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Professional Development

Deepening educators' mathematical understanding.

Carnegie Learning Content AcademiesThese intensive workshops are designed to deepen teachers' understanding of mathematics, provide an environment in which teachers can learn to problem-solve in a student-centered environment, and to facilitate teachers' reflection on their own teaching practices.

The Carnegie Learning Math Academies outline three key elements that correspond to the Common Core State Standard Initiative Content Standards and Standards for Mathematical Practice:

  • Grade appropriate content
    Focuses on implementing grade appropriate content through coherent mathematics with grade span and stretch (Lovin and Van de Walle, 2006).

  • Problem-solving in a student-centered classroom
    At the core of the Carnegie Learning's pedagogical approach to mathematics instruction. By facilitating learning in this context, educators have the opportunity to experience learning as students would, actively engaging in discourse with colleagues and peers around the math.

  • Heightened awareness about teaching
    Facilitating teachers' meta-cognitive reflection on their own teaching practice, providing access points for teachers to change their instructional practices.

Problem-solving in a student-centered classroom is at the core of the Carnegie Learning's pedagogical approach to mathematics instruction. By facilitating learning in this context, educators have the opportunity to experience learning as students would, actively engaging in discourse with colleagues and peers around the math. The final objective refers to facilitating teachers' meta-cognitive reflection on their own teaching practice, providing access points for teachers to change their instructional practices.

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Math Academy Big Mathematical Idea Grade Band(s)
Deepening Mathematical Understanding:
Early Number Concepts - Building to Integers
  • Analyze mathematical tasks
  • Develop whole number properties
  • Consider alternative algorithms for whole number operations
  • Investigate properties of the base-10 number system
  • Explore operations with integers
K-3

Deepening Mathematical Understanding:
Early Fraction Concepts
  • Analyze mathematical tasks
  • Investigate multiple representations of fractions
  • Connect fractions as parts to whole and whole to parts
  • Explore equivalent fractions
  • Determine fractional representations given parts of the whole
  • Compare and order fractions
  • Examine fractions as division
  • Use models of fractions to solve problems
K-5
Deepening Mathematical Understanding:
Fraction Sense and Operations
  • Analyze mathematical tasks
  • Investigate multiple representations of fractions
  • Develop understanding of fraction algorithms.
  • Examine alternative algorithms for fraction operations.
  • Connect fraction operations to algebraic concepts.
  • Model operations with fractions
K-5
Deepening Mathematical Understanding:
Connecting Decimals and Percents to Fractions
  • Analyze mathematical tasks
  • Relate decimals and percents to fractional models
  • Examine the place value system
  • Develop decimal and percent number sense
  • Reason with decimals and percents
  • Apply fraction, decimals and percents in practical application
4-8

Deepening Mathematical Understanding:
Proportional Reasoning

  • Analyze mathematical tasks
  • Distinguish between part-to-part and part-to-whole ratios
  • Compare ratios and solve proportions
  • Compare proportional and non-proportional relationships
  • Extend the understanding of ratios and proportions to include scale models
  • Analyze and create scale drawings and maps
  • Represent ratios with symbols, tables, double number lines, and graphs.
  • Develop multiple strategies for determining equivalent ratios.
  • Scale up and scale down proportions

4-8
Deepening Mathematical Understanding:
Algebraic Thinking
  • Analyze mathematical tasks
  • Examine multiple representations of functions
  • Explore ratio, rate and proportional reasoning from a functional perspective
  • Compare linear, quadratic and exponential functions
  • Use technology to explore functions
6-8