NCTM CAEP Standards (2012) Reviewer Rubrics Middle Grades (Initial Preparation)

NCTM CAEP Standards (2012) Reviewer Rubrics – Middle Grades (Initial Preparation)

Standard 1: Content Knowledge Standard 1: Effective teachers of middle grades mathematics demonstrate and apply knowledge of major mathematics concepts, algorithms, procedures, connections, and applications within and among mathematical content domains.

Program evidence of completers’ attainment of Standard 1: - Assessments are aligned to mathematical domain competencies of NCTM CAEP Mathematics Content for Middle Grades. - 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 1 is based on four considerations: - Two or three years (depending on number of current year program completers) of individual completer performance data (scores and subscores) on state-required mathematics content licensure tests aligned to mathematical domain competencies of NCTM CAEP Mathematics Content for Middle Grades and demonstrating an 80% or better overall pass rate - At least two additional assessments accompanied by completer performance data from a minimum of two applications for an initial report or a minimum of one application for a response to conditions or revised report and selected from: o Grades in required mathematics or mathematics education courses aligned to elements of NCTM CAEP Standards (2012) and to mathematical domain competencies of NCTM CAEP Mathematics Content for Middle Grades and overall mathematics GPAs in required mathematics coursework  Transcript analysis (required for candidates where mathematics or equivalent coursework was not taken at program’s institution) that includes course alignment to NCTM CAEP Mathematics Content for Middle Grades and course data reported by individual completer o Content-based assessment such as projects, course portfolio, or other course products aligned to mathematical domain competencies of NCTM CAEP Mathematics Content for Middle Grades - Content-based assessments (state licensure test, course grades, projects, course portfolio, or other course products) collectively demonstrating at least an 80% alignment to each domain of NCTM CAEP Mathematics Content for Middle Grades and accompanied by completer performance data - A preponderance of evidence drawn from the elements o SASB policy defines preponderance of evidence as “an overall confirmation that candidates meet standards in the strength, weight, or quality of evidence,” rather than satisfactory performance for each element. A commonly accepted definition of preponderance of evidence is a requirement that more than 50% of the evidence favors a given outcome. NCTM program review decisions are based on the preponderance of evidence at the standard level using this definition. Specifically, more than 50% of the elements of each standard must be met at the acceptable or target level. o Element 1a must be met at the acceptable or target level in order to satisfy the preponderance of evidence for Standard 1.

NCTM CAEP Standards (2012) Reviewer Rubrics - Middle Grades (Revised 4/27/2015) 2

NCTM Element Unacceptable Acceptable Target Preservice teacher candidates: 1. State-required Licensure Test: 1. State-required Licensure Test: 1. State-required Licensure Test: - Less than 80% of completers - At least 80% of completers - 100% of completers pass the pass the assessment pass the assessment assessment - Lack of alignment to - Alignment to mathematical - Alignment to mathematical mathematical domain domain competencies of domain competencies of competencies of NCTM CAEP NCTM CAEP Mathematics NCTM CAEP Mathematics Mathematics Content for Content for Middle Grades Content for Middle Grades Middle Grades - Two or three years - Two or three years - Less than two or three years (depending on the number of (depending on the number of (depending on the number of current year program current year program current year program completers) of individual completers) of individual completers) of individual completer performance data completer performance data completer performance data 2. At least two additional 2. At least two additional 2. Fewer than two additional assessments demonstrate assessments demonstrate assessments demonstrate alignment to mathematical alignment to mathematical domain alignment to mathematical domain domain competencies of NCTM competencies of NCTM CAEP competencies of NCTM CAEP CAEP Mathematics Content for Mathematics Content for Middle Mathematics Content for Middle Middle Grades Grades Grades 3. Three assessments collectively 3. Three assessments collectively 3. Three or fewer assessments demonstrate at least an 80% demonstrate at least an 80% collectively demonstrate less than alignment to each domain of alignment to each domain of 80% alignment to each domain of NCTM CAEP Mathematics NCTM CAEP Mathematics NCTM CAEP Mathematics Content for Middle Grades and Content for Middle Grades and Content for Middle Grades and provide evidence that middle provide evidence that middle provide little or no evidence that grades completers: grades completers: middle grades completers: Element 1a - Demonstrate knowledge of major - Demonstrate knowledge of major - Demonstrate knowledge of major Demonstrate and apply knowledge of concepts, algorithms, and concepts, algorithms, and concepts, algorithms, and procedures major concepts, algorithms, procedures within and among procedures within and among within and among mathematical procedures, applications in varied mathematical domains (Number, mathematical domains (Number, domains (Number, Algebra, contexts, and connections within and Algebra, Geometry, Trigonometry, Algebra, Geometry, Trigonometry, Geometry, Trigonometry, Statistics, among mathematical domains Statistics, Probability, and Statistics, Probability, and Probability, and Calculus) as (Number, Algebra, Geometry, Calculus) as outlined in the NCTM Calculus) as outlined in the NCTM outlined in the NCTM CAEP Trigonometry, Statistics, Probability, CAEP Mathematics Content for CAEP Mathematics Content for Mathematics Content for Middle and Calculus) as outlined in the Middle Grades. Middle Grades. Grades.

