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Concept

According to Chi et al., 1989, knowing a concept involves knowing:

  1. The conditions of application of the actions;
  2. The consequences of actions;
  3. The relationship of actions to goals;
  4. The relationship of goals and actions to natural laws and other principles.

Conceptual instruction

Rittle-Johnson & Alibali, 1999 conclude that “conceptual knowledge may have a greater influence of procedural knowledge than the reverse.” In their experiments on solving mathematical equivalence problems, while both conceptual and procedural teaching led to learning some of the other, conceptual teaching led to greater transfer.

Developing conceptual understanding and procedural skill in mathematics: An iterative process. consider learning mathematics an iterative process of conceptual understanding and procedural skill. They find that both the procedural and conceptual knowledge that students learned helped them develop a better representation of decimal numbers.

Rittle-Johnson & Alibali, 1999 uses this lesson:

Because there is an equal sign (point to the equal sign), the amount before it (sweep hand under left side of equation) needs to equal the amount after it (sweep hand under right side of equation). That means that the numbers after the equal sign (sweep hand under right side of equation) need to add up to the same amount as the numbers before the equal sign (sweep hand under left side of equation).

in contrast to a procedural lesson:

There is more than one way to solve these problems, but one way is like this. Because there is a (number) here and a (number) here (point to the repeated addends), all you need to do is add the (number) and the (number) together (point to the nonrepeated addends).

Measuring conceptual knowledge

Three measures are used by Chi et al., 1989:

  1. Solutions to isomorphic problems;
  2. Solutions for far transfer problems;
  3. Explanations generated while studying examples.

An example for mathematical equivalence from Rittle-Johnson & Alibali, 1999:

Rittle-Johnson et al., 2011 develop a more complete “construct model” for mathematical equivalence:

See the paper's appendix for the assessment items.

Conceptual change

Chi, 2008 identifies entity vs. process and direct process vs. emergent process as common categorical mistakes that prevent conceptual change

Carey, 2009 covers many aspects of conceptual change in development and in the history of science. She talks about incommensurate conceptual change, where the ideas in one theory can be expressed in the same language as the ideas in another (e.g. the concept of density is not understand in young children)

  • Black - heat and temperature
  • Kepler: shift from self-provided motion to motion from distance object
  • Maxwell

Examples:

  • Newton's third law: big car crashing into little car exerts more force → forces are equal and opposite
  • Fraction equivalence: 1/2 != 2/4 != 0.5 → a number can be written many ways but represents the same physical amount
  • Adding fractions: add all the stuff above the lines and add all the stuff below the lines → when dominators are equal, we just need to add up the numerators
  • A small amount of stuff is nothing → stuff is continuous; it can be divided forever (→ actually stuff really is quantized)
  • Teleologic process → natural evolution, improvement as an emergent process

Analogy and generalization

See Analogy and Generalization.

According to Chi et al., 1989, two theories:

Bibliography

Publications with keyword "conceptual knowledge"

