Developing and Assessing Mathematics Understandings

“With common sense and some algebra you can understand the world better than with common sense alone.”
Ethan Bolker, University of Massachusetts

In MEC’s 9-day Extending Algebraic Reasoning content course, K-20 teachers of mathematics  build on and extend understandings developed in the Patterns, Numerical Reasoning, Geometry, and Probability courses.  Algebra is presented as a language to describe patterns and model relationships. In addition, the role and importance of clear communication using proper mathematical language and notation are emphasized.
Participants develop and/or deepen their own mathematical understandings of a range of mathematical ideas, including:

  • generalizing patterns using symbols, words, tables, and pictures
  • symbol sense by building geometric models of equivalent algebraic expressions
  • proof via counterexample and symbolic reasoning
  • graph interpretation: analyzing slope (as a rate of change), interpreting intercepts in a given context, and assigning reasonable domain and range in given context
  • variables: discrete, continuous, independent, dependent
  • a variety of functions and relations with particular emphasis on linear functions
  • representation of functions: connections among, conversions among, interpretation of, and strengths and limitations of verbal, symbolic, numerical, and graphical representations of functions
  • functional notation used to represent slope, signed lengths, and signed areas
  • simplifying algebraic expressions and solving equations
  • anticipating results and judging the reasonableness of results
  • appropriate use of technology in the classroom.

The TI-84 and CBR2 motion sensor are used as exploration tools that allow teachers and students to ask questions, anticipate, check, and explain answers, and distinguish between exact and approximate solutions. Participants reflect on instructional strategies modeled including use of the TI-84 and CBR2 and discuss how to provide all students with the mathematical knowledge the 21st Century demands.
Participants consider how to effectively implement strategies modeled in the course, including:

  • mathematics inquiry
  • differentiation and appropriate interventions
  • probing student thinking with productive questioning
  • building on student thinking and interactions with peers and teacher
  • creating an optimal learning environment based on the nature of learning
  • effective formative and summative assessment of mathematical understanding that enhances student learning and performance.

Teachers, mathematics leaders, math coaches/mentors and university and college faculty