Equitable Mathematics Teaching Practices Proficiency Scale

219 North Main Street, Suite 402Barre, VT 05641 (p) 802-479-1030 (f) 802-479-1835Equitable Mathematics Teaching Practices Proficiency ScaleBased on NCTM’s Catalyzing Change in High School Mathematics (2018) and Principles to Actions (2014)Developed by Heidi E. Whipple, M.A., M.S.TVermont Agency of EducationPurpose of document:Support Teachers and Coaches to be able to collaborate on improving teaching practices.1. This tool is meant to be used by teachers and coaches to guide and support continuous improvement.2. This tool is meant to be a self-assessment for teachers to determine their proficiency with NCTM’s eight math teaching practices(2014)3. This tool is NOT meant to be an evaluative tool.4. Like students, teachers need to try new learning, make mistakes, make adjustments, and try again.5. Teachers are NOT meant to work on all eight practices at the same time. Teachers recognize that the practices are interconnectedand that by working on one of the practices deeply, this can affect other practices. Selecting one practice at a time and working toimprove that practice can effectively support continuous improvement.6. The Proficient level is the equity practices published in NCTM’s Catalyzing Change for High School Mathematics and isappropriate for grade K-12.7. The Expanding level is focused on how students can take ownership of the teaching practices and learn to advocate for theirlearning.

Teacher’s Name:Class:Date:Teaching Practice: #1 Establish mathematics goals to focus learning. (NCTM 2014)Performance Indicator: Effective teaching of mathematics establishes clear goals for the mathematics that students are learning, situates goalswithin learning progressions, and uses the goals to guide instructional decisions.BeginningDevelopingProficient(NCTM 2018)ExpandingI establish goals formathematicalunderstanding.I establish learning progressionsthat build students’mathematical understanding.I establish learning progressions that buildstudents’ mathematical understanding,increase their confidence, and support theirmathematical identities as doers ofmathematics.Students see themselves as doers of mathematicsand refer to learning progressions to advancetheir progress.I establish goals formathematicalunderstanding.I establish expectations sostudents can meet themathematical goals.I establish high expectations to ensure thateach and every student has the opportunityto meet the mathematical goals.Students understand the mathematical goals andhow to achieve them and advocate forthemselves when needed.I establish goals formathematicalunderstanding.I establish classroom norms forparticipation.I establish classroom norms for participationthat position each and every student as acompetent mathematics thinker.Students see themselves as competentmathematics thinkers and share ideas based onclassroom norms.I establish goals formathematicalunderstanding.I establish classroomenvironments that promotelearning mathematics.I establish classroom environments thatpromote learning mathematics as just,equitable, and inclusive.Students promote a mathematics classroomenvironment that is just, equitable, and inclusive.Observation/Reflection:Equitable Mathematics Teaching PracticesProficiency Scales(Revised: February 28, 2019)Page 2 of 9

Teacher’s Name:Class:Date:Teaching Practice: #2 Implement tasks that promote reasoning and problem solving. (NCTM 2014)Performance Indicator: Effective teaching of mathematics engages students in solving and discussing tasks that promote mathematicalreasoning and problem solving and allow multiple entry points and varied solution strategies.BeginningDevelopingProficient(NCTM 2018)ExpandingI engage students intasks.I engage students in tasks thatprovide that require reasoning,problem solving, and modeling.I engage students in tasks that providemultiple pathways for success and thatrequire reasoning, problem solving, andmodeling, thus enhancing each student’smathematical identity and sense of agency.Students collaboratively engage in tasks thatprovide multiple pathways for success and thatrequire reasoning, problem solving, andmodeling, and support the mathematical identityand sense of agency of others.I engage students intasks.I engage students in tasks thatare relevant.I engage students in tasks that are culturallyrelevant.Students connect understanding to the culturalrelevance of the tasks in class.I engage students intasks.I engage students in tasks thatallow them to draw on theirknowledge.I engage students in tasks that allow them todraw on their funds of knowledge (i.e., theresources that students bring to theclassroom, including their home, cultural,and language experiences).Students support each other in tasks that allowthem to draw on their funds of knowledge (i.e.,the resources that students bring to theclassroom, including their home, cultural, andlanguage experiences).Observation/Reflection:Equitable Mathematics Teaching PracticesProficiency Scales(Revised: February 28, 2019)Page 3 of 9

