Content-specific conceptual examples of how the standard might be met.

Evidence Type/Name 

Rationale of how the evidence supports the indicator.

Standard 1: Learner Development. The teacher understands how learners grow and develop, recognizing that patterns of learning and development vary individually within and across the cognitive, linguistic, social, emotional, and physical areas, and designs and implements developmentally appropriate and challenging learning experiences.

Standard Rationale

Evidence and assessments related to this standard attend to individuals and their unique developmental needs. This includes using and building upon language and mathematical representations within individualized, small group, and whole class settings.

Mathematics examples of what might apply

1(a) The teacher knows how to recognize students’ mathematical development, knowledge, understandings, ways of thinking, mathematical dispositions, interests, and experiences. 

1(b) The teacher knows of learning progressions and learning trajectories that move students toward more sophisticated mathematical reasoning.

1(c) The teacher encourages students to make connections and develop a cohesive framework for mathematical ideas. 

1(d) The teacher applies knowledge of learning progressions and trajectories when creating assignments, assessments, and lessons. 

1(e) The teacher plans and facilitates learning activities that value students’ ideas and guide the development of students’ ways of thinking, and mathematical dispositions in line with research-based learning progressions.

1a. EDUC 4470: Classroom Analysis of Learning, 3 Act Task 

1.b. EDUC 4470: Lesson Modification, Leveraging Discourse, 3 Act Task

1.c. EDUC 4470: Leveraging Discourse, 3 Act Task

1.d. EDUC 4470: Lesson Modification

1.e. EDUC 4470: Lesson Modification, Leveraging Discourse, 3 Act Task

1.a. These assessments focus on attending to students ways of thinking, the progression of the mathematics, and using this knowledge to support students’ mathematical thinking and interest in mathematics

1.b. These assessments require teacher candidates to demonstrate various levels of differentiation, based on students’ mathematical understanding, to allow for a tiered progression of learning

1.c. These assessments are student-centered and student-driven to promote students’ development of reasoning and sensemaking in mathematics

1.d. This assessment specifically targets how to differentiate learning based on the mathematical progression of concepts

1.e. These assessments are grounded in high-leverage research-based practices that build on student-centered and student-driven to promote students’ development of reasoning and sensemaking in mathematics

Standard 2:  Learning Differences. The teacher uses understanding of individual differences and diverse cultures and communities to ensure inclusive learning environments that enable each learner to meet high standards. 

Standard Rationale

Evidence and assessments related to this standard attend to students’ unique needs, readiness, and backgrounds through deliberate differentiation and flexible, student-centered learning experiences.

Mathematics examples of what might apply

2(a) The teacher knows how to design lessons at appropriate levels of mathematical development, knowledge, understanding, and experience. 

2(b) The teacher knows how to use assessment data and appropriate interventions for students.

2(c) The teacher adjusts and modifies instruction while adhering to the content standards, in order to ensure mathematical understanding for all students.

2.a. EDUC 4470: Lesson Modification, Leveraging Discourse, 3 Act Task

2.b. EDUC 4470: Classroom Analysis of Learning, Leveraging Discourse

2.c. EDUC 4470:  Leveraging Discourse, 3 Act Task

2.a. These assessments focus on attending to students ways of thinking, the progression of the mathematics, and using this knowledge to support students’ mathematical thinking and interest in mathematics

2.b. These assessments focus on understanding the ways in which students think about mathematics and demonstrate how to use these understandings to support the development of their reasoning

2.c. These assessments require teacher candidates to demonstrate adaptability and flexibility with support students learning and development of mathematical thinking

Standard 3: Learning Environments. The teacher candidate works with others to create environments that support individual and collaborative learning, and that encourage positive social interaction, active engagement in learning, and self-motivation.

Standard Rationale

Evidence and assessments related to this standard attend to the collaborative nature of being a professional mathematics teacher. Teacher candidates are required to work together to understand the nuances of ideal, student-centered classrooms and effective, high-leverage teaching practices. Additional connections applicable to teaching mathematics can be found in the Foundational Coursework evidence.

Covered in the Foundational Coursework

EDUC 4470: Standards of Mathematics Practice Group presentations

This assessment requires teacher candidates to work in collaborative groups to understand how to support mathematical ways of thinking and content proficiency in students

Standard 4: Content Knowledge. The teacher understands the central concepts, tools of inquiry, and structures of the discipline(s) he or she teaches and creates learning experiences that make the discipline accessible and meaningful for learners to assure mastery of the content. 

Standard Rationale

Evidence and assessments related to this standard attend to knowing what it means to do mathematics and be a mathematician. This includes understanding the content deeply as well as recognizing the nature and nuances of inquiry-based learning in mathematics.

