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Crossing the cognitive gap between arithmetic and algebra: Operating on the unknown in the context of equations
9 references·9 citing·34 second hop
Crossing the cognitive gap between arithmetic and algebra: Operating on the unknown in the context of equations (1996)Crossing the cognitive gap between arithm…The Learning and Teaching of School Algebra (2006)The Learning and Teaching of …The gains and the pitfalls of reification — The case of algebra (1994)The gains and the pitfalls of…The Gains and the Pitfalls of Reification — The Case of Algebra (1994)The Gains and the Pitfalls of…A cognitive gap between arithmetic and algebra (1994)A cognitive gap between arith…Handbook of research on mathematics teaching and learning (1992)Handbook of research on mathe…Research issues in the learning and teaching of algebra (1990)Research issues in the learni…A Beginning Teacher's View of Problem Solving (1985)A Beginning Teacher's View of…Children's Understanding of Numerical Variables. (1978)Children's Understanding of N…The Process of Education (1960)The Process of EducationInterfacing practices: domain theory emerges via collaborative reflection (2015)Interfacing practices: domain…Prerequisite algebra skills and associated misconceptions of middle grade students: A review (2013)Prerequisite algebra skills a…Years 2 to 6 Students’ Ability to Generalise: Models, Representations and Theory for Teaching and Learning (2011)Years 2 to 6 Students’ Abilit…Argumentation and algebraic proof (2008)Argumentation and algebraic p…The effect of different representations on Years 3 to 5 students’ ability to generalise (2007)The effect of different repre…The role of arithmetic structure in the transition from arithmetic to algebra (2003)The role of arithmetic struct…Focusing on informal strategies when linking arithmetic to early algebra (2003)Focusing on informal strategi…The Impact of Preservice Teachers' Content Knowledge on Their Evaluation of Students' Strategies for Solving Arithmetic and Algebra Word Problems (2002)The Impact of Preservice Teac…Building a versatile understanding of algebraic variables with a graphic calculator (2000)Building a versatile understa…Mathematics as an Educational Task (1972)Functions, Graphs, and Graphing: Tasks, Learning, and Teaching (1990)How Students Understand Physics Equations (2001)Characterizing a Classroom Practice that Promotes Algebraic Reasoning. (2005)Does Understanding the Equal Sign Matter? Evidence from Solving Equations (2006)Translations from the Philosophical Writings of GOTTLOB FREGE. (1954)Handbook of Research on the Psychology of Mathematics Education (2006)Concepts associated with the equality symbol (1981)Interest and effort in education. (1913)The Discovery of Grounded Theory: Strategies for Qualitative Research. (1968)Field Research: Strategies for a Natural Sociology. (1974)Chapter 9: Classrooms as Learning Environments for Teachers and Researchers (1990)A Study of Whole Classroom Mathematical Discourse and Teacher Change (2003)Viewing Mathematics Teachers’ Beliefs as Sensible Systems* (2006)National Council of Teachers of Mathematics (1979)Those Who Understand: Knowledge Growth in Teaching (1986)The development of studients' algebraic thinking in earlier grades: (2005)Teachers’ Beliefs and Conceptions: A Synthesis of the Research (2006)Development of the process conception of function (1992)On Reform Movement and the Limits of Mathematical Discourse (2000)Cognition as Communication: Rethinking Learning-by-Talking Through Multi-Faceted Analysis of Students' Mathematical Interactions (2001)Students’ Reasoning With Reversible Multiplicative Relationships (2010)THE DISTRIBUTION OF PIAGETIAN STAGES OF THINKING IN BRITISH MIDDLE AND SECONDARY SCHOOL CHILDREN (1976)Grade 6 Students' Preinstructional Use of Equations to Describe and Represent Problem Situations (2000)Middle School Mathematics Teachers' Knowledge of Students' Understanding of Core Algebraic Concepts: Equal Sign and Variable (2007)Middle School Students’ Understanding of Core Algebraic Concepts: Equivalence & Variable (2011)Arithmetic and Algebra in Early Mathematics Education (2006)Supporting students' learning with multiple representations in a dynamic simulation-based learning environment (2006)Misconceptions Reconceived: A Constructivist Analysis of Knowledge in Transition (1994)What Do New Views of Knowledge and Thinking Have to Say About Research on Teacher Learning? (2000)Teachers’ Mathematical Knowledge, Cognitive Activation in the Classroom, and Student Progress (2009)Self-Concept: Validation of Construct Interpretations (1976)Design Experiments: Theoretical and Methodological Challenges in Creating Complex Interventions in Classroom Settings (1992)Adding It Up: Helping Children Learn Mathematics (2013)
this work references cited by second hop

References

  • 1992Handbook of research on mathematics teaching and learning6,121 cited
  • 1960The Process of Education6,018 cited
  • 2006The Learning and Teaching of School Algebra599 cited
  • 1994The Gains and the Pitfalls of Reification — The Case of Algebra387 cited
  • 1994A cognitive gap between arithmetic and algebra364 cited
  • 1985A Beginning Teacher's View of Problem Solving322 cited
  • 1990Research issues in the learning and teaching of algebra319 cited
  • 1994The gains and the pitfalls of reification — The case of algebra311 cited
  • 1978Children's Understanding of Numerical Variables.152 cited

Cited by

  • 2002The Impact of Preservice Teachers' Content Knowledge on Their Evaluation of Students' Strategies for Solving Arithmetic and Algebra Word Problems114 cited
  • 2013Prerequisite algebra skills and associated misconceptions of middle grade students: A review113 cited
  • 2003The role of arithmetic structure in the transition from arithmetic to algebra112 cited
  • 2000Building a versatile understanding of algebraic variables with a graphic calculator97 cited
  • 2003Focusing on informal strategies when linking arithmetic to early algebra87 cited
  • 2008

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Argumentation and algebraic proof
77 cited
  • 2011Years 2 to 6 Students’ Ability to Generalise: Models, Representations and Theory for Teaching and Learning69 cited
  • 2007The effect of different representations on Years 3 to 5 students’ ability to generalise67 cited
  • 2015Interfacing practices: domain theory emerges via collaborative reflection7 cited