NCTM CAEP Mathematics Content - Apply knowledge of major - Apply knowledge of major - Apply knowledge of major concepts, for Middle Grades. concepts, algorithms, procedures, concepts, algorithms, procedures, algorithms, procedures, applications applications in varied contexts, and applications in varied contexts, and in varied contexts, and connections connections within and among connections within and among within and among mathematical mathematical domains as outlined mathematical domains as outlined domains as outlined in the NCTM in the NCTM CAEP Mathematics in the NCTM CAEP Mathematics CAEP Mathematics Content for Content for Middle Grades. Content for Middle Grades. Middle Grades. - Explain how concepts, algorithms, - Explain how concepts, algorithms, - Explain how concepts, algorithms, procedures, and applications have procedures, and applications have procedures, and applications have developed. developed. 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 middle grades 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: - At least two assessments aligned to elements of NCTM CAEP Standards (2012) and accompanied by candidate performance data from a minimum of two applications for an initial report or a minimum of one application for a response to conditions or revised report and selected from: o Grades in required mathematics or mathematics education courses and overall mathematics GPAs for completers  Transcript analysis (required for candidates where mathematics or equivalent coursework was not taken at program’s institution) that includes course data reported by individual completer o Projects, course or student teaching/internship portfolio, or course products and accompanied by candidate performance data - A preponderance of evidence drawn from the elements o SASB policy defines preponderance of evidence as “an overall confirmation that candidates meet standards in the strength, weight, or quality of evidence,” rather than satisfactory performance for each element. A commonly accepted definition of preponderance of evidence is a requirement that more than 50% of the evidence favors a given outcome. NCTM program review decisions are based on the preponderance of evidence at the standard level using this definition. Specifically, more than 50% of the elements of each standard must be met at the acceptable or target level. o Elements 2a, 2b, and at least 2 additional elements must be met at the acceptable or target level in order to satisfy the preponderance of evidence for Standard 2.

NCTM Element Unacceptable Acceptable Target Preservice teacher candidates: Fewer than two assessments or At least two assessments provide At least two assessments provide assessments provide little or no evidence that middle grades candidates: evidence that middle grades candidates: evidence that middle grades candidates: Element 2a - Use problem solving to develop - Use problem solving to develop - Use problem solving to develop Use problem solving to develop conceptual understanding and conceptual understanding and to conceptual understanding and to conceptual understanding, make sense to formulate and test formulate and test generalizations. formulate and test generalizations. of a wide variety of problems and generalizations. - Make sense of a wide variety of - Make sense of a wide variety of persevere in solving them, apply and - Make sense of a wide variety of problems and persevere in solving problems and persevere in solving adapt a variety of strategies in solving

