progressions impact the teaching of secondary students at different developmental levels. Element 3b Analyze and consider research in planning for and leading students in rich mathematical learning experiences. - Analyze and consider research in planning for mathematics instruction. - Incorporate research-based methods when leading students in rich mathematical learning experiences. - Analyze and consider research in planning for mathematics instruction. - Incorporate research-based methods when leading students in rich mathematical learning experiences. - Analyze and consider research in planning for mathematics instruction. - Incorporate research-based methods when leading students in rich mathematical learning experiences. - Extend their repertoire of instructional methods that address students’ diverse learning needs through participation in leadership opportunities such as conferences, use of journals and resources, and engagement with professional organizations. Element 3c Plan lessons and units that incorporate a variety of strategies, differentiated instruction for diverse populations, and mathematics-specific and instructional technologies in building all students’ conceptual understanding and procedural proficiency. - Plan lessons and units that incorporate a variety of strategies. - Plan lessons and units addressing student differences and diverse populations and how these differences influence student learning of mathematics. - Include mathematics-specific and instructional technologies in planned lessons and units. - Build all students’ conceptual understanding and procedural proficiency in planned lessons and units. - Plan lessons and units that incorporate a variety of strategies. - Plan lessons and units addressing student differences and diverse populations and how these differences influence student learning of mathematics. - Include mathematics-specific and instructional technologies in planned lessons and units. - all students’ conceptual understanding and procedural proficiency in planned lessons and units. - Plan lessons and units that incorporate a variety of strategies. - Plan lessons and units addressing student differences and diverse populations and how these differences influence student learning of mathematics. - Include mathematics-specific and instructional technologies in planned lessons and units. - Build all students’ conceptual understanding and procedural proficiency in planned lessons and units.
- Include in planned lessons and units multiple opportunities and solution avenues for students to demonstrate conceptual understanding and procedural proficiency. Element 3d Provide students with opportunities to communicate about mathematics and make connections among mathematics, other content areas, everyday life, and the workplace. - Design and implement activities and investigations that require communication about mathematics. - Design and implement activities and investigations that foster students making mathematical connections with other content areas, everyday life events, and the workplace. - Design and implement activities and investigations that require communication about mathematics. - Design and implement activities and investigations that foster students making mathematical connections with other content areas, everyday life events, and the workplace. - Design and implement activities and investigations that require communication about mathematics. - Design and implement activities and investigations that foster students making mathematical connections with other content areas, everyday life events, and the workplace. - Encourage students to employ a variety of forms of communication that target varied audiences and purposes across content areas. Element 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. - Implement techniques for actively engaging students in learning and doing mathematics. - Provide instruction that incorporates high quality tasks and a range of questioning strategies. productive mathematical discussions in classrooms centered on key mathematical ideas. - Select and instructional techniques that assist in identifying and addressing student misconceptions. - Implement techniques for actively engaging students in learning and doing mathematics. - Provide instruction that incorporates high quality tasks and a range of questioning strategies. Guide productive mathematical discussions in classrooms centered on key mathematical ideas. - Select and apply instructional techniques that assist in identifying and addressing student misconceptions. - Implement techniques for actively engaging students in learning and mathematics. - Provide instruction that incorporates high quality tasks and a range of questioning strategies. Guide productive mathematical discussions in classrooms centered on key mathematical ideas. - Select and apply instructional techniques that assist in identifying and addressing student misconceptions.
- Engage students in communicating about mathematics. Engage students in communicating mathematics. - Engage students in communicating about mathematics. - Use students’ misconceptions as opportunities for learning. Element 3f Plan, select, implement, interpret, and use formative and summative assessments to inform instruction by reflecting on mathematical proficiencies essential for all students. - Plan, select, and implement formative and summative assessments. Interpret and use formative and summative assessments to inform instruction by reflecting on mathematical proficiencies essential for all students. - Plan, select, and implement formative and summative assessments. Interpret and use formative and summative assessments to inform instruction by reflecting on mathematical proficiencies essential for all students. Plan, select, and implement formative and summative assessments. - Interpret and use formative and summative assessments to inform instruction by reflecting on mathematical proficiencies essential for all students. - Use assessment results for subsequent instructional planning. Element 3g Monitor students’ progress, make instructional decisions, and measure students’ mathematical understanding and ability using formative and summative assessments. Use both formative and summative assessment data in making instructional decisions. - Monitor students’ progress a variety of assessment tools that gauge advancement toward stated learning goals. - Use both formative and summative assessments to measure students’ mathematical understanding and ability. Use both formative and summative assessment data in making instructional decisions. - Monitor students’ progress using a variety of assessment tools that gauge advancement toward stated learning goals. - Use both formative and summative assessments to measure students’ mathematical understanding and ability. Use both formative and summative assessment data in making instructional decisions. - Monitor students’ progress using a variety of assessment tools that gauge advancement toward stated learning goals. - Use, modify, and/or design both formative and summative assessments based upon students’ prior knowledge and experiences to measure students’ mathematical understanding and ability. - Design assessment processes that distinguish among developmental