Mathematics examples of what might apply

4(a) The teacher knows a variety of problem-solving approaches for investigating and understanding mathematics. 

4(b) The teacher understands concepts (as recommended by state and national mathematics education organizations) and applications of number and quantity, algebra, geometry (Euclidean and transformational), statistics (descriptive and inferential) and data analysis, and probability, functions, and trigonometry, and has the specialized and pedagogical content knowledge for teaching necessary for those concepts and applications to be implemented in the 6-12 curriculum. 

4(c) The teacher knows how to make use of hands-on, visual, and symbolic mathematical models in all domains of mathematics. 

4(d) The teacher knows how to use mathematical argument and proof to evaluate the legitimacy and efficiency of alternative algorithms, strategies, conceptions, and makes connections between them. 

4(e) The teacher knows the standards for mathematical practice, how to engage students in the use of those practices, and how they have shaped the discipline.

4(f) The teacher connects the abstract and the concrete and asks useful questions to clarify or improve reasoning. 

4(g) The teacher uses hands-on, visual, and symbolic mathematical models in all domains of mathematics.

4(h) The teacher uses mathematical argument and proof to evaluate the legitimacy and efficiency of alternative algorithms, strategies, and conceptions, and makes connections between them. 

4(i) The teacher implements the standards for mathematical practice and engages students in the use of those practices.

4.a. MATH 1170: Quizzes, Homework, Exams; MATH 1175: Quizzes, Homework, Exams; MATH 2287: Proof Portfolio, Exams, Homework

4.b. MATH 1170: Quizzes, Homework, Exams; MATH 1175: Quizzes, Homework, Exams; MATH 2287: Quizzes, Homework, Exams, Proof Portfolio; MATH 2240: Group Work, Homework; MATH 3343: Exam; MATH 3352: Quizzes, Homework, Exams 

4.c. MATH 1170: Quizzes, Homework, Exams; MATH 1175: Quizzes, Homework, Exams; MATH 2240: Group Work, Homework

4.d. MATH 1170: Quizzes, Homework, Exams; MATH 1175: Quizzes, Homework, Exams; MATH 2287: Proof Portfolio, Exams, Homework; EDUC 4470:  Leveraging Discourse, 3 Act Task

4.e. EDUC 4470: Lesson Modification, Leveraging Discourse, 3 Act Task

4.f. MATH 1170: Quizzes, Homework, Exams; MATH 1175: Quizzes, Homework, Exams; MATH 2240: Group Work, Homework; MATH 2287: Proof Portfolio, Exams, Homework

4.g. MATH 1170: Quizzes, Homework, Exams; MATH 1175: Quizzes, Homework, Exams; MATH 2240: Group Work, Homework; MATH 3343: Exam; 

4.h. MATH 2240: Group Work, Homework; MATH 2287: Proof Portfolio, Exams, Homework; MATH 3343: Exam; EDUC 4470

4.i. EDUC 4470: Leveraging Discourse, 3 Act Task, Lesson Modification

4.a. These assessments require students to conceptualize, approach, and solve problems in various contexts

4.b. Each quiz, exam, homework or other type of assessment develops particular content knowledge for grades 6-12

4.c. Assessments in these courses use various tools and representations to demonstrate understanding of content within each domain

4.d. Assessments in these courses focus specifically on developing and using proof and logical argumentation to justify mathematical relationships

4.e. These assessments specifically build on the mathematical habits of mind and interaction built into the standards of mathematical practice

4.f. The assessments for these courses specifically deal with contextualizing and decontextualizing the mathematics 

4.g. The assessments from these courses require the use of various representations and models to demonstrate understanding

4.h. Assessments from these courses focus specifically on proof, argumentation, and the ways in which various representations and strategies support mathematical understanding

4.i. These assessments specifically build on the mathematical habits of mind and interaction built into the standards of mathematical practice

Standard 5: Application of Content. The teacher understands how to connect concepts and use differing perspectives to engage learners in critical thinking, creativity, and collaborative problem solving related to authentic local and global issues. 

Standard Rationale

Evidence and assessments related to this standard attend to the ways in which teacher candidates can leverage mathematics to consider real-life scenarios and situations. In doing so, teacher candidates help students develop their mathematical understanding and critical thinking through written language, discourse, and problem solving.

Mathematics examples of what might apply

5(a) The teacher knows how to apply mathematics content and practice to other disciplines, including (but not limited to) engineering, science, personal finance, and business.

