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Bringing Out the Algebraic Character of Arithmetic
16 references·6 citing·30 second hop
Bringing Out the Algebraic Character of Arithmetic (2006)Bringing Out the Algebraic Character of A…Child's Conception of Movement and Speed (2013)Child's Conception of Movemen…The Learning and Teaching of School Algebra (2006)The Learning and Teaching of …Windows on mathematical meanings: learning cultures and computers (1997)Windows on mathematical meani…Expressing Generality and Roots of Algebra (1996)Expressing Generality and Roo…Emergence and Development of Algebra as a Problem-Solving Tool: Continuities and Discontinuities with Arithmetic (1996)Emergence and Development 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…High school geometry students' justification for their views of empirical evidence and mathematical proof (1993)High school geometry students…Notations and Representations as Mediators of Constructive Processes (1991)Notations and Representations…On intelligence - more or less : a bio-ecological treatise on intellectual development (1990)On intelligence - more or les…The effect of make‐believe play on deductive reasoning (1988)The effect of make‐believe pl…National Council of Teachers of Mathematics (1979)National Council of Teachers …The Grasp of Consciousness. Action and Concept in the Young Child (1978)The Grasp of Consciousness. A…Children's Minds (1978)Children's MindsMental Imagery in the Child (1972)Mental Imagery in the ChildScience of Education and the Psychology of the Child (1971)Science of Education and the …A Systematic Review on Algebraic Thinking in Education (2022)A Systematic Review on Algebr…Scaffolding learner-centered curricular coherence using learning maps and diagnostic assessments designed around mathematics learning trajectories (2017)Scaffolding learner-centered …A progression in first-grade children’s thinking about variable and variable notation in functional relationships (2017)A progression in first-grade …Physical and Virtual Manipulatives: What Is “Concrete”? (2016)Physical and Virtual Manipula…Children’s Use of Variables and Variable Notation to Represent Their Algebraic Ideas (2015)Children’s Use of Variables a…Algebra in the Middle School: Developing Functional Relationships Through Quantitative Reasoning (2011)Algebra in the Middle School:…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 mathematics teaching and learning (1992)Arithmetic and Algebra in Early Mathematics Education (2006)Handbook of Research on the Psychology of Mathematics Education (2006)Concepts associated with the equality symbol (1981)The gains and the pitfalls of reification — The case of algebra (1994)An exploration in the space of mathematics educations (1996)Managing the Complexity of Human/Machine Interactions in Computerized Learning Environments: Guiding Students’ Command Process through Instrumental Orchestrations (2004)Towards new documentation systems for mathematics teachers? (2008)Ambiguity and self-evaluation: The role of idiosyncratic trait definitions in self-serving assessments of ability. (1989)Reasoning independently of prior belief and individual differences in actively open-minded thinking. (1997)Students' questions: a potential resource for teaching and learning science (2008)Educational Implications of the Theory of Multiple Intelligences (1989)Student Peer Assessment in Higher Education: A Meta-Analysis Comparing Peer and Teacher Marks (2000)A meta-analysis of the efficacy of teaching mathematics with concrete manipulatives. (2012)Imagery and Children's Learning: Putting the Picture in Developmental Perspective (1977)Domain‐Specific Principles Affect Learning and Transfer in Children (1990)Stereotypes and Prejudice in Conflict (2005)Inducing strategic learning from texts by means of informed, self-control training (1982)A review of research on metacognition in science education: current and future directions (2013)The power of internal feedback: exploiting natural comparison processes (2020)Signs and meanings in students' emergent algebraic thinking: A semiotic analysis (2000)What Do New Views of Knowledge and Thinking Have to Say About Research on Teacher Learning? (2000)What Makes Professional Development Effective? Results From a National Sample of Teachers (2001)Scaffolding and Achievement in Problem-Based and Inquiry Learning: A Response to Kirschner, Sweller, and Clark (2006) (2007)
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References

  • 1979National Council of Teachers of Mathematics8,499 cited
  • 1971Science of Education and the Psychology of the Child1,893 cited
  • 1978Children's Minds1,859 cited
  • 2006The Learning and Teaching of School Algebra599 cited
  • 1997Windows on mathematical meanings: learning cultures and computers543 cited
  • 1996Expressing Generality and Roots of Algebra397 cited
  • 1994The Gains and the Pitfalls of Reification — The Case of Algebra387 cited
  • 1994A cognitive gap between arithmetic and algebra364 cited
  • 1972Mental Imagery in the Child363 cited
  • 1978The Grasp of Consciousness. Action and Concept in the Young Child346 cited
  • 1993High school geometry students' justification for their views of empirical evidence and mathematical proof340 cited
  • 1988The effect of make‐believe play on deductive reasoning260 cited
  • 1990On intelligence - more or less : a bio-ecological treatise on intellectual development241 cited
  • 2013Child's Conception of Movement and Speed232 cited
  • 1991Notations and Representations as Mediators of Constructive Processes151 cited
  • 1996

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Emergence and Development of Algebra as a Problem-Solving Tool: Continuities and Discontinuities with Arithmetic
147 cited

Cited by

  • 2016Physical and Virtual Manipulatives: What Is “Concrete”?73 cited
  • 2017Scaffolding learner-centered curricular coherence using learning maps and diagnostic assessments designed around mathematics learning trajectories72 cited
  • 2011Algebra in the Middle School: Developing Functional Relationships Through Quantitative Reasoning69 cited
  • 2017A progression in first-grade children’s thinking about variable and variable notation in functional relationships67 cited
  • 2015Children’s Use of Variables and Variable Notation to Represent Their Algebraic Ideas65 cited
  • 2022A Systematic Review on Algebraic Thinking in Education64 cited