The Arithmetic Teacher · 1989 · 87 citations · 3 references
EducationMathematicsMathematics EducationCognitive DevelopmentCognitive PsychologyMathematics InstructionMental ComputationNumber SenseNumeracy DevelopmentNumerical Cognition DevelopmentPart-whole RelationshipsPlace ValueMagnitudes Of NumbersNumber Sense DifficultiesNumber Sense InstructionPlace-value InstructionPlace-value RelationshipsPlace-value RepresentationReasoning About Number SenseReasoning With Place Value
When a student mentally computes 32 + 59 by thinking 30 + 50 is 80, 9 + 2 is 11, and 80 + 11 is 91, that student has had to call on some well-developed concepts of numerical partwhole relationships and place value. People with good number sense make frequent and flexible use of these two related concepts to perform mental computations and numeric estimates. Students find these concepts difficult; their understanding develops slowly over a period of several years. To be successful at teaching number sense, we must design instruction that respects students' need to construct their own knowledge.
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