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The Acquisition of Addition and Subtraction Concepts in Grades One through Three
431
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1984
Year
3-Year Longitudinal StudyEducational PsychologyEducationSocial SciencesMathematics EducationSubtraction ConceptsLanguage AcquisitionCognitive DevelopmentNumerical CompetenceSophisticated Counting StrategiesCognitive ScienceSubtraction Word ProblemsLearning SciencesClassroom InstructionNumeracyGradingChild DevelopmentProblem-based LearningProblem SolvingSpecial EducationEducational AssessmentSecondary Mathematics EducationMathematics Teacher EducationGrades One
Children's solutions to simple addition and subtraction word problems were studied in a 3-year longitudinal study that followed 88 children from Grades 1 through 3. The children were able to solve the problems using a variety of modeling and counting strategies even before they received formal instruction in arithmetic. The invented strategies continued to be used after several years of formal instruction. Four levels of problem-solving ability were found. At the first level, children could solve problems only by externally modeling them with physical objects. Modeling strategies were gradually replaced with more sophisticated counting strategies. The results of the study are at variance with important aspects of models of children's performance proposed by Briars and Larkin and by Riley, Greeno, and Heller.