NCTM CAEP Standards (2012) Reviewer Rubrics - Middle Grades (Revised 4/27/2015) 5 problems confronted within the field problems and persevere in them. them. of mathematics and other contexts, solving them. - Apply and adapt a variety of - Apply and adapt a variety of strategies and formulate and test conjectures in - Apply and adapt a variety of strategies in solving problems in solving problems confronted within order to frame generalizations. strategies in solving problems confronted within the field of the field of mathematics and other confronted within the field of mathematics and other contexts. contexts. mathematics and other - Formulate and test conjectures in - Formulate and test conjectures in contexts. order to frame generalizations. order to frame generalizations. - Formulate and test conjectures - Monitor and reflect on the process of in order to frame mathematical problem solving. generalizations. Element 2b - Reason abstractly, reflectively, - Reason abstractly, reflectively, and - Reason abstractly, reflectively, and Reason abstractly, reflectively, and and quantitatively with quantitatively with attention to units, quantitatively with attention to units, quantitatively with attention to units, attention to units, constructing constructing viable arguments and constructing viable arguments and constructing viable arguments and viable arguments and proofs, proofs, and critiquing the reasoning proofs, and critiquing the reasoning of proofs, and critiquing the reasoning of and critiquing the reasoning of of others. others. others; represent and model others. - Represent and model generalizations - Represent and model generalizations generalizations using mathematics; - Represent and model using mathematics. using mathematics. recognize structure and express generalizations using regularity in patterns of mathematical - Recognize structure and express - Recognize structure and express mathematics. reasoning; use multiple regularity in patterns of mathematical regularity in patterns of mathematical representations to model and describe - Recognize structure and reasoning. reasoning. mathematics; and utilize appropriate express regularity in patterns of - Use multiple representations to - Use multiple representations to model mathematical vocabulary and mathematical reasoning. model and describe mathematics. and describe mathematics. symbols to communicate - Use multiple representations to - Use appropriate mathematical - Use appropriate mathematical mathematical ideas to others. model and describe vocabulary and symbols to vocabulary and symbols to mathematics. communicate mathematical ideas to communicate mathematical ideas to - Use appropriate mathematical others. others. vocabulary and symbols to - Demonstrate an appreciation for communicate mathematical mathematical rigor and inquiry. ideas to others. Element 2c - Formulate, represent, analyze, - Formulate, represent, analyze, and - Formulate, represent, analyze, Formulate, represent, analyze, and and interpret mathematical interpret mathematical models interpret, and validate mathematical interpret mathematical models models derived from real-world derived from real-world contexts or models derived from real-world derived from real-world contexts or contexts or mathematical mathematical problems. contexts or mathematical problems. mathematical problems. problems. - Demonstrate flexibility in mathematical modeling when confronted with different purposes or

contexts. Element 2d - Organize mathematical - Organize mathematical thinking. - Organize mathematical thinking. Organize mathematical thinking and thinking. - Use the language of mathematics to - Use the language of mathematics to use the language of mathematics to - Use the language of express ideas precisely, both orally express ideas precisely, both orally express ideas precisely, both orally mathematics to express ideas and in writing to peers, teachers, or and in writing to multiple audiences and in writing to multiple audiences. precisely, both orally and in students. including peers, teachers, students, writing to peers, teachers, or school professionals, and/or other students. stakeholders. Element 2e - Demonstrate the - Demonstrate the interconnectedness - Demonstrate the interconnectedness of Demonstrate the interconnectedness interconnectedness of of mathematical ideas and how they mathematical ideas and how they of mathematical ideas and how they mathematical ideas and how build on one another. build on one another. build on one another and recognize they build on one another. - Recognize and apply mathematical and apply mathematical connections - Recognize and apply mathematical - Recognize and apply connections among mathematical among mathematical ideas and across connections among mathematical mathematical connections ideas and across various content areas various content areas and real-world ideas and across various content areas among mathematical ideas and and real-world contexts. contexts. and real-world contexts. across various content areas - Seek opportunities to promote linkages and real-world contexts. of mathematical ideas in their teaching. Element 2f - Model how the development of - Model how the development of - Model how the development of Model how the development of mathematical understanding mathematical understanding within mathematical understanding within mathematical understanding within within and among and among mathematical domains and among mathematical domains and among mathematical domains mathematical domains intersects with the mathematical intersects with the mathematical intersects with the mathematical intersects with the practices of problem solving, practices of problem solving, practices of problem solving, mathematical practices of reasoning, communicating, reasoning, communicating, reasoning, communicating, problem solving, reasoning, connecting, and representing. connecting, and representing. connecting, and representing. communicating, connecting, - Reflect on how the mathematical and representing. practices of problem solving, reasoning, communicating, connecting, and representing impact mathematical understanding.