Fewer than two assessments or assessments provide little or no evidence that secondary candidates: Element 4a Exhibit knowledge of adolescent learning, development, and behavior and demonstrate a positive disposition toward mathematical processes and learning. - Exhibit knowledge of adolescent learning, development, and behavior. - Demonstrate a positive disposition toward mathematical processes and learning. - Exhibit knowledge of adolescent learning, development, and behavior. - Demonstrate a positive disposition toward mathematical processes and learning. - Exhibit knowledge of adolescent learning, development, and behavior. - Demonstrate a positive disposition toward mathematical processes and learning. - Know how students construct knowledge, acquire skills, and develop disciplined thinking processes. Element 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. - Plan and create sequential learning opportunities in which students connect new learning to prior knowledge and experiences. - Create a sequence of developmentally appropriate and challenging learning opportunities grounded in mathematics education research in which students are actively engaged in building new knowledge. - Plan and create sequential learning opportunities in students connect new learning to prior knowledge and experiences - Create a sequence of developmentally appropriate and challenging learning opportunities grounded in mathematics education research in which students are actively engaged in building new knowledge. - Plan and create sequential learning opportunities in which students connect new learning to prior knowledge and experiences - Create a sequence of developmentally appropriate and challenging learning opportunities grounded in mathematics education research in which students are actively engaged in building new knowledge. - Create a developmentally appropriate and challenging sequence of instruction for all students that shows a progression of learning over time toward proficiency and understanding. Element 4c Incorporate knowledge of individual differences and the cultural and language diversity that exists within classrooms and - Incorporate knowledge of individual differences and the cultural and language diversity that exists within classrooms to motivate and engage students. - Incorporate knowledge of individual differences and the cultural and language diversity that exists within classrooms to motivate and engage students. - Incorporate knowledge of individual differences and the cultural and language diversity that exists within classrooms to motivate and engage students.
include culturally relevant perspectives as a means to motivate and engage students. - Include culturally relevant perspectives as a means to motivate and engage students. - Include culturally relevant perspectives as a means to motivate and engage students. - Include culturally relevant perspectives as a means to motivate 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 ethical treatment of and high expectations for all students. - Demonstrate equitable and ethical treatment of all students. - Have high expectations for all students. - Demonstrate equitable and ethical treatment of all students. - Have high expectations for all students. - Demonstrate equitable and ethical treatment of all students. - Have high expectations for all 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 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); and make sound decisions about when such tools enhance teaching and learning, - 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. - Make sound decisions about when instructional tools enhance teaching and learning and recognize both the insights to be gained and possible limitations of such tools. - 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. Make decisions about when instructional tools enhance teaching and learning and recognize both the insights to be gained and possible limitations of such tools. - 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. - Make sound decisions about when instructional tools enhance teaching and learning and recognize both the insights to be gained and possible limitations of such tools. - Participate in learning opportunities that address current and emerging
Fewer than two assessments or assessments provide little or no evidence that secondary candidates: Element 5a Verify that secondary students demonstrate conceptual understanding; procedural fluency; the ability to formulate, represent, and solve problems; logical reasoning and continuous reflection on that reasoning; productive disposition toward mathematics; and the application of mathematics in a variety of contexts within major mathematical domains. Verify that secondary students demonstrate conceptual understanding and procedural fluency. Verify that secondary students demonstrate the ability to formulate, represent, and solve problems. Verify that secondary students reason logically and reflect on their reasoning. Verify that secondary students demonstrate a productive disposition toward mathematics. Verify that secondary students apply the mathematics they learn in a variety of contexts within major mathematical domains. Verify that secondary students demonstrate conceptual understanding and procedural fluency. Verify that secondary students demonstrate the ability to formulate, represent, and problems. Verify that secondary students reason logically and reflect on their reasoning. Verify that secondary students demonstrate a productive disposition toward mathematics. Verify that secondary students apply the mathematics they learn in a variety of contexts within major mathematical domains. Verify that secondary students demonstrate conceptual understanding and procedural fluency. Verify that secondary students demonstrate the ability to formulate, represent, and problems. Verify that secondary students reason logically and reflect on their reasoning. Verify that secondary students demonstrate a productive disposition toward mathematics. Verify that secondary students apply the mathematics they learn in a variety of contexts within major mathematical domains. Demonstrate sustained and meaningful use of data to inform practice. Element 5b Engage students in developmentally appropriate mathematical activities and investigations that require active engagement and include mathematics-specific technology in building new knowledge. Engage students in developmentally appropriate mathematical activities and investigations that require active engagement in building new knowledge. Engage students in developmentally appropriate mathematical activities and investigations that include Engage students in developmentally appropriate mathematical activities and investigations that require active engagement in building new knowledge. Engage students in developmentally appropriate mathematical activities and investigations that include Engage students in developmentally appropriate mathematical activities and investigations that require active engagement in building new knowledge. Engage students in developmentally appropriate mathematical activities and investigations that include