Book2006

Bringing Out the Algebraic Character of Arithmetic

Analucia Dias Schliemann · David William Carraher · Bárbara M. Brizuela

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Mathematics Education and Teaching Techniques Mathematics Education and Pedagogy Cognitive and developmental aspects of mathematical skills

Abstract

Contents: Preface: Rethinking Early Mathematics Education. Interpreting Research About Learning Algebra. Part I: Interview Studies. Young Children's Understanding of Equivalences. Can Young Students Solve Equations? Part II: Classroom Studies. Addition Operations as Functions. From Quantities to Ratio, Functions, and Algebraic Notation. On Children's Written Notation to Solve Problems. Discussion.

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References

1979National Council of Teachers of Mathematics 1971Science of Education and the Psychology of the Child 1978Children's Minds 2006The Learning and Teaching of School Algebra 1997Windows on mathematical meanings: learning cultures and computers 1996Expressing Generality and Roots of Algebra 1994The Gains and the Pitfalls of Reification — The Case of Algebra 1994A cognitive gap between arithmetic and algebra

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2016Physical and Virtual Manipulatives: What Is “Concrete”?2017Scaffolding learner-centered curricular coherence using learning maps and diagnostic assessments designed around mathematics learning trajectories 2011Algebra in the Middle School: Developing Functional Relationships Through Quantitative Reasoning 2017A progression in first-grade children’s thinking about variable and variable notation in functional relationships 2015Children’s Use of Variables and Variable Notation to Represent Their Algebraic Ideas 2022

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