Standard 3: Content Pedagogy Standard 3: Effective teachers of middle grades mathematics apply knowledge of curriculum standards for mathematics and their relationship to student learning within and across mathematical domains. They incorporate research-based mathematical experiences and include multiple instructional strategies and mathematics-specific technological tools in their teaching to develop all students’ mathematical understanding and proficiency. They provide students with opportunities to do mathematics – talking about it and connecting it to both theoretical and real-world contexts. They plan, select, implement, interpret, and use formative and summative assessments for monitoring student learning, measuring student mathematical understanding, and informing practice. Program evidence of candidates’ attainment of Standard 3: - 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 3 is based on two considerations: - At least two assessments aligned to elements of NCTM CAEP Standards (2012) and based on course products or student teaching/internship artifacts such as lesson and/or unit plan(s), student teaching/internship evaluation, or portfolio and accompanied by candidate performance data from a minimum of two applications for an initial report or a minimum of one application for a response to conditions or revised report - A preponderance of evidence drawn from the elements o SASB policy defines preponderance of evidence as “an overall confirmation that candidates meet standards in the strength, weight, or quality of evidence,” rather than satisfactory performance for each element. A commonly accepted definition of preponderance of evidence is a requirement that more than 50% of the evidence favors a given outcome. NCTM program review decisions are based on the preponderance of evidence at the standard level using this definition. Specifically, more than 50% of the elements of each standard must be met at the acceptable or target level. o Elements 3a, 3c, and 3f and at least 1 additional element must be met at the acceptable or target level in order to satisfy the preponderance of evidence for Standard 3.

NCTM Element Unacceptable Acceptable Target Preservice teacher candidates: Fewer than two assessments or At least two assessments provide At least two assessments provide assessments provide little or no evidence that middle grades evidence that middle grades candidates: evidence that middle grades candidates: candidates: Element 3a - Apply knowledge of - Apply knowledge of mathematics - Apply knowledge of mathematics Apply knowledge of curriculum mathematics curriculum curriculum standards for middle curriculum standards for middle standards for middle grades standards for middle grades grades within and across grades in their teaching within and mathematics and their relationship to within and across mathematical mathematical domains. across mathematical domains. student learning within and across domains. - Relate mathematics curriculum - Relate mathematics curriculum mathematical domains. - Relate mathematics curriculum standards to student learning. standards to student learning. standards to student learning.

- Demonstrate how mathematics curriculum standards and learning progressions impact the teaching of middle grades students at different developmental levels. Element 3b - Analyze and consider research - Analyze and consider research in - Analyze and consider research in Analyze and consider research in in planning for mathematics planning for mathematics planning for mathematics instruction. planning for and leading students in instruction. instruction. - Incorporate research-based methods rich mathematical learning - Incorporate research-based - Incorporate research-based methods when leading students in rich experiences. methods when leading students when leading students in rich mathematical learning experiences. in rich mathematical learning mathematical learning experiences. - Extend their repertoire of research- experiences. based instructional methods that address students’ diverse learning needs through participation in leadership opportunities such as conferences, use of journals and on- line resources, and engagement with professional organizations. Element 3c - Plan lessons and units that - Plan lessons and units that - Plan lessons and units that incorporate Plan lessons and units that incorporate a variety of incorporate a variety of strategies. a variety of strategies. incorporate a variety of strategies, strategies. - Plan lessons and units addressing - Plan lessons and units addressing differentiated instruction for diverse - Plan lessons and units student differences and diverse student differences and diverse populations, and mathematics- addressing student differences populations and how these populations and how these differences specific and instructional and diverse populations and how differences influence student influence student learning of technologies in building all students’ these differences influence learning of mathematics. mathematics. conceptual understanding and student learning of mathematics. procedural proficiency. - Include mathematics-specific and - Include mathematics-specific and - Include mathematics-specific instructional technologies in planned instructional technologies in planned and instructional technologies in lessons and units. lessons and units. planned lessons and units. - Build all students’ conceptual - Build all students’ conceptual - Build all students’ conceptual understanding and procedural understanding and procedural understanding and procedural proficiency in planned lessons and proficiency in planned lessons and proficiency in planned lessons units. units. and units. - Include in planned lessons and units multiple opportunities and solution avenues for students to demonstrate conceptual understanding and