chi1981categorization Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). {Categorization and Representation of Physics Problems by Experts and Novices}. Cognitive Science, 5(2), 121–152. doi: 10.1207/s15516709cog0502_2. PDF
servan1990learning Servan-Schreiber, E., & Anderson, J. R. (1990). Learning artificial grammars with competitive chunking.. Journal of Experimental Psychology: Learning, Memory, and Cognition, 16(4), 592. American Psychological Association. PDF
mestre1993promoting Mestre, J. P., Dufresne, R. J., Gerace, W. J., Hardiman, P. T., & Touger, J. S. (1993). {Promoting skilled problem-solving behavior among beginning physics students}. Journal of Research in Science Teaching, 30(3), 303–317. Wiley Online Library. PDF
smith1994misconceptions Smith III, J. P., diSessa, A. A., & Roschelle, J. (1994). Misconceptions reconceived: A constructivist analysis of knowledge in transition. The journal of the learning sciences, 3(2), 115–163. Taylor \& Francis. PDF
rittle1999conceptual Rittle-Johnson, B., & Alibali, M. W. (1999). Conceptual and procedural knowledge of mathematics: Does one lead to the other?.. Journal of educational psychology, 91(1), 175. American Psychological Association. PDF
murphy2004big Murphy, G. L. (2004). The big book of concepts. The MIT Press. PDF
smith2007bootstrapping Smith, C. L. (2007). Bootstrapping processes in the development of students' commonsense matter theories: Using analogical mappings, thought experiments, and learning to measure to promote conceptual restructuring. Cognition and Instruction, 25(4), 337–398. Taylor \& Francis. PDF
chi2008three Chi, M. T. H. (2008). Three types of conceptual change: Belief revision, mental model transformation, and categorical shift. International handbook of research on conceptual change, 61–82. Routledge New York. PDF
muller2008raising Muller, D. A., Sharma, M. D., & Reimann, P. (2008). Raising cognitive load with linear multimedia to promote conceptual change. Science Education, 92(2), 278–296. Wiley Online Library. PDF
chi2008three Chi, M. T. H. (2008). Three types of conceptual change: Belief revision, mental model transformation, and categorical shift. International handbook of research on conceptual change, 61–82. Routledge New York. PDF
frank2011overcoming Frank, M. C., & Gibson, E. J. (2011). Overcoming Memory Limitations in Rule Learning. Language Learning and Development, 7(2), 130-148. doi: 10.1080/15475441.2010.512522. PDF
koedinger2011knowledge Koedinger, K. R., Corbett, A. T., & Perfetti, C. (2011). The Knowledge-Learning-Instruction (KLI) Framework: Bridging the Science-Practice Chasm to Enhance Robust Student Learning. Cognition. PDF
gadgil2011effectiveness Gadgil, S., Nokes-Malach, T. J., & Chi, M. T. H. (2011). Effectiveness of holistic mental model confrontation in driving conceptual change. Learning and Instruction. Elsevier. PDF
chi1989self Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). {Self-Explanations: How Students Study and Use Examples in Learning to Solve Problems}. Cognitive science, 13, 145–182. PDF
ross1990generalizing Ross, B. H., & Kennedy, P. T. (1990). {Generalizing From the Use of Earlier Examples in Problem Solving,}. Journal of Experimental Psychology: Learning, Memory, and Cognition, 16(1), 55–42.
vosniadou1994capturing Vosniadou, S. (1994). Capturing and modeling the process of conceptual change. Learning and instruction, 4(1), 45–69. Elsevier. PDF
wu1999basic Wu, H.-H. (1999). {Basic Skills Versus Conceptual Understanding}. American Educator, 23(3), 14–19. Citeseer. PDF
wiser2002computer Wiser, M., & Amin, T. (2002). Computer-based interactions for conceptual change in science. Reconsidering conceptual change: Issues in theory and practice, 357–387. Springer.
hummel2003symbolic Hummel, Je., & Holyoak, K. J. (2003). {A symbolic-connectionist theory of relational inference and generalization.}. Psychological Review, 110(2), 220 –264. doi: 10.1037/0033-295X.110.2.220. PDF
hummel2003symbolic Hummel, Je., & Holyoak, K. J. (2003). {A symbolic-connectionist theory of relational inference and generalization.}. Psychological Review, 110(2), 220 –264. doi: 10.1037/0033-295X.110.2.220. PDF
rittle2007does Rittle-Johnson, B., & Star, J. R. (2007). Does comparing solution methods facilitate conceptual and procedural knowledge? An experimental study on learning to solve equations.. Journal of Educational Psychology, 99(3), 561. American Psychological Association. PDF
klenk2008learning Klenk, M., Friedman, S., & Forbus, K. D. (2008). {Learning modeling abstractions via generalization}. PDF
rittle2009importance Rittle-Johnson, B., Star, J. R., & Durkin, K. (2009). The importance of prior knowledge when comparing examples: Influences on conceptual and procedural knowledge of equation solving.. Journal of educational psychology, 101(4), 836. American Psychological Association. PDF
carey2009origin Carey, S. (2009). The origin of concepts. USA Oxford University Press.
namy2010differing Namy, L. L., & Clepper, L. E. (2010). The differing roles of comparison and contrast in children's categorization. Journal of experimental child psychology, 107(3), 291–305. Elsevier. PDