The equitable and ethical treatment of and high expectations for all students is abundantly evident.

4e.1) Apply mathematical content and pedagogical knowledge to select and use instructional tools such as manipulatives and physical models, drawings, virtual environments, spreadsheets, presentation tools, and mathematics-specific technologies (e.g., graphing tools, interactive geometry software, computer algebra systems, and statistical packages).

The application of mathematical content and pedagogical knowledge to select and use instructional tools such as manipulatives and physical models, drawings, virtual environments, spreadsheets, presentation tools, and mathematics-specific technologies is not evident.

The application of mathematical content and pedagogical knowledge to select and use instructional tools such as manipulatives and physical models, drawings, virtual environments, spreadsheets, presentation tools, and mathematics-specific technologies is somewhat evident.

The application of mathematical content and pedagogical knowledge to select and use instructional tools such as manipulatives and physical models, drawings, virtual environments, spreadsheets, presentation tools, and mathematics-specific technologies is sufficiently evident.

The application of mathematical content and pedagogical knowledge to select and use instructional tools such as manipulatives and physical models, drawings, virtual environments, spreadsheets, presentation tools, and mathematics-specific technologies is abundantly evident.

4e.2) Make sound decisions about when instructional tools such as manipulatives and physical models, drawings, virtual environments, spreadsheets, presentation tools, and mathematics-specific technologies (e.g., graphing tools, interactive geometry software, computer algebra systems, and statistical packages) enhance teaching and learning, recognizing both the insights to be gained and possible limitations of such tools.

Sound decisions about when instructional tools such as manipulatives and physical models, drawings, virtual environments, spreadsheets, presentation tools, and mathematics-specific technologies enhance teaching and learning and the recognition of both the insights to be gained and possible limitations of such tools is not evident.

Sound decisions about when instructional tools such as manipulatives and physical models, drawings, virtual environments, spreadsheets, presentation tools, and mathematics-specific technologies enhance teaching and learning and the recognition of both the insights to be gained and possible limitations of such tools is somewhat evident.

Sound decisions about when instructional tools such as manipulatives and physical models, drawings, virtual environments, spreadsheets, presentation tools, and mathematics-specific technologies enhance teaching and learning and the recognition of both the insights to be gained and possible limitations of such tools is sufficiently evident.

Sound decisions about when instructional tools such as manipulatives and physical models, drawings, virtual environments, spreadsheets, presentation tools, and mathematics-specific technologies enhance teaching and learning and the recognition of both the insights to be gained and possible limitations of such tools is abundantly evident.

5a.1) Verify that secondary students demonstrate conceptual understanding within major mathematical domains.

Verification that secondary students demonstrate conceptual understanding within major mathematical domains is not evident or is minimally evident.

Verification that secondary students demonstrate conceptual understanding within major mathematical domains is somewhat evident.

Verification that secondary students demonstrate conceptual understanding within major mathematical domains is sufficiently evident.

Verification that secondary students demonstrate conceptual understanding within major mathematical domains is abundantly evident.

5a.2) Verify that secondary students demonstrate procedural fluency within major mathematical domains.

Verification that secondary students demonstrate procedural fluency within major mathematical domains is not evident or is minimally evident.

Verification that secondary students demonstrate procedural fluency within major mathematical domains is somewhat evident.

Verification that secondary students demonstrate procedural fluency within major mathematical domains is sufficiently evident.

Verification that secondary students demonstrate procedural fluency within major mathematical domains is abundantly evident.

5a.3) Verify that secondary students demonstrate the ability to formulate, represent, and solve problems within major mathematical domains.

Verification that secondary students demonstrate the ability to formulate, represent, and solve problems within major mathematical domains is not evident or is minimally evident.

Verification that secondary students demonstrate the ability to formulate, represent, and solve problems within major mathematical domains is somewhat evident.

Verification that secondary students demonstrate the ability to formulate, represent, and solve problems within major mathematical domains is sufficiently evident.

Verification that secondary students demonstrate the ability to formulate, represent, and solve problems within major mathematical domains is abundantly evident.

