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If teachers have opportunities to learn mathematics in ways that fully model all of the following then they will continue to grow in their ability to…

  • Anticipate typical student responses, misconceptions, and common errors
  • Recognize mathematical principles and logic as the basis for determining the validity of students’ mathematical reasoning
  • Make flexible and responsive classroom decisions guided by the reasoning revealed by students in the moment
  • Probe to understand student thinking rather than ask questions to guide student thinking
  • Work to stimulate productive cognitive dissonance
  • Focus teaching and learning on the significant mathematical ideas and concepts (big ideas) at the unit level rather than the individual lesson level or CCSS standard level
  • Encourage students to solve problems in ways that make sense to them and examine diverse approaches in order to deepen their understanding of mathematical ideas and connections among those ideas
  • Recognize that when it comes to mathematics, what is efficient might differ for each student; honor those differences and help all students learn increasingly more efficient approaches and strategies
  • Make public their own authentic moments when they are trying to mathematize problems and willingly learn mathematics alongside their students
  • Believe that ALL students, and they themselves, are inherently capable of thinking mathematically
  • Actively work to help students develop a sense of agency
  • Employ multiple assessment practices that are aligned with the mathematical outcomes (mathematical big ideas in the unit, mathematical communications, and mathematizing problems)
  • Establish a classroom culture that fosters constructive discourse and promotes mathematical habits of mind (socio-mathematical norms)


Then students will grow in their ability to…

  • Analyze complex problems to identify assumptions, constraints, and make meaning of the context
  • Identify and carry out multiple mathematical approaches to solve problems
  • Verify solutions within the context of the original problem
  • Construct viable arguments to explain and justify their reasoning mathematically
  • Critique the reasoning of others using mathematical principals and logic
  • Use multiple perspectives including geometric, algebraic, numeric, verbal and graphical to understand, represent, and communicate mathematical ideas and to solve problems
  • Look closely to discern patterns or structures as they work to identify or generalize a mathematical idea across seemingly unrelated contexts and problem situations
  • Believe in themselves as inherently capable of thinking mathematically
  • Have a sense of agency and a disposition to actively engage in mathematical reasoning and persevere in making sense of and solving complex problems and situations


Then students will

  • Be motivated to pursue further study and exploration of mathematics
  • Increase achievement on mathematics assessments




A subjective awareness that one is initiating, executing, and controlling one’s own volitional action in mathematics and beyond; A sense of agency is closely associated with one’s sense of ownership; ‘Aha’ moments help to build a sense of agency



Students understand that the level of satisfaction they get from solving a problem is often directly proportional to the amount of time and struggle it took to solve it, and they work on a problem until they are convinced that they understand it



Students can take a complex problem or situation and identify and carry out the mathematics needed to solve the problem or analyze the situation


Classroom Culture

A classroom culture that adheres to the socio-mathematical norms, for example, the desired classroom culture is one where:

  • Students are encouraged to ask questions
  • Curiosity is fostered and valued
  • Answers are important, yet it is the mathematical reasoning and communication of ideas that is of utmost importance
  • Mistakes are springboards to learning
  • Discourse is the norm
  • Diverse approaches are examined and valued