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- Vol 2 RE: Chapter 8
mathematical proficiencyconceptual understandingprocedural fluencystrategic competenceadaptive reasoningproductive dispositionmathematical problem solvingReport Evidence summaryAt a glance
Adding It Up synthesises research on how children from prekindergarten through grade eight learn number and operations. Its influential model defines mathematical proficiency as five interwoven strands: conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition.
Key ideas
No strand is sufficient alone, and progress in one can strengthen the others. The report examines children’s developing ideas about whole numbers, rational numbers, computation, and problem solving, then considers teaching, curriculum, assessment, teacher knowledge, and school organisation. Effective instruction builds on learners’ strategies, connects representations and procedures to meaning, asks students to reason and explain, and provides sustained opportunities for practice and problem solving. It rejects both a facts-versus-understanding dichotomy and the expectation that proficiency emerges from unguided activity.
Why it matters
For educators, assessment should sample all five strands and reveal thinking; improvement requires coherent materials, knowledgeable teachers, equitable expectations, and systems that give learners enough time to develop durable and confident mathematical competence.
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Edition abbreviations
- TE
- Teacher Edition
- PE
- Practice Edition
- RE
- Research Edition
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