Mathematics-specific Characteristic (incorporating MA Framework Standard for Mathematical Practice #3) N/A No Developing Providing Sustaining Evidence Examples of Practice Examples of Practice Examples of Practice Students articulate their thinking and reasoning in mathematics. A few students dominate The majority of students make thinking and All students reflect on their own and on their the discussion and are the reasoning public. peers’ reasoning. only ones who their Students compare and contrast their thinking and Students identify and explain the flaws in peers’ thinking and reasoning. opinions to those of others and distinguish reasoning. They are able to recognize and use is an opportunity for between plausible and flawed arguments. counterexamples. discussion, but the process Students demonstrate an understanding of the big Students build a logical progression of is neither modeled nor ideas by drawing inferences, making predictions, statements to explore the truth of their facilitated for students. and defending hypotheses through discourse and conjectures and to make connections to prior Use of specific content through work they produce. learning and activities. vocabulary during Students use various means (verbally or in Students understand and use stated classroom discourse is writing) to develop, record, and represent their assumptions, definitions, and previously minimal or inaccurate. ideas and/or plausible arguments. established results in constructing arguments. Students make their Students ask questions that clarify or improve Students reason inductively about data, making thinking public, but the their peers’ arguments. plausible arguments that take into account the majority of the discourse context. Strategic use of techniques (such as focuses on procedures and turn-and-talk) supports student rather than concepts or engagement and advances student thinking and mathematical reasoning. reasoning related to key concepts and big ideas. Students respond only to All students use academic vocabulary to express the teacher and not to the ideas and understandings. ideas of their peers. Students openly process one another’s thinking Students have limited or no by actively listening, rephrasing, or agreeing/ opportunities to openly disagreeing and providing a rationale. process their teacher’s and peers’ thinking. Universal Design for Learning (UDL) provides a framework for the maximization of learning opportunities for students with special needs as well as all students and their different learning needs. Download UDL Guidelines at .
Mathematics-specific Characteristic (incorporating MA Framework Standard for Mathematical Practice #3) N/A No Evidence Developing Examples of Practice Providing Examples of Practice Sustaining Examples of Practice Students articulate their thinking and reasoning in mathematics. A few students dominate the discussion and are the only ones who their thinking and reasoning. is an opportunity for discussion, but the process is neither modeled nor facilitated for students. Use of specific content vocabulary during classroom discourse is minimal or inaccurate. Students make their thinking public, but the majority of the discourse focuses on procedures rather than concepts or mathematical reasoning. Students respond only to the teacher and not to the ideas of their peers. Students have limited or no opportunities to openly process their teacher’s and peers’ thinking. The majority of students make thinking and reasoning public. Students compare and contrast their thinking and opinions to those of others and distinguish between plausible and flawed arguments. Students demonstrate an understanding of the big ideas by drawing inferences, making predictions, and defending hypotheses through discourse and through work they produce. Students use various means (verbally or in writing) to develop, record, and represent their ideas and/or plausible arguments. Students ask questions that clarify or improve their peers’ arguments. Strategic use of techniques (such as and turn-and-talk) supports student engagement and advances student thinking and reasoning related to key concepts and big ideas. All students use academic vocabulary to express ideas and understandings. Students openly process one another’s thinking by actively listening, rephrasing, or agreeing/ disagreeing and providing a rationale. All students reflect on their own and on their peers’ reasoning. Students identify and explain the flaws in peers’ reasoning. They are able to recognize and use counterexamples. Students build a logical progression of statements to explore the truth of their conjectures and to make connections to prior learning and activities. Students understand and use stated assumptions, definitions, and previously established results in constructing arguments. Students reason inductively about data, making plausible arguments that take into account the context. Universal Design for Learning (UDL) provides a framework for the maximization of learning opportunities for students with special needs as well as all students and their different learning needs. Download UDL Guidelines at .