procedural proficiency. Element 3d - Design and implement activities - Design and implement activities and - Design and implement activities and Provide students with opportunities to and investigations that require investigations that require investigations that require communicate about mathematics and communication about communication about mathematics. communication about mathematics. make connections among mathematics. - Design and implement activities and - Design and implement activities and mathematics, other content areas, - Design and implement activities investigations that foster students investigations that foster students everyday life, and the workplace. and investigations that foster making mathematical connections making mathematical connections students making mathematical with other content areas, everyday with other content areas, everyday life connections with other content life events, and the workplace. events, and the workplace. areas, everyday life events, and - Encourage students to employ a the workplace. variety of forms of communication that target varied audiences and purposes across content areas. Element 3e - Implement techniques for - Implement techniques for actively - Implement techniques for actively Implement techniques related to actively engaging students in engaging students in learning and engaging students in learning and student engagement and learning and doing mathematics. doing mathematics. doing mathematics. communication including selecting - Provide instruction that - Provide instruction that incorporates - Provide instruction that incorporates high quality tasks, guiding incorporates high quality tasks high quality tasks and a range of high quality tasks and a range of mathematical discussions, identifying and a range of questioning questioning strategies. questioning strategies. key mathematical ideas, identifying strategies. and addressing student - Guide productive mathematical - Guide productive mathematical misconceptions, and employing a - Guide productive mathematical discussions in classrooms centered discussions in classrooms centered on range of questioning strategies. discussions in classrooms on key mathematical ideas. key mathematical ideas. centered on key mathematical - Select and apply instructional - Select and apply instructional ideas. techniques that assist in identifying techniques that assist in identifying - Select and apply instructional and addressing student and addressing student techniques that assist in misconceptions. misconceptions. identifying and addressing - Engage students in communicating student misconceptions. - Engage students in communicating about mathematics. about mathematics. - Engage students in - Use students’ misconceptions as communicating about opportunities for learning. mathematics. Element 3f - Plan, select, and implement - Plan, select, and implement - Plan, select, and implement formative Plan, select, implement, interpret, and formative and summative formative and summative and summative assessments. use formative and summative assessments. assessments. assessments to inform instruction by - Interpret and use formative and

NCTM CAEP Standards (2012) Reviewer Rubrics - Middle Grades (Revised 4/27/2015) 10 reflecting on mathematical - Interpret and use formative and - Interpret and use formative and summative assessments to inform proficiencies essential for all students. summative assessments to summative assessments to inform instruction by reflecting on inform instruction by reflecting instruction by reflecting on mathematical proficiencies essential on mathematical proficiencies mathematical proficiencies essential for all students. essential for all students. for all students. - Use assessment results for subsequent instructional planning. Element 3g - Use both formative and - Use both formative and summative - Use both formative and summative Monitor students’ progress, make summative assessment data in assessment data in making assessment data in making instructional decisions, and measure making instructional decisions. instructional decisions. instructional decisions. students’ mathematical understanding and ability using formative and - Monitor students’ progress using - Monitor students’ progress using a - Monitor students’ progress using a summative assessments. a variety of assessment tools that variety of assessment tools that variety of assessment tools that gauge gauge advancement toward gauge advancement toward stated advancement toward stated learning stated learning goals. learning goals. goals. - Use both formative and - Use both formative and summative - Use, modify, and/or design both summative assessments to assessments to measure students’ formative and summative assessments measure students’ mathematical mathematical understanding and based upon students’ prior knowledge understanding and ability. ability. and experiences to measure students’ mathematical understanding and ability. - Design assessment processes that distinguish among developmental levels of students’ mathematical knowledge and skills.

Standard 4: Mathematical Learning Environment Standard 4: Effective teachers of middle grades mathematics exhibit knowledge of pre-adolescent and adolescent learning, development, and behavior. They use this knowledge to plan and create sequential learning opportunities grounded in mathematics education research where students are actively engaged in the mathematics they are learning and building from prior knowledge and skills. They demonstrate a positive disposition toward mathematical practices and learning, include culturally relevant perspectives in teaching, and demonstrate equitable and ethical treatment of and high expectations for all students. They use instructional tools such as manipulatives, digital tools, and virtual resources to enhance learning while recognizing the possible limitations of such tools. Program evidence of candidates’ attainment of Standard 4: - 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 4 is based on two considerations: - At least two assessments aligned to elements of NCTM CAEP Standards (2012) and based on course products or student teaching/internship artifacts such as lesson and/or unit plan(s), student teaching/internship evaluation, or portfolio and accompanied by candidate performance data from a minimum of two applications for an initial report or a minimum of one application for a response to conditions or revised report - A preponderance of evidence drawn from the elements o SASB policy defines preponderance of evidence as “an overall confirmation that candidates meet standards in the strength, weight, or quality of evidence,” rather than satisfactory performance for each element. A commonly accepted definition of preponderance of evidence is a requirement that more than 50% of the evidence favors a given outcome. NCTM program review decisions are based on the preponderance of evidence at the standard level using this definition. Specifically, more than 50% of the elements of each standard must be met at the acceptable or target level. o Elements 4b, 4d, and 4e must be met at the acceptable or target level in order to satisfy the preponderance of evidence for Standard 4.

