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Understanding Qualitative Calculus: A Structural Synthesis of Learning Research
16 references·4 citing·38 second hop
Understanding Qualitative Calculus: A Structural Synthesis of Learning Research (2002)Understanding Qualitative Calculus: A Str…Number Concepts and Operations in the Middle Grades (2025)Number Concepts and Operation…Naive Theories of Motion (2014)Naive Theories of MotionChild's Conception of Movement and Speed (2013)Child's Conception of Movemen…Body Motion and Graphing (1998)Body Motion and GraphingTalking about Rates Conceptually, Part II: Mathematical Knowledge for Teaching (1996)Talking about Rates Conceptua…The development of multiplicative reasoning in the learning of mathematics (1995)The development of multiplica…Images of rate and operational understanding of the fundamental theorem of calculus (1994)Images of rate and operationa…Exponential Functions, Rates of Change, and the Multiplicative Unit (1994)Exponential Functions, Rates …General system theory: Toward a conceptual framework for science and technology education for all (1993)General system theory: Toward…Functions, Graphs, and Graphing: Tasks, Learning, and Teaching (1990)Functions, Graphs, and Graphi…The impact of microcomputer‐based labs on children's ability to interpret graphs (1987)The impact of microcomputer‐b…The effect of real‐time laboratory graphing on learning graphic representations of distance and velocity (1987)The effect of real‐time labor…Student difficulties in connecting graphs and physics: Examples from kinematics (1987)Student difficulties in conne…Cognitive consequences of microcomputer-based laboratories: Graphing skills development (1987)Cognitive consequences of mic…Students' understanding of differentiation (1983)Students' understanding of di…Investigation of student understanding of the concept of velocity in one dimension (1980)Investigation of student unde…Secondary Students’ Quantification of Ratio and Rate: A Framework for Reasoning about Change in Covarying Quantities (2015)Secondary Students’ Quantific…CALCULUS STUDENTS’ AND INSTRUCTORS’ CONCEPTUALIZATIONS OF SLOPE: A COMPARISON ACROSS ACADEMIC LEVELS (2013)CALCULUS STUDENTS’ AND INSTRU…Intersecting representation and communication infrastructures (2009)Intersecting representation a…Statistical Mechanics for Secondary School: The GasLab Multi-agent Modeling Toolkit (2003)Statistical Mechanics for Sec…MANUAL FOR KIT OF REFERENCE TESTS FOR COGNITIVE FACTORS (REVISED 1963) (1963)Toward a Theory of Intrinsically Motivating Instruction* (1981)Students’ preconceptions in introductory mechanics (1982)Calculus-Based Physics Without Lectures (1991)The impact of video motion analysis on kinematics graph interpretation skills (1996)Using Smartphones as Experimental Tools—Effects on Interest, Curiosity, and Learning in Physics Education (2018)Criticism and the Growth of Knowledge (1970)The Body in the Mind (1987)A Calculus Graphing Schema (2000)The Psychology Of Intelligence (2005)Foundational Reasoning Abilities that Promote Coherence in Students' Function Understanding (2008)In the Absence of Meaning… (2013)The growth of logical thinking: From childhood to adolescence. (1958)Frames of Mind: The Theory of Multiple Intelligences (1984)Supporting students' learning with multiple representations in a dynamic simulation-based learning environment (2006)Challenges with graph interpretation: a review of the literature (2011)Learning with Multiple Representations (2012)Expert and Novice Performance in Solving Physics Problems (1980)Categorization and Representation of Physics Problems by Experts and Novices* (1981)Number Sense as Situated Knowing in a Conceptual Domain (1991)Designing learning environments to promote conceptual change in science (2001)Three Types of Conceptual Change: Belief Revision, Mental Model Transformation, and Categorical Shift (2009)Those Who Understand: Knowledge Growth in Teaching (1986)Those Who Understand: Knowledge Growth in Teaching (1986)Knowledge and Teaching:Foundations of the New Reform (1987)Exploring visuospatial thinking in chemistry learning (2004)The Learning and Teaching of School Algebra (2006)How Students Understand Physics Equations (2001)The development of students’ understanding of the numerical value of fractions (2004)Developing Children's Understanding of the Rational Numbers: A New Model and an Experimental Curriculum (1999)Applying Covariational Reasoning While Modeling Dynamic Events: A Framework and a Study (2002)Participating in Classroom Mathematical Practices (2010)Metarepresentation: Native Competence and Targets for Instruction (2004)The Influence of Teachers’ Knowledge on Student Learning in Middle School Physical Science Classrooms (2013)Synthesis of discipline-based education research in physics (2014)Computer simulations in physics teaching and learning: a case study on students' understanding of trajectory motion (2001)Learning Conceptual Knowledge in the Engineering Sciences: Overview and Future Research Directions (2008)The development of students' graphical understanding of the derivative (1997)
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References

  • 1990Functions, Graphs, and Graphing: Tasks, Learning, and Teaching1,040 cited
  • 1995The development of multiplicative reasoning in the learning of mathematics686 cited
  • 2025Number Concepts and Operations in the Middle Grades595 cited
  • 2014Naive Theories of Motion595 cited
  • 1987Student difficulties in connecting graphs and physics: Examples from kinematics581 cited
  • 1980Investigation of student understanding of the concept of velocity in one dimension381 cited
  • 1994Images of rate and operational understanding of the fundamental theorem of calculus366 cited
  • 1987The impact of microcomputer‐based labs on children's ability to interpret graphs343 cited
  • 1983Students' understanding of differentiation308 cited
  • 1987The effect of real‐time laboratory graphing on learning graphic representations of distance and velocity258 cited
  • 2013Child's Conception of Movement and Speed232 cited
  • 1998Body Motion and Graphing231 cited
  • 1994Exponential Functions, Rates of Change, and the Multiplicative Unit177 cited
  • 1996Talking about Rates Conceptually, Part II: Mathematical Knowledge for Teaching170 cited
  • 1993General system theory: Toward a conceptual framework for science and technology education for all

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167 cited
  • 1987Cognitive consequences of microcomputer-based laboratories: Graphing skills development111 cited
  • Cited by

    • 2003Statistical Mechanics for Secondary School: The GasLab Multi-agent Modeling Toolkit77 cited
    • 2009Intersecting representation and communication infrastructures73 cited
    • 2015Secondary Students’ Quantification of Ratio and Rate: A Framework for Reasoning about Change in Covarying Quantities71 cited
    • 2013CALCULUS STUDENTS’ AND INSTRUCTORS’ CONCEPTUALIZATIONS OF SLOPE: A COMPARISON ACROSS ACADEMIC LEVELS67 cited