Silicon Valley Mathematics Initiative

The Mathematics Teaching Rubric Silicon Valley Mathematics Initiative Mathematics Teaching Rubric Worthwhile Tasks 4 – Exemplary Teaching 3– Successful Teaching 2– Improving Teaching 1– Limited Teaching

The teacher engages the students in Often the teacher engages the students Fairly often the teacher engages the Occasionally the teacher engages the worthwhile tasks. in worthwhile tasks. students in worthwhile tasks. students in worthwhile tasks. The tasks are all part of a coherent Most of the tasks are part of a coherent The tasks are usually a balance between The tasks are usually a part of an curriculum that develops student curriculum that develops student adopted textbooks and investigations adopted textbook curriculum. understanding and facility with understanding and facility with or non-routine problems. The mathematics of the tasks focuses mathematics. mathematics. The mathematics of the tasks is usually on skill acquisition and developing The mathematics of the tasks is clear The mathematics of the tasks is often clear and aligned with core standards procedural knowledge. and aligned with core standards and clear and aligned with core standards and developed to make sense of the A few of the tasks engage student developed to make sense of the world. and developed to make sense of the world. thinking, conceptual development, The tasks engage student thinking, world. Some of the tasks engage student problem solving as well as skills. conceptual development, problem Many of the tasks engage student thinking, conceptual development, solving as well as skills. A few tasks involve a range of thinking, conceptual development, problem solving as well as skills. mediums. The tasks involve a wide range of problem solving as well as skills. Some tasks involve a range of mediums. mediums (graphs, problems, symbols, Occasionally the teacher selects The tasks involve a range of mediums. equations, manipulatives, technology). The teacher sometimes selects materials and tasks that build on and The teacher often selects materials and materials and tasks that build on and extend from their students’ The teacher selects materials and tasks tasks that build on and extend from extend from their students’ understanding. that build on and extend from their their students’ understanding. understanding. students’ understanding. A few of the tasks foster students’ Many of the tasks foster students’ Some of the tasks foster students’ ability to solve problems, reason, Most of the tasks foster students’ ability ability to solve problems, reason and ability to solve problems, reason and and communicate. to solve problems, reason and communicate. communicate. communicate. Most of the tasks involve direct The tasks range across many learning Some of the tasks range across learning instruction and modalities. The tasks range across most learning styles and modalities. The tasks may styles and modalities. A few of the styles and modalities. The tasks may A few of the tasks may be grow out of students’ conjecture of tasks may grow out of students’ grow out of students’ conjecture of approached in more than one questions. conjecture of questions. questions. interesting and legitimate way. Many of the tasks may be approached Some of the tasks may be approached in Often the tasks may be approached in A few of the tasks require more time in more than one interesting and more than one interesting and more than one interesting and to develop solutions. legitimate way. legitimate way. legitimate way. Many of the tasks vary in length of time Some of the tasks require more time to Most of the tasks vary in length of time required to develop solutions. develop solutions. required to develop solutions.

Draft version #4 Page 2 of 6 © Noyce Foundation 2005. To reproduce this document, permission must be granted by the Noyce Foundation: [email protected]. Silicon Valley Mathematics Initiative Mathematics Teaching Rubric The Learning Environment 4 – Exemplary Teaching 3– Successful Teaching 2– Improving Teaching 1– Limited Teaching

