This 440-page report explores how students in pre-K through grade 8 learn mathematics, with a focus on number and operations, and recommends how teaching, curricula, and teacher education should change to improve mathematics learning. (A 39-page summary, Helping Children Learn Mathematics, is catalogued separately.) The authors identify five interdependent components of mathematical proficiency and describe how students develop this proficiency. The report presents a portrait of mathematics learning: research findings on what children know about numbers before they arrive in pre-K and the implications for instruction; details on the processes by which students acquire mathematical proficiency; what is known from research about teaching for mathematics proficiency and developing proficiency in teaching. Visitors to this website may read the full text online, download a copy (pdf), or purchase a hard copy.


  • Mathematics > General
  • Education > General

Education Levels:

  • Grade 1
  • Grade 2
  • Grade 3
  • Grade 4
  • Grade 5
  • Grade 6
  • Grade 7
  • Grade 8
  • Grade 9
  • Grade 10
  • Grade 11
  • Grade 12


Grade 2,Assessment of students,Statistics,Make use of structure,NSDL,Grade 4,Teaching strategies,Addition,Equity,Early Elementary,Kindergarten,Professional development,Grade 1,Express regularity,Representation,Number concepts,Arithmetic,Analyze and persevere,Fractions,Division,Number and operations,Visual representation,Algebra,Rational numbers,Place value,Curriculum,Engineering,Properties of operations,Model with mathematics,Concept formation,Ratio and proportion,Subtraction,Multiplication,Modeling,Patterns and sequences,Grade 5,Instructional materials,Achievement,Informal Education,Integers,Whole numbers,Middle School,Vocational/Professional Development Education,NSDL_SetSpec_ncs-NSDL-COLLECTION-000-003-112-027,Geometry,Reason abstractly,Practice Standards,Educational research,Parent involvement,Grade 6,Elementary School,Algorithms,Teacher content knowledge,Number patterns,Reason quantitatively,History/Policy/Law,oai:nsdl.org:2200/20140728160606764T,Decimals,General Public,Computing and Information,Operations,Education,Upper Elementary,Probability,Inclusion,Communication,Teacher preparation,Mathematics,Learning theory,Grade 3,Problem solving,Measurement,Pre-Kindergarten,Process skills,School improvement,Counting,Construct arguments,Reasoning



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