5.a. EDUC 4470: Classroom Analysis of Learning, 3 Act Task, Lesson Modification, Leveraging Discourse

5.a. These assessments all focus on developing teachers' pedagogical content knowledge of teaching mathematics by focusing on reasoning and sensemaking, developing conceptual understanding through various representations and discourse, while some (e.e. 3 Act Tasks) are highly grounded in authentic scenarios.

Standard 6: Assessment. The teacher understands and uses multiple methods of assessment to engage learners in their own growth, to monitor learner progress, and to guide the teacher’s and learner’s decision making.

Standard Rationale

Evidence and assessments related to this standard attends to the diverse ways in which teacher candidates elicit, interpret, and adapt to students’ mathematical thinking. This includes using dynamic assessments such as number/reasoning talks, whole class discussions, and problem-based learning experiences.

Mathematics examples of what might apply

6(a) The teacher knows how to assess students’ mathematical reasoning.

6(b) The teacher assesses students’ mathematical reasoning

6.a. EDUC 4470: Classroom Analysis of Learning, 3 Act Task, Lesson Modification, Leveraging Discourse

6.b. EDUC 4470: 3 Act Task, Lesson Modification, Leveraging Discourse 

6.a. These assessments focus on understanding the ways in which students think about mathematics and demonstrate how to use these understandings to support the development of their reasoning

6.b. These assessments focus on attending to, interpreting, and supporting students’ mathematical reasoning

Standard 7: Planning for Instruction. The teacher plans instruction that supports every student in meeting rigorous learning goals by drawing upon knowledge of content areas, curriculum, cross- disciplinary skills, and pedagogy, as well as knowledge of learners and the community context.

Standard Rationale

Evidence and assessments related to this standard attends specifically to the ways in which teacher candidates develop various learning experiences to develop conceptual/relational understanding of mathematics. This planning also includes attention to developing students’ productive habits of mind and habits of interaction as evident in the standards of mathematical practice.

Mathematics examples of what might apply

7(a) The teacher knows content and practice standards for mathematics and understands how to design instruction to help students meet those standards. 

7(b) The teacher knows how to plan learning activities that help students move from their current understanding through research-based learning progressions.

7(c) The teacher plans and assesses instructional sequences that engage students in learning the formal structure and content of mathematics with and through mathematical practices.

7.a. EDUC 4470: 3 Act Task, Lesson Modification, Leveraging Discourse

7.b. EDUC 4470: 3 Act Task, Lesson Modification, Leveraging Discourse

7.c. EDUC 4470: 3 Act Task, Lesson Modification, Leveraging Discourse

7.a. These assessments focus different aspects of designing and adapting instruction based on content and practice standards for mathematics

7.b. These assessments focus different aspects of designing and adapting instruction to support students individually, when working in small groups, and within a whole-class setting

7.c. These assessments require an understanding of progressions and supporting students’ habits of mind and mathematical habits of interaction through student-centered inquiry-based experiences

Standard 8: Instructional Strategies. The teacher understands and uses a variety of instructional strategies to encourage learners to develop deep understanding of content areas and their connections, and to build skills to apply knowledge in meaningful ways. 

Standard Rationale

Evidence and assessments related to this standard attends to various high-leverage instructional techniques needed to teach for mastery. As such, the evidence highlights teacher candidates’ ability to use strategies for individual, small group and whole class learning experiences.

Mathematics examples of what might apply

8(a) The teacher knows how to formulate or access questions and tasks that elicit students’ use of mathematical reasoning and problem-solving strategies. 

8(b) The teacher knows a variety of instructional strategies for investigating and understanding mathematics including inquiry, discourse, and problem-solving approaches. 

8(c) The teacher knows how to facilitate expression of concepts using various mathematical representations (e.g., symbolic, numeric, graphic, visual, verbal, concrete models) and precise language. 

8(d) The teacher understands the appropriate use of technology in teaching and learning of mathematics (e.g., graphing calculators, dynamic geometry software, statistical software). 

8(e) The teacher knows how to use student conceptions and misconceptions to guide and facilitate learning.

8(f) The teacher poses questions and tasks that elicit students’ use of mathematical reasoning and problem-solving strategies. 

8(g) The teacher uses a variety of instructional strategies for investigating and understanding mathematics, including inquiry and problem-solving approaches. 

8(h) The teacher facilitates exploration of concepts using various mathematical representations (e.g., symbolic, numeric, graphic, visual, verbal, concrete models) and precise language. 

8(i) The teacher uses technology appropriately in the teaching and learning of (e.g., graphing calculators, dynamic geometry software, statistical software). 

8(j) The teacher uses student conceptions and misconceptions to guide and facilitate learning.

