Mathematical Learning Progression

A Mathematical Learning Progression is a research-based developmental learning progression that describes cognitive pathways through which mathematical learners advance from concrete mathematical reasoning to abstract mathematical reasoning.

• AKA: Mathematical Development Trajectory, Mathematical Learning Trajectory, Mathematical Cognitive Progression.
• Context:
  • It can typically map Mathematical Cognitive Development through mathematical milestone identification.
  • It can typically inform Mathematical Instructional Decisions through mathematical readiness assessment.
  • It can typically predict Mathematical Learning Pathways based on mathematical cognition research.
  • It can typically guide Mathematical Curriculum Sequencing using mathematical developmental principles.
  • It can typically identify Mathematical Prerequisite Knowledge for mathematical concept mastery.
  • ...
  • It can often reveal Mathematical Conceptual Connections across mathematical domains.
  • It can often suggest Mathematical Intervention Timing for mathematical struggling learners.
  • It can often validate Mathematical Instructional Approaches against mathematical developmental evidence.
  • It can often support Mathematical Differentiation Strategies in mathematical classrooms.
  • ...
  • It can range from being a Fine-Grained Mathematical Learning Progression to being a Broad-Strokes Mathematical Learning Progression, depending on its mathematical progression granularity.
  • It can range from being a Linear Mathematical Learning Progression to being a Branching Mathematical Learning Progression, depending on its mathematical pathway complexity.
  • ...
  • It can facilitate Mathematical Assessment Design aligned with mathematical cognitive stages.
  • It can enhance Mathematical Teacher Understanding of mathematical student thinking.
  • It can support Mathematical Learning Research through mathematical development frameworks.
  • It can enable Mathematical Learning Acceleration through mathematical progression awareness.
  • ...
• Example(s):
  • Domain-Specific Mathematical Learning Progressions, such as:
    • Number Sense Mathematical Learning Progressions, such as:
      • Counting Mathematical Learning Progression from one-to-one correspondence to mathematical skip counting.
      • Place Value Mathematical Learning Progression from mathematical grouping understanding to mathematical base-ten mastery.
    • Mathematical Operation Learning Progressions, such as:
      • Addition Mathematical Learning Progression from mathematical counting all to mathematical derived facts.
      • Multiplication Mathematical Learning Progression from mathematical repeated addition to mathematical multiplicative thinking.
  • Mathematical Reasoning Stages within progressions, such as:
    • Early Mathematical Learning Stages, such as:
      • Direct Modeling Stage characterized by mathematical physical representation use.
      • Counting Strategies Stage featuring mathematical mental counting methods.
    • Advanced Mathematical Learning Stages, such as:
      • Number Facts Stage demonstrating mathematical fact fluency.
      • Algebraic Thinking Stage showing mathematical generalization ability.
  • ...
• Counter-Example(s):
  • Mathematical Skill Checklist, which lists mathematical abilities without developmental connections.
  • Mathematical Grade Level Standard, which specifies mathematical expectations without cognitive trajectories.
  • Mathematical Performance Rubric, which measures mathematical achievement rather than mathematical developmental paths.
• See: Learning Sciences Theory, Cognitively Guided Instruction, Mathematical Development Research, Educational Psychology Framework.

---