5a.4) Verify that secondary students demonstrate productive disposition toward mathematics within major mathematical domains.

Verification that secondary students demonstrate productive disposition toward mathematics within major mathematical domains is not evident or is minimally evident.

Verification that secondary students demonstrate productive disposition toward mathematics within major mathematical domains is somewhat evident.

Verification that secondary students demonstrate productive disposition toward mathematics within major mathematical domains is sufficiently evident.

Verification that secondary students demonstrate productive disposition toward mathematics within major mathematical domains is abundantly evident.

5a.5) Verify that secondary students demonstrate the application of mathematics in a variety of contexts within major mathematical domains.

Verification that secondary students demonstrate the application of mathematics in a variety of contexts within major mathematical domains is not evident or is minimally evident.

Verification that secondary students demonstrate the application of mathematics in a variety of contexts within major mathematical domains is somewhat evident.

Verification that secondary students demonstrate the application of mathematics in a variety of contexts within major mathematical domains is sufficiently evident.

Verification that secondary students demonstrate the application of mathematics in a variety of contexts within major mathematical domains is abundantly evident.

5b) Engage students in developmentally appropriate mathematical activities and investigations that require active engagement and include mathematics-specific technology in building new knowledge.

The engagement of students in developmentally appropriate mathematical activities and investigations that require active engagement and inclusion of mathematics-specific technology in building new knowledge is not evident.

The engagement of students in developmentally appropriate mathematical activities and investigations that require active engagement and inclusion of mathematics-specific technology in building new knowledge is somewhat evident.

The engagement of students in developmentally appropriate mathematical activities and investigations that require active engagement and inclusion of mathematics-specific technology in building new knowledge is sufficiently evident.

The engagement of students in developmentally appropriate mathematical activities and investigations that require active engagement and inclusion of mathematics-specific technology in building new knowledge is abundantly evident.

6c) Utilize resources from professional mathematics education organizations such as print, digital, and virtual resources/collections.

The use of resources from professional mathematics education organizations such as print, digital, and virtual resources/collections is not evident.

The use of resources from professional mathematics education organizations such as print, digital, and virtual resources/collections is somewhat evident.

The use of resources from professional mathematics education organizations such as print, digital, and virtual resources/collections is sufficiently evident.

The use of resources from professional mathematics education organizations such as print, digital, and virtual resources/collections is abundantly evident.

7c.1) Demonstrate knowledge, skills, and professional behaviors at both middle and high school settings.

The demonstration of knowledge, skills, and professional behaviors is not evident or is minimally evident.

The demonstration of knowledge, skills, and professional behaviors is somewhat evident.

The demonstration of knowledge, skills, and professional behaviors is sufficiently evident.

The demonstration of knowledge, skills, and professional behaviors is abundantly evident.

7c.2) Examine the nature of mathematics, how mathematics should be taught, and how students learn mathematics.

Examination of the nature of mathematics, how mathematics should be taught, and how students learn mathematics is not evident or is minimally evident.

Examination of the nature of mathematics, how mathematics should be taught, and how students learn mathematics is somewhat evident.

Examination of the nature of mathematics, how mathematics should be taught, and how students learn mathematics is sufficiently evident.

Examination of the nature of mathematics, how mathematics should be taught, and how students learn mathematics is abundantly evident.

7c.3) Observe and analyze a range of approaches to mathematics teaching and learning, focusing on tasks, discourse, environment, and assessment.

The observation and analysis of a range of approaches to mathematics teaching and learning, focusing on tasks, discourse, environment, and assessment is not evident or is minimally evident.

The observation and analysis of a range of approaches to mathematics teaching and learning, focusing on tasks, discourse, environment, and assessment is somewhat evident.

The observation and analysis of a range of approaches to mathematics teaching and learning, focusing on tasks, discourse, environment, and assessment is sufficiently evident.

The observation and analysis of a range of approaches to mathematics teaching and learning, focusing on tasks, discourse, environment, and assessment is abundantly evident.