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The importance of prior knowledge when comparing examples: Influences on conceptual and procedural knowledge of equation solving.
16 references·16 citing·41 second hopsampled
The importance of prior knowledge when comparing examples: Influences on conceptual and procedural knowledge of equation solving. (2009)The importance of prior knowledge when co…Adding It Up: Helping Children Learn Mathematics (2013)Adding It Up: Helping Childre…Expertise Reversal Effect and Its Implications for Learner-Tailored Instruction (2007)Expertise Reversal Effect and…Learning and transfer: A general role for analogical encoding. (2003)Learning and transfer: A gene…Learning Together and Alone: Cooperative, Competitive, and Individualistic Learning (1998)Learning Together and Alone: …Cognitive Architecture and Instructional Design (1998)Cognitive Architecture and In…A Time For Telling (1998)A Time For TellingDistributed representations of structure: A theory of analogical access and mapping. (1997)Distributed representations o…Variability of worked examples and transfer of geometrical problem-solving skills: A cognitive-load approach. (1994)Variability of worked example…With an Eye on the Mathematical Horizon: Dilemmas of Teaching Elementary School Mathematics (1993)With an Eye on the Mathematic…Handbook of research on mathematics teaching and learning (1992)Handbook of research on mathe…When the Problem Is Not the Question and the Solution Is Not the Answer: Mathematical Knowing and Teaching (1990)When the Problem Is Not the Q…Similarity and Analogical Reasoning (1989)Similarity and Analogical Rea…Structure‐Mapping: A Theoretical Framework for Analogy* (1983)Structure‐Mapping: A Theoreti…Schema induction and analogical transfer (1983)Schema induction and analogic…National Council of Teachers of Mathematics (1979)National Council of Teachers …Aptitudes and Instructional Methods: A Handbook for Research on Interactions (1978)Aptitudes and Instructional M…Self-motivated and directed learning across the lifespan (2022)Self-motivated and directed l…Teaching by Analogy: From Theory to Practice (2021)Teaching by Analogy: From The…What is made possible to learn when using the variation theory of learning in teaching mathematics? (2017)What is made possible to lear…The longitudinal effects of peer feedback in the development and transfer of student teamwork skills (2017)The longitudinal effects of p…Scaffolding learner-centered curricular coherence using learning maps and diagnostic assessments designed around mathematics learning trajectories (2017)Scaffolding learner-centered …Relational categories as a bridge between cognitive and educational research. (2016)Relational categories as a br…Learning from direct instruction: Best prepared by several self-regulated or guided invention activities? (2016)Learning from direct instruct…Inventing a solution and studying a worked solution prepare differently for learning from direct instruction (2015)Inventing a solution and stud…Analogy, higher order thinking, and education (2015)Analogy, higher order thinkin…Learning from comparison in algebra (2014)Learning from comparison in a…Delayed benefits of learning elementary algebraic transformations through contrasted comparisons (2014)Delayed benefits of learning …How Teachers Link Ideas in Mathematics Instruction Using Speech and Gesture: A Corpus Analysis (2013)How Teachers Link Ideas in Ma…The effects of feedback during exploratory mathematics problem solving: Prior knowledge matters. (2012)The effects of feedback durin…Teaching the Conceptual Structure of Mathematics (2012)Teaching the Conceptual Struc…Student Learning: What Has Instruction Got to Do With It? (2012)Student Learning: What Has In…The Power of Comparison in Learning and Instruction: Learning Outcomes Supported by Different Types of Comparisons (2011)The Power of Comparison in Le…Features of similarity. (1977)SCRIPTS, PLANS, GOALS, AND UNDERSTANDING (1988)What's basic about basic emotions? (1990)Design Experiments: Theoretical and Methodological Challenges in Creating Complex Interventions in Classroom Settings (1992)On Two Metaphors for Learning and the Dangers of Choosing Just One (1998)The Interpretation of Cultures (1974)Mind in Society: The Development of Higher Psychological Processes (1978)Knowledge and Teaching:Foundations of the New Reform (1987)Building Student Capacity for Mathematical Thinking and Reasoning: An Analysis of Mathematical Tasks Used in Reform Classrooms (1996)The situativity of knowing, learning, and research. (1998)Orchestrating Productive Mathematical Discussions: Five Practices for Helping Teachers Move