NCTM Element Unacceptable Acceptable Target Preservice teacher candidates: Fewer than two assessments or At least two assessments provide At least two assessments provide assessments provide little or no evidence that middle grades evidence that middle grades candidates: evidence that middle grades candidates: candidates: Element 4a - Exhibit knowledge of pre- - Exhibit knowledge of pre- - Exhibit knowledge of pre-adolescent adolescent and adolescent adolescent and adolescent learning, and adolescent learning, development, Exhibit knowledge of pre-adolescent learning, development, and development, and behavior. and behavior. and adolescent learning, behavior. development, and behavior and - Demonstrate a positive disposition - Demonstrate a positive disposition demonstrate a positive disposition - Demonstrate a positive toward mathematical processes and toward mathematical processes and toward mathematical processes and disposition toward mathematical learning. learning. learning. processes and learning. - Know how students construct knowledge, acquire skills, and develop

disciplined thinking processes. Element 4b - Plan and create sequential - Plan and create sequential learning - Plan and create sequential learning learning opportunities in which opportunities in which students opportunities in which students Plan and create developmentally students connect new learning to connect new learning to prior connect new learning to prior appropriate, sequential, and prior knowledge and knowledge and experiences knowledge and experiences challenging learning opportunities experiences. grounded in mathematics education - Create a sequence of - Create a sequence of developmentally research in which students are - Create a sequence of developmentally appropriate and appropriate and challenging learning actively engaged in building new developmentally appropriate and challenging learning opportunities opportunities grounded in knowledge from prior knowledge and challenging learning grounded in mathematics education mathematics education research in experiences. opportunities grounded in research in which students are which students are actively engaged in mathematics education research actively engaged in building new building new knowledge. in which students are actively knowledge. - Create a developmentally appropriate engaged in building new and challenging sequence of knowledge. instruction for all students that shows a progression of learning over time toward proficiency and understanding. Element 4c - Incorporate knowledge of - Incorporate knowledge of individual - Incorporate knowledge of individual individual differences and the differences and the cultural and differences and the cultural and Incorporate knowledge of individual cultural and language diversity language diversity that exists within language diversity that exists within differences and the cultural and that exists within classrooms to classrooms to motivate and engage classrooms to motivate and engage language diversity that exists within motivate and engage students. students. students. classrooms and include culturally relevant perspectives as a means to - Include culturally relevant - Include culturally relevant - Include culturally relevant motivate and engage students. perspectives as a means to perspectives as a means to motivate perspectives as a means to motivate motivate and engage students. and engage students. and engage students. - Access information about and incorporate resources related to cultural, ethnic, linguistic, gender, and learning differences in their teaching. Element 4d - Demonstrate equitable and - Demonstrate equitable and ethical - Demonstrate equitable and ethical ethical treatment of all students. treatment of all students. treatment of all students. Demonstrate equitable and ethical treatment of and high expectations for - Have high expectations for all - Have high expectations for all - Have high expectations for all all students. students. students. students and persist in helping each student reach his/her full potential. - Demonstrate respect for and responsiveness to the cultural

backgrounds and differing perspectives students bring to the classroom. Element 4e - Apply mathematical content and - Apply mathematical content and - Apply mathematical content and Apply mathematical content and pedagogical knowledge to select pedagogical knowledge to select and pedagogical knowledge to select and pedagogical knowledge to select and and use instructional tools such use instructional tools such as use instructional tools such as use instructional tools such as as manipulatives and physical manipulatives and physical models, manipulatives and physical models, manipulatives and physical models, models, drawings, virtual drawings, virtual environments, drawings, virtual environments, drawings, virtual environments, environments, spreadsheets, spreadsheets, presentation tools, and spreadsheets, presentation tools, and spreadsheets, presentation tools, and presentation tools, and mathematics-specific technologies. mathematics-specific technologies. mathematics-specific technologies mathematics-specific (e.g., graphing tools and interactive technologies. - Make sound decisions about when - Make sound decisions about when geometry software); and make sound instructional tools enhance teaching instructional tools enhance teaching decisions about when such tools - Make sound decisions about and learning and recognize both the and learning and recognize both the enhance teaching and learning, when instructional tools enhance insights to be gained and possible insights to be gained and possible recognizing both the insights to be teaching and learning and limitations of such tools. limitations of such tools. gained and possible limitations of recognize both the insights to be such tools. gained and possible limitations of such tools. - Participate in learning opportunities that address current and emerging technologies in support of mathematics learning and teaching.