The teacher creates a classroom The teacher often allows students to The teacher regularly encourages Some assigned problems require environment where students actively actively construct their own understanding students to learn to use students to learn to use construct their own understanding of of mathematics and learn to use mathematics to make sense of the mathematics to make sense of the mathematics and learn to use mathematics mathematics to make sense of the world. world. world. to make sense of the world. The culture often fosters the development The culture fosters the The class is usually taught in a The teacher creates a culture that fosters of each student’s mathematical power and development of student’s direct instruction format. the development of each student’s supports the class as a community of mathematical skills and some Usually the focus of the lesson is mathematical power and supports the class learners. problem solving. on skill attainment or learning as a community of learners. The teacher provides and structures a lot of Occasionally the teacher supports mathematical procedures and The teacher provides and structures the time to explore sound mathematics and the class to function as a definitions. time necessary to explore sound grapple with significant ideas and community of learners. Some times the teacher assigns mathematics and grapple with significant problems. The teacher provides and non-routine or word problems. ideas and problems. The physical space and materials are structures some time to explore The physical space and materials The physical space and materials are arranged and allocated in ways that can non-routine problems and are arranged and allocated in ways purposely arranged and allocated in ways facilitate students’ learning. grapple with conceptual ideas. that structure students’ work. that facilitate students’ learning. The teacher provides context that often The physical space and materials The teacher’s goal is to develop the The teacher provides context that encourages the development of are arranged and allocated in students’ numerical skills and encourages the development of mathematical skill and proficiency. ways that attempts to facilitate proficiency. mathematical skill and proficiency. students’ learning. Respect and value of students’ ideas, ways Students are required to practice Respect and value of students’ ideas, ways of thinking and positive disposition to The teacher strives to develop during class and complete of thinking and positive disposition to mathematics are often part of the learning the student’s numerical skill and homework. mathematics are essential attributes of the community. proficiency. learning community. The teacher often expects students The teacher often expects and encourages Students’ ideas and ways of to work independently and may The teacher consistently expects and students to work independently or thinking are sometimes part of use some collaborative groups. encourages students to work collaboratively to make sense of the learning activity. independently or collaboratively to make mathematics. Often the teacher asks the students The teacher often expects sense of mathematics. to show work on individual Students occasionally take intellectual risks students to work independently problems. Students take intellectual risks by raising by raising questions, sharing results and and may use some collaborative questions, sharing results and formulating formulating conjectures. groups. Occasionally students are asked to conjectures. share answers with the class. The students may display a sense of Often the teacher involves The students display a sense of mathematical competence by validating students by having them raise Students are encouraged to ask mathematical competence by validating and supporting ideas with mathematical questions and share results. questions if they lack and supporting ideas with mathematical arguments. understanding. arguments.

Draft version #4 Page 3 of 6 © Noyce Foundation 2005. To reproduce this document, permission must be granted by the Noyce Foundation: [email protected]. Silicon Valley Mathematics Initiative Mathematics Teaching Rubric Teacher’s Role in Discourse 4 – Exemplary Teaching 3– Successful Teaching 2– Improving Teaching 1– Limited Teaching

The teacher orchestrates discourse in the The teacher often orchestrates discourse The teacher directs the class and The teacher directs the class. class. in the class. attempts to foster discourse. The teacher poses questions and The teacher poses questions and tasks that The teacher often poses questions and Sometimes the teacher poses tasks that focus students’ work. elicit, engage, and challenge each student’s tasks that elicit, engage, and challenge questions and tasks that elicit, The teacher may listen to some of thinking. each student’s thinking. engage, and challenge students’ the students’ responses. The thinking. The teacher listens carefully to the students’ Often the teacher listens to the students’ teacher may have difficulty ideas and discerns mathematical meaning ideas and makes sense of their responses. The teacher listens to some of the following students’ math thinking and relevancy from student responses. students’ ideas. The teacher may and usually ignores those Often students are asked to clarify and have difficulty following students’ responses. Students are asked to clarify and justify justify their ideas orally and in writing. math thinking. their ideas orally and in writing. Rarely are students asked to The teacher may decide what to pursue Sometimes students are asked to clarify and justify their ideas orally The teacher decides what to pursue in depth in depth from ideas that students bring clarify and justify their ideas orally and in writing. from among the ideas that students bring up up during a discussion. and in writing. during a discussion. The teacher rarely deviates from Some care is given by the teacher to The teacher sometimes deviates the textbook to pursue ideas that Care is given by the teacher to develop develop concepts and to encourage from lesson plan to pursue ideas that students bring up during a concepts thoroughly and insure students’ students’ ownership and understanding. students bring up during a discussion. ownership and understanding. The teacher The teacher attempts to attach discussion. decides when and how to attach mathematical notation and language to The teacher usually follows the mathematical notation and language to students’ ideas. Some care is given by the teacher to textbook in deciding when and students’ ideas. develop concepts and to encourage how to attach mathematical The teacher has good understanding of students’ ownership. The teacher notation and language to students’ The teacher has full understanding of the the mathematical goals of the lesson and follows the textbook in deciding ideas. mathematical goals of the lesson and is often successful in determining when when and how to introduce decides when to provide information, when to provide information, when to clarify an The teacher follows the curricula mathematical notation and language. to clarify an issue, when to model, when to issue, when to model, when to lead, and math goals of the lesson. lead, and when to let a student struggle with when to let a student struggle with The teacher follows the curricula The instructional decisions may be difficulty. These decisions are consistent difficulty. These decisions are often math goals of the lesson. aligned with state standards and with the goal and pace of the lesson. consistent with the goal and pace of the The teacher is improving his/her with the goal of covering the lesson. The teacher monitors students’ questioning strategies. The teacher is topics on state test. participation in discussions and decides The teacher attempts to monitor developing the pacing and The teacher modifies expectation when and how to encourage each student to students’ participation in discussions and generating good questioning. The from student to student. participate. decides when and how to encourage instructional decisions may be students to participate. aligned with lesson goals. Decisions are predicated on insuring all students will learn and be successful in Attempts are made to reach all students. The teacher attempts include all mathematics. students.

