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The role of operation sense in transitions from arithmetic to algebraic thought
14 references·1 citing·45 second hop
The role of operation sense in transitions from arithmetic to algebraic thought (1998)The role of operation sense in transition…Students' understanding of algebraic notation: 11-15 (2007)Students' understanding of al…The Learning and Teaching of School Algebra (2006)The Learning and Teaching of …Research on Whole Number Addition and Subtraction (2006)Research on Whole Number Addi…Learning and Teaching With Understanding (2006)Learning and Teaching With Un…An Alternate Route to the Reification of Function (1997)An Alternate Route to the Rei…Splitting, Covariation, and Their Role in the Development of Exponential Functions (1995)Splitting, Covariation, and T…Symbol Sense: Informal Sense-Making in Formal Mathematics. (1994)Symbol Sense: Informal Sense-…A cognitive gap between arithmetic and algebra (1994)A cognitive gap between arith…Notations, Conventions, and Constraints: Contributions to Effective Uses of Concrete Materials in Elementary Mathematics (1992)Notations, Conventions, and C…Development of the process conception of function (1992)Development of the process co…A Constructivist Alternative to the Representational View of Mind in Mathematics Education (1992)A Constructivist Alternative …A theory of developing competence with written mathematical symbols (1988)A theory of developing compet…Learning Mathematics: The Cognitive Science Approach to Mathematics Education (1985)Learning Mathematics: The Cog…Towards a computational theory of algebraic competence. (1980)Towards a computational theor…Bringing Out the Algebraic Character of Arithmetic (2006)Bringing Out the Algebraic Ch…Cognitive Science and Mathematics Education (1987)An Exploration of Aspects of Language Proficiency and Algebra Learning (1999)The Co-Emergence of Machine Techniques, Paper-and-Pencil Techniques, and Theoretical Reflection: A Study of Cas use in Secondary School Algebra (2006)How students blend conceptual and formal mathematical reasoning in solving physics problems (2012)The Process of Education (1960)The Methodology of Scientific Research Programmes (1978)Situated Cognition and the Culture of Learning (1989)Examining Pedagogical Content Knowledge (2002)Education for Life and Work: Developing Transferable Knowledge and Skills in the 21st Century (2012)Adding It Up: Helping Children Learn Mathematics (2013)Japan's High Schools (1983)Using Knowledge of Children's Mathematics Thinking in Classroom Teaching: An Experimental Study (1989)Understanding teachers’ self-sustaining, generative change in the context of professional development (1998)Constructivism in Theory and Practice: Toward a Better Understanding (2001)An Alternative Reconceptualization of Procedural and Conceptual Knowledge. (2007)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)Concepts associated with the equality symbol (1981)The Gains and the Pitfalls of Reification — The Case of Algebra (1994)The gains and the pitfalls of reification — The case of algebra (1994)Arithmetic and Algebra in Early Mathematics Education (2006)Handbook of Research on the Psychology of Mathematics Education (2006)Truth and Method (1960)Reason, Truth and History (1981)Actual Minds, Possible Worlds. (1986)Instructional Tasks, Classroom Discourse, and Students' Learning in Second-Grade Arithmetic (1993)Cognitively Guided Instruction: A Knowledge Base for Reform in Primary Mathematics Instruction (1996)Explicating the Role of Mathematical Tasks in Conceptual Learning: An Elaboration of the Hypothetical Learning Trajectory (2004)Piaget’s Theory (1976)Mind in Society: The Development of Higher Psychological Processes (1978)Understanding the limit concept: Beginning with a coordinated process scheme (1996)Advances in Instructional Psychology (2019)Metaphors We Live By (2003)Middle School Students’ Understanding of Core Algebraic Concepts: Equivalence & Variable (2011)Knowledge of Algebra for Teaching: A Framework of Knowledge and Practices (2012)Relationships Between Students' Fractional Knowledge and Equation Writing (2015)Knowing, Doing, and Teaching Multiplication (1986)An analytical model for studying the development of learners’ mathematical ideas and reasoning using videotape data (2003)Cur r iculum Resear ch : Tow ar d a Fr amew or k for "Resear ch -based Cur r icula" (2007)Re-thinking co-variation from a quantitative perspective: Simultaneous continuous variation (1998)Learning Electricity with NIELS: Thinking with Electrons and Thinking in Levels (2009)The Development of Children's Algebraic Thinking: The Impact of a Comprehensive Early Algebra Intervention in Third Grade (2014)
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References

  • 2006Learning and Teaching With Understanding965 cited
  • 2006The Learning and Teaching of School Algebra599 cited
  • 1992A Constructivist Alternative to the Representational View of Mind in Mathematics Education545 cited
  • 1992Development of the process conception of function400 cited
  • 2006Research on Whole Number Addition and Subtraction377 cited
  • 1995Splitting, Covariation, and Their Role in the Development of Exponential Functions368 cited
  • 1994A cognitive gap between arithmetic and algebra364 cited
  • 1985Learning Mathematics: The Cognitive Science Approach to Mathematics Education362 cited
  • 1994Symbol Sense: Informal Sense-Making in Formal Mathematics.307 cited
  • 2007Students' understanding of algebraic notation: 11-15151 cited
  • 1988A theory of developing competence with written mathematical symbols122 cited
  • 1992Notations, Conventions, and Constraints: Contributions to Effective Uses of Concrete Materials in Elementary Mathematics119 cited
  • 1980Towards a computational theory of algebraic competence.108 cited
  • 1997An Alternate Route to the Reification of Function94 cited

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  • 2006Bringing Out the Algebraic Character of Arithmetic

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75 cited