Standard 5: Impact on Student Learning Standard 5: Effective teachers of middle grades mathematics provide evidence demonstrating that as a result of their instruction, middle grades students’ conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and application of major mathematics concepts in varied contexts have increased. These teachers support the continual development of a positive disposition toward mathematics. They show that new student mathematical knowledge has been created as a consequence of their ability to engage students in mathematical experiences that are developmentally appropriate, require active engagement, and include mathematics-specific technology in building new knowledge. Program evidence of candidates’ attainment of Standard 5: - 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 5 is based on two considerations: - At least two assessments aligned to elements of NCTM CAEP Standards (2012) and based on course products or student teaching/internship artifacts such as lesson and/or unit plan(s), student teaching/internship evaluation, or portfolio and accompanied by candidate performance data from a minimum of two applications for an initial report or a minimum of one application for a response to conditions or revised report - A preponderance of evidence drawn from the elements o SASB policy defines preponderance of evidence as “an overall confirmation that candidates meet standards in the strength, weight, or quality of evidence,” rather than satisfactory performance for each element. A commonly accepted definition of preponderance of evidence is a requirement that more than 50% of the evidence favors a given outcome. NCTM program review decisions are based on the preponderance of evidence at the standard level using this definition. Specifically, more than 50% of the elements of each standard must be met at the acceptable or target level. o Element 5c and at least 1 additional element must be met at the acceptable or target level in order to satisfy the preponderance of evidence for Standard 5.

NCTM Element Unacceptable Acceptable Target Preservice teacher candidates: Fewer than two assessments or At least two assessments provide At least two assessments provide assessments provide little or no evidence that middle grades evidence that middle grades candidates: evidence that middle grades candidates: candidates: Element 5a - Verify that middle grades - Verify that middle grades - Verify that middle grades students students demonstrate conceptual students demonstrate conceptual demonstrate conceptual understanding Verify that middle grades students understanding and procedural understanding and procedural and procedural fluency. demonstrate conceptual fluency. fluency. - Verify that middle grades students understanding; procedural fluency; - Verify that middle grades - Verify that middle grades demonstrate the ability to formulate, the ability to formulate, represent, and students demonstrate the ability students demonstrate the ability to represent, and solve problems. solve problems; logical reasoning and to formulate, represent, and formulate, represent, and solve - Verify that middle grades students continuous reflection on that solve problems. problems. reason logically and reflect on their

NCTM CAEP Standards (2012) Reviewer Rubrics - Middle Grades (Revised 4/27/2015) 15 reasoning; productive disposition - Verify that middle grades - Verify that middle grades reasoning. toward mathematics; and the students reason logically and students reason logically and reflect - Verify that middle grades students application of mathematics in a reflect on their reasoning. on their reasoning. demonstrate a productive disposition variety of contexts within major - Verify that middle grades - Verify that middle grades toward mathematics. mathematical domains. students demonstrate a students demonstrate a productive - Verify that middle grades students productive disposition toward disposition toward mathematics. apply the mathematics they learn in a mathematics. - Verify that middle grades variety of contexts within major - Verify that middle grades students apply the mathematics they mathematical domains. students apply the mathematics learn in a variety of contexts within - Demonstrate sustained and they learn in a variety of major mathematical domains. meaningful use of data to inform contexts within major practice. mathematical domains.

Element 5b - Engage students in - Engage students in developmentally - Engage students in developmentally Engage students in developmentally developmentally appropriate appropriate mathematical activities appropriate mathematical activities appropriate mathematical activities mathematical activities and and investigations that require active and investigations that require active and investigations that require active investigations that require active engagement in building new engagement in building new engagement and include engagement in building new knowledge. knowledge. mathematics-specific technology in knowledge. building new knowledge. - Engage students in - Engage students in developmentally - Engage students in developmentally appropriate appropriate mathematical activities developmentally appropriate mathematical activities and and investigations that include mathematical activities and investigations that include mathematics-specific technology in investigations that include mathematics-specific technology in building new knowledge. mathematics-specific technology building new knowledge. in building new knowledge. - Facilitate students’ ability to develop future inquiries based on current analyses. Element 5c - Collect, organize, - Collect, organize, analyze, - Collect, organize, analyze, and Collect, organize, analyze, and reflect analyze, and reflect on and reflect on diagnostic, formative, reflect on diagnostic, formative, and on diagnostic, formative, and diagnostic, formative, and and summative assessment data. summative assessment data. summative assessment data. summative assessment evidence and - Determine the extent to - Determine the extent to which determine the extent to which - Determine the extent to which students’ mathematical students’ mathematical proficiencies students’ mathematical proficiencies which students’ mathematical proficiencies have increased. have increased. have increased as a result of their proficiencies have increased. instruction. - Use assessment results as a basis for designing and modifying their instruction as a means to meet