Draft version #4 Page 4 of 6 © Noyce Foundation 2005. To reproduce this document, permission must be granted by the Noyce Foundation: [email protected]. Silicon Valley Mathematics Initiative Mathematics Teaching Rubric Students’ Role in Discourse 4 – Exemplary Teaching 3– Successful Teaching 2– Improving Teaching 1– Limited Teaching

The teacher of mathematics promotes The teacher of mathematics often The teacher of mathematics tries to The teacher of mathematics classroom discourse in which students promotes classroom discourse in which promote classroom discourse in which structures the discourse of the have ownership and responsibility. students have ownership and students have some ownership and students. responsibility. responsibility. Students listen to, respond to and Often students are asked questions question the teacher and one another. Students often listen to, respond to and Occasionally students listen to, respond by the teacher and are expected to question the teacher and one another. to and question the teacher and one respond with answers. The students use a variety of tools to another. reason, make connections, solve The students use some tools to reason, The students use a few tools to problems and communicate. make connections, solve problems and The students use a few tools to reason, solve problems and do math tasks. communicate. make connections, solve problems and Students often initiate problems and For specific assignments students communicate. questions for the class to ponder and Students sometimes initiate problems create problems and questions for study. Students regularly make and questions for the class to ponder Occasionally students initiate problems the class to do. conjectures and present solutions. and study. Students often make and questions for the class to ponder Students are asked to present Students explore examples and conjectures and present solutions. and study. answers or solutions. Students counterexamples to investigate Students may explore examples and Students occasionally make conjectures learn and practice mathematics conjectures. counterexamples to investigate and present solutions. Students procedures, vocabulary and facts. conjectures. Students try to convince themselves occasionally explore examples and Occasionally students work in and one another of the validity of Students occasionally try to convince counterexamples to investigate small groups on problems, particular representations, solutions, themselves and one another of the conjectures. In a few situations students discussing answers. In large conjectures and answers. Students rely validity of particular representations, rely on mathematical evidence and groups, students go over problems on mathematical evidence and solutions, conjectures and answers. argument to determine validity. and solutions usually facilitated by argument to determine validity. Sometimes students rely on In small or large groups, students are the teacher. mathematical evidence and argument In small or large groups, students are occasionally an audience for one to determine validity. The discourse involves learning an audience for one another’s another’s comments, explanations or procedures and methods to solve comments, explanations or questions. In small or large groups, students are questions. problems and activities to often an audience for one another’s The discourse is focused on making The discourse sometimes focuses on memorize facts and vocabulary. comments, explanations or questions. sense of mathematical ideas and/or on making sense of mathematical ideas using mathematical ideas sensibly in The discourse often is focused on and/or on using mathematical ideas setting up and solving problems. making sense of mathematical ideas sensibly in setting up and solving and/or on using mathematical ideas problems. sensibly in setting up and solving problems.

Draft version #4 Page 5 of 6 © Noyce Foundation 2005. To reproduce this document, permission must be granted by the Noyce Foundation: [email protected]. Silicon Valley Mathematics Initiative Mathematics Teaching Rubric Tools for Enhancing Discourse 4 – Exemplary Teaching 3– Successful Teaching 2– Improving Teaching 1– Limited Teaching