8.a. EDUC 4470: 3 Act Task, Lesson Modification, Leveraging Discourse

8.b. EDUC 4470: 3 Act Task, Lesson Modification, Leveraging Discourse

8.c. EDUC 4470: 3 Act Task, Lesson Modification, Leveraging Discourse

8.d. MATH 1170: Quizzes, Homework, Exams; MATH 1175: Quizzes, Homework, Exams; MATH 2287: Proof Portfolio, Exams, Homework; MATH 2240: Group Work, Homework; MATH 3343: Exam; EDUC 4470: 3 Act Task, Lesson Modification

8.e. EDUC 4470: 3 Act Task, Lesson Modification, Leveraging Discourse

8.f. MATH 2287: Quizzes, Homework, Exams, Proof Portfolio; MATH 2240: Group Work, Homework; EDUC 4470: 3 Act Task, Lesson Modification, Leveraging Discourse

8.g. EDUC 4470: 3 Act Task, Lesson Modification, Leveraging Discourse

8.h. EDUC 4470: 3 Act Task, Lesson Modification, Leveraging Discourse

8.i. EDUC 4470: 3 Act Task, Lesson Modification,

8.j. EDUC 4470: Classroom Analysis of Learning, 3 Act Task, Lesson Modification, Leveraging Discourse

8.a. These assessments attend to the ways in which questions are posed to elicit and build on students reasoning and mathematical thinking

8.b. Collectively, these assessments support teacher candidates’ ability to design and implement flexible and differentiated learning experiences, high-leverage discourse practices, and technology-supported inquiry

8.c. These assessment center on using student-centered ways of representing and explaining mathematical relationships

8.d. These assessments require the use of technology, and explore how to use various technology (e.g. graphing software, dynamic geometry software, videos, and spreadsheets) to support the learning of mathematics  

8.e. These assessments focus on attending to students ways of thinking and using this knowledge to support their mathematical thinking

8.f. These assessments focus on discourse, which requires using appropriate questioning strategies to elicit reasoning and mathematical thinking

8.g. The assessments for these courses have inquiry, problem solving and varied instructional strategies as a core aspect of the courses.

8.h. Assessments from these courses focus specifically on the ways in which various representations and strategies support mathematical understanding

8.i. These assessments require the use of technology, and explore how to use various technology (e.g. graphing software, dynamic geometry software, videos, and spreadsheets) to support the learning of mathematics

8.j. These assessments focus on attending to students ways of thinking and using this knowledge to support their mathematical thinking

Standard 9: Professional Learning and Ethical Practice. The teacher candidate engages in ongoing professional learning and uses evidence to continually evaluate his/her practice, particularly the effects of his/her choices and actions on others (learners, families, other professionals, and the community), and adapts practice to meet the needs of each learner.

Standard Rationale

Mathematics teachers review the professional learning and ethical practice concepts in their Foundational Coursework with performance evidence seen in EDUC 4408 and EDUC 4493 Student Teaching.

Standard 10: Leadership and Collaboration. The teacher candidate seeks appropriate leadership roles and opportunities to take responsibility for student learning, to collaborate with learners, families, colleagues, other school professionals, and community members to ensure learner growth, and to advance the profession.

Standard Rationale

Mathematics teachers review leadership and collaboration concepts in their Foundational Coursework with performance evidence seen in EDUC 4408 and EDUC 4493 Student Teaching.

Standard 11: American Indian Tribes in Idaho. The teacher candidate should be able to distinguish between each of the federally recognized tribes with respect to the retention of their ancestral lands in Idaho: Coeur d’Alene Tribe, Kootenai Tribe of Idaho, Nez Perce Tribe, Shoshone-Bannock Tribes, and the Shoshone-Paiute Tribes. Teacher candidates build capacity in learners to utilize the assets that each learner brings to the learning community based on their backgrounds and experiences.

Standard Rationale

Mathematics teachers review the American Indian Tribes in Idaho concepts in their Foundational Coursework. An implementation plan is currently underdevelopment.

Standard 12: Code of Ethics for Idaho Professional Educators. The teacher candidate understands the Code of Ethics for Idaho Professional Educators and its place in supporting the integrity of the profession.

Standard Rationale

Mathematics teachers review leadership and collaboration concepts in their Foundational Coursework with performance evidence seen in EDUC 4408 and EDUC 4493 Student Teaching.

Standard 13: Digital Technology and Online Learning. The teacher candidate knows how to use digital technology to create lessons and facilitate instruction and assessment in face-to-face, blended, and online learning environments to engage students and enhance learning.

Standard Rationale

Mathematics teachers review digital technology and online learning concepts in their Foundational Coursework with performance evidence seen in EDUC 3311 and EDUC 4493 Student Teaching.