Developing & Assessing Mathematics Understandings

“When children are given the chance to compute in their own ways, to play with relationships and operations, they see themselves as mathematicians and their understanding deepens.  Such playing with numbers forms the basis for algebra and will take children a long way in being able to compute not only efficiently but elegantly!
Fosnot & Dolk, Young Mathematicians at Work: Constructing Number Sense, Addition, and Subtraction, pg. 151.

In MEC’s 9-day Numerical Reasoning content course, participants focus on making sense of number relationships as a foundation for success in algebra and beyond. K-20 teachers of mathematics have opportunities to explore their own ways to solve challenging problems, compute, verify and share solutions. They learn to work with numbers in ways that help them support all students in learning to reason mathematically. Participants experience and reflect on the utility and beauty of mathematics.
Participants develop and/or deepen their own mathematical understandings of a range of mathematical ideas, including:

  • concepts and properties of the real number system
  • number relationships that build fluency with computation
  • number and computation proficiency – developing a deep understanding of numerous diverse computational algorithms
  • strategies for computing mentally
  •  place value
  •  order of operations
  • properties of primes and composites
  • use of multiple models for equivalency and operations on rational numbers including fractions, decimals and percents
  • mathematically convincing arguments that include geometric and algebraic representations.

The K-20 nature of all MEC courses enables MEC instructors to model differentiated instruction and intervention strategies to meet a wide range of learner needs.
Participants consider how to effectively implement strategies modeled in the course, including:

    • mathematics investigation and inquiry as an integral part of mathematical
    • mathematical learning through problem solving
    • 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
    • differentiation and appropriate interventions
    • 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