Teacher’s Name:Class:Date:Teaching Practice: #3 Use and connect mathematical representations. (NCTM 2014)Performance Indicator: Effective teaching of mathematics engages students in making connections among mathematical representations todeepen understanding of mathematics concepts and procedures and to use as tools for problem solving.BeginningDevelopingProficient(NCTM 2018)ExpandingI use representations inmathematics instruction.I use representations so thatstudents draw on resources ofknowledge.I use multiple representations so thatstudents draw on multiple resources ofknowledge to position them as competent.Students use multiple representations to explaintheir thinking to their peers and demonstratecompetency.I use representations inmathematics instruction.I use multiple representationsto draw on knowledge andexperiences related tomathematics.I use multiple representations to draw onknowledge and experiences related to theresources that students bring to mathematics(culture, contexts, and experiences).Students use multiple representations that areculturally relevant to students’ experience todeepen conceptual understanding and to solveproblems.I use representations inmathematics instruction.I use multiple representationsto promote the creation anddiscussion of uniquemathematical representations.I use multiple representations to promotethe creation and discussion of uniquemathematical representations to positionstudents as mathematically competent.Students use multiple representations to explainunique solutions to their peers and able Mathematics Teaching PracticesProficiency Scales(Revised: February 28, 2019)Page 4 of 9

Teacher’s Name:Class:Date:Teaching Practice: #4 Facilitate meaningful mathematical discourse. (NCTM 2014)Performance Indicator: Effective teaching of mathematics facilitates discourse among students to build shared understanding of mathematicalideas by analyzing and comparing student approaches and arguments.BeginningDevelopingProficient(NCTM 2018)ExpandingI encourage students toengage in discourse.I use discourse to elicitstudents’ ideas and strategies.I use discourse to elicit students’ ideas andstrategies and create space for students tointeract with peers to value multiplecontributions and diminish hierarchicalstatus among students (i.e., perceptions ofdifferences in smartness and ability toparticipate).Students use discourse to promote ideas andstrategies with peers to value multiplecontributions and diminish hierarchical statusamong each other. Students recognize that everystudent can participate and have thoughtfulideas.I encourage students toengage in discourse.I use discourse to positionstudents as capable of doingmathematics.I use discourse to attend to ways in whichstudents position one another as capable ornot capable of doing mathematics.Students use discourse to position each other asbeing capable of doing mathematics.I encourage students toengage in discourse.I make discourse a part ofmathematical thinking andreasoning.I make discourse an expected and naturalpart of mathematical thinking andreasoning, providing students with the spaceand confidence to ask questions thatenhance their own mathematical learning.Students use discourse to uphold a climate whereproviding students with the space andconfidence to ask questions that enhance theirown mathematical learning is the norm.I encourage students toengage in discourse.I use discourse as a means touncover studentmisconceptions.I use discourse as a means to disruptstructures and language that marginalizestudents.Students recognize structures and language thatmarginalize students and correct or address thatthrough discourse.Observation/Reflection:Equitable Mathematics Teaching PracticesProficiency Scales(Revised: February 28, 2019)Page 5 of 9

Teacher’s Name:Class:Date:Teaching Practice: #5 Pose purposeful questions. (NCTM 2014)Performance Indicator: Effective teaching of mathematics uses purposeful questions to assess and advance students’ reasoning and sense makingabout important mathematical ideas and relationships.BeginningDevelopingProficient(NCTM 2018)ExpandingI pose questions in themathematics class.I pose purposeful questions andthen listen to and understandstudents’ thinking.I pose purposeful questions and then listento and understand students’ thinking tosignal to students that their thinking isvalued and makes sense.Students pose purposeful questions and thenlisten to and understand students’ thinking tosignal to students that their thinking is valuedand makes sense.I pose questions in themathematics class.I pose purposeful questions toassign competence to students.I pose purposeful questions to assigncompetence to students, verbally markstudents’ ideas as interesting or identify animportant aspect of students’ strategies toposition them as competent.Students pose purposeful questions to assigncompetence to students, verbally mark students’ideas as interesting or identify an importantaspect of students’ strategies to position them ascompetent.I pose questions in themathematics class.I am mindful of the questions Iask a student and how I followup on the student’s response.I am mindful of the fact that the questionsthat a teacher asks a student and how theteacher follows up on the student’s responsecan support the student’s development of apositive mathematical identity and sense ofagency as a thinker and doer of mathematics.Students are mindful of the fact that thequestions that students ask each other and howthe students follow up on the response cansupport the student’s development of a positivemathematical identity and sense of agency as athinker and doer of mathematics.Observation/Reflection:Equitable Mathematics Teaching PracticesProficiency Scales(Revised: February 28, 2019)Page 6 of 9