The teacher supports discourse and a The teacher usually supports discourse The teacher structures the tools that The teacher directs the class as to positive classroom culture by by encouraging and supporting will adapt to the particular when they may use a certain encouraging and supporting students to students to use tools to do and learn mathematics lessons. mathematics tool. use tools to do and learn mathematics. mathematics. The teacher finds times to use The teacher may do an activity The teacher supports the doing of Often the teacher values and computers and other technology. with the computer or use it for mathematics in the manner that encourages the use of a variety of tools those that either need practice or Teacher attempts to balance the time mathematics is done outside of school. such as computers, calculators and have finished their assignments. ] when students use calculators, paper other technology in addition to The teacher values and encourages the and pencil, and mental math. The teacher will allow students to traditional paper and pencil and mental use of a variety of tools such as use a calculator after they have math. The teacher will, at certain times, computers, calculators and other shown they can calculate encourage the students to technology in addition to traditional Often the teacher has the students accurately using paper and pencil. communicate using pictures, diagrams, paper and pencil mental math. communicate orally and in writing tables, graphs, notation, symbols, The teacher directs the type of using pictures, diagrams, tables, graphs, Students communicate orally and in narratives, metaphors, justifications outputs expected such as charts, notation, symbols, narratives, writing using pictures, diagrams, tables, and proofs. graphs, equations or proofs. metaphors, justifications and proofs. graphs, notation, symbols, narratives, Students use manipulatives on When called for in a lesson, the metaphors, justifications and proofs. Often the teacher has students use appropriate activities. class may use manipulatives. models and concrete materials to make Students use models and concrete sense of mathematics and understand The teacher introduces conventional The teacher regularly introduces materials to make sense of mathematics concepts. notation often after students had some the conventional notation to the and understand concepts. kind of concrete experience or when class. Occasionally students are responsible Students are responsible for selecting the textbook suggests the teacher do for selecting and using appropriate There may be special projects or and using appropriate tools to solve so. tools to solve and investigate problems. assignments where students and investigate problems. Occasionally students communicate communicate using alternative The teacher attempts to introduce The teacher introduces conventional their solutions and explanations using materials or tools. conventional notation at points when notation at points when doing so can a variety of tools. doing so can further the work and the further the work and the discourse at discourse at hand. hand. Occasionally students are expected to Students are expected to communicate communicate their conjectures, their conjectures, explanations and explanations and arguments in a arguments in a complete manner using complete manner using appropriate appropriate tools. tools.

Draft version #4 Page 6 of 6 © Noyce Foundation 2005. To reproduce this document, permission must be granted by the Noyce Foundation: [email protected]. Silicon Valley Mathematics Initiative Mathematics Teaching Rubric Teaching and Learning Analysis 4 – Exemplary Teaching 3– Successful Teaching 2– Improving Teaching 1– Limited Teaching

The teacher understands that Often the teacher links assessment with The teacher attempts to link assessment The teacher assesses the students on assessment of students, analysis of the curriculum. with the curriculum. mathematical ideas and problems instruction and the learning experience after the students have been taught. The teacher routinely engages in The teacher assesses mostly by examining are fundamentally interconnected. analysis of teaching and learning by written products but also by observing, The teacher bases his/her evaluation The teacher engages in ongoing analysis observing, listening to, and gathering listening to, and gathering information mostly by examining written of teaching and learning by observing, information about the students to about the students. products, which are usually tests and listening to, and gathering information assess what they know and are able to quizzes. The teacher may also grade Periodically the teacher will reflect on the about the students to assess what they do. students on homework and class lessons and learning experiences and know and are able to do. participation. Classroom behavior is The teacher often examines the effects compare their effectiveness with student often a factor in the students’ grades. The teacher examines the effects of the of the tasks, discourse and learning progress. tasks, discourse and learning environment on students’ mathematical The teacher is diligent about following The teacher paces the class based on what environment on students’ mathematical knowledge, skills and dispositions. the timeline of instruction based on a most of the students are accomplishing. knowledge, skills and dispositions. set of standards, a continuum and/or The teacher routinely assesses what The teacher will attempt to differentiate the textbook. The teacher assesses what every student many of students are learning and the instruction and activities for the most is learning, the concepts they understand concepts they understand. The teacher may provide extra credit successful and most challenged students. and that they are doing significant to those students who are the most Usually the teacher changes and adapts mathematics. The teacher may revisit lessons where successful and remedial assignments instruction based on the ongoing students have been unsuccessful. to the most challenged students. The teacher changes and adapts students’ understandings. instruction based on the ongoing The teacher attempts to use multiple Depending on time available the The teacher may revise short and long assessment of the students. representations to address learning teacher may re-teach lessons where range plans. The teacher often styles. students have been unsuccessful. The teacher regularly revises short and challenges and extends students’ ideas. long range plans. The teacher challenges The teacher follows conference and The teacher uses mostly direct The teacher attends to an array of and extends students’ ideas. report card procedures to keep the parent instruction for efficiency. dimensions that contribute to students’ informed of students’ progress. The teacher attends to the broad array of mathematical competence. The teacher follows the district dimensions that contribute to students’ The teacher uses different evaluation reporting policy for report cards. The teacher routinely describes and mathematical competence. measures such as test, quizzes, comments on each student’s learning to The teacher may use different homework, classwork, reports, The teacher regularly describes and the parent, other involved educators evaluation measures but tests have participation, etc. to base the students’ comments on each student’s learning to and the students themselves. the most weight. grade. the parent, other involved educators and The teacher uses a variety of the students themselves. assessment measures and mediums to The teacher uses a large variety of develop a fair evaluation of students. assessment measures and mediums to develop a robust evaluation of students.

Draft version #4 Page 7 of 6 © Noyce Foundation 2005. To reproduce this document, permission must be granted by the Noyce Foundation: [email protected].