Beyond Show and Tell (2008)Toward a model of text comprehension and production. (1978)Mental Models (1983)Toward a design theory of problem solving (2000)Problem-Based Learning: What and How Do Students Learn? (2004)Motivational processes affecting learning. (1986)Educating the Reflective Practitioner: Toward a New Design for Teaching and Learning in the Professions (1987)Mathematical Knowledge for Teaching and the Mathematical Quality of Instruction: An Exploratory Study (2008)Professional Noticing of Children's Mathematical Thinking (2010)The Common Core State Standards in Mathematics (2015)Models and Analogies in Science (1965)Metaphor: A Practical Introduction (2002)Metaphors We Live By (2003)Cognitive Linguistics (2004)The magical number seven, plus or minus two: Some limits on our capacity for processing information. (1956)Cognitive Load During Problem Solving: Effects on Learning (1988)The magical number seven, plus or minus two: Some limits on our capacity for processing information. (1994)Why Minimal Guidance During Instruction Does Not Work: An Analysis of the Failure of Constructivist, Discovery, Problem-Based, Experiential, and Inquiry-Based Teaching (2006)Focus on Formative Feedback (2008)Cognitive Load Theory (2011)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)Research on Cooperative Learning and Achievement: What We Know, What We Need to Know (1996)The laboratory in science education: Foundations for the twenty‐first century (2003)An Educational Psychology Success Story: Social Interdependence Theory and Cooperative Learning (2009)The Case Against Statistical Significance Testing (1978)Not Another Inventory, Rather a Catalyst for Reflection (1992)STEM integration in K-12 education : status, prospects, and an agenda for research (2014)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
  • 1992Handbook of research on mathematics teaching and learning6,121 cited
  • 1998Cognitive Architecture and Instructional Design6,017 cited
  • 1983Structure‐Mapping: A Theoretical Framework for Analogy*5,058 cited
  • 2013Adding It Up: Helping Children Learn Mathematics4,090 cited
  • 1983Schema induction and analogical transfer2,933 cited
  • 1998Learning Together and Alone: Cooperative, Competitive, and Individualistic Learning2,598 cited
  • 1989Similarity and Analogical Reasoning2,390 cited
  • 1978Aptitudes and Instructional Methods: A Handbook for Research on Interactions1,479 cited
  • 1990When the Problem Is Not the Question and the Solution Is Not the Answer: Mathematical Knowing and Teaching1,368 cited
  • 1994Variability of worked examples and transfer of geometrical problem-solving skills: A cognitive-load approach.1,198 cited
  • 2007Expertise Reversal Effect and Its Implications for Learner-Tailored Instruction1,055 cited
  • 1998A Time For Telling1,036 cited
  • 1993With an Eye on the Mathematical Horizon: Dilemmas of Teaching Elementary School Mathematics1,008 cited
  • 1997Distributed representations of structure: A theory of analogical access and mapping.

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911 cited
  • 2003Learning and transfer: A general role for analogical encoding.866 cited
  • Cited by

    • 2015Analogy, higher order thinking, and education217 cited
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    • 2016Relational categories as a bridge between cognitive and educational research.149 cited
    • 2015Inventing a solution and studying a worked solution prepare differently for learning from direct instruction146 cited
    • 2012Student Learning: What Has Instruction Got to Do With It?134 cited
    • 2012The effects of feedback during exploratory mathematics problem solving: Prior knowledge matters.125 cited
    • 2017What is made possible to learn when using the variation theory of learning in teaching mathematics?111 cited
    • 2014Learning from comparison in algebra108 cited
    • 2011The Power of Comparison in Learning and Instruction: Learning Outcomes Supported by Different Types of Comparisons101 cited
    • 2021Teaching by Analogy: From Theory to Practice96 cited
    • 2016Learning from direct instruction: Best prepared by several self-regulated or guided invention activities?88 cited
    • 2014Delayed benefits of learning elementary algebraic transformations through contrasted comparisons73 cited
    • 2022Self-motivated and directed learning across the lifespan72 cited
    • 2017Scaffolding learner-centered curricular coherence using learning maps and diagnostic assessments designed around mathematics learning trajectories72 cited
    • 2017The longitudinal effects of peer feedback in the development and transfer of student teamwork skills72 cited