group and individual needs and increase student performance.

Standard 6: Professional Knowledge and Skills Standard 6: Effective teachers of middle grades mathematics are lifelong learners and recognize that learning is often collaborative. They participate in professional development experiences specific to mathematics and mathematics education, draw upon mathematics education research to inform practice, continuously reflect on their practice, and utilize resources from professional mathematics organizations. Program evidence of candidates’ attainment of Standard 6: - 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 6 is based on two considerations: - At least two assessments aligned to elements of NCTM CAEP Standards (2012) and based on course products or student teaching/internship artifacts such as student teaching/internship evaluation or portfolio and accompanied by candidate performance data from a minimum of two applications for an initial report or a minimum of one application for a response to conditions or revised report - A preponderance of evidence drawn from the elements o SASB policy defines preponderance of evidence as “an overall confirmation that candidates meet standards in the strength, weight, or quality of evidence,” rather than satisfactory performance for each element. A commonly accepted definition of preponderance of evidence is a requirement that more than 50% of the evidence favors a given outcome. NCTM program review decisions are based on the preponderance of evidence at the standard level using this definition. Specifically, more than 50% of the elements of each standard must be met at the acceptable or target level. o Element 6b and at least 1 additional element must be met at the acceptable or target level in order to satisfy the preponderance of evidence for Standard 6.

NCTM Element Unacceptable Acceptable Target Preservice teacher candidates: Fewer than two assessments or At least two assessments provide At least two assessments provide assessments provide little or no evidence that middle grades candidates: evidence that middle grades candidates: evidence that middle grades candidates:

Element 6a - Participate in professional - Participate in professional - Participate in professional Take an active role in their development experiences that development experiences that directly development experiences that professional growth by participating directly relate to the learning and relate to the learning and teaching of directly relate to the learning and in professional development teaching of mathematics. mathematics. teaching of mathematics. experiences that directly relate to the - Incorporate into their teaching new learning and teaching of mathematics. learning acquired from professional development experiences. Element 6b - Engage in continuous and - Engage in continuous and - Engage in continuous and

Engage in continuous and collaborative learning as a collaborative learning as a means of collaborative learning as a means of collaborative learning that draws means of enhancing students’ enhancing students’ learning enhancing students’ learning upon research in mathematics learning opportunities in opportunities in mathematics. opportunities in mathematics. education to inform practice; enhance mathematics. - Use research in mathematics - Use research in mathematics learning opportunities for all students’ - Use research in mathematics education to inform practice. education to inform practice. mathematical knowledge education to inform practice. - Enhance all students’ knowledge of - Enhance all students’ knowledge of development; involve colleagues, - Enhance all students’ knowledge mathematics. mathematics. other school professionals, families, of mathematics. - Involve colleagues, other school - Involve colleagues, other school and various stakeholders; and - Involve colleagues, other school professionals, families, and various professionals, families, and various advance their development as a professionals, families, and stakeholders in the educational stakeholders in the educational reflective practitioner. various stakeholders in the process. process. educational process. - Continue their development as a - Continue their development as a - Continue their development as a reflective practitioner. reflective practitioner. reflective practitioner. - Use resources, analyses of instruction, and professional development experiences to enhance student learning of mathematics. Element 6c - Use resources from professional - Use resources from professional - Use resources from professional mathematics education mathematics education organizations mathematics education organizations Use resources from professional organizations such as print, such as print, digital, and virtual such as print, digital, and virtual mathematics education organizations digital, and virtual resources and resources and collections. resources and collections. such as print, digital, and virtual collections. resources and collections. - Use research-based resources from professional mathematics education organizations that target positively impacting student learning.

NCTM CAEP Standards (2012) Reviewer Rubrics - Middle Grades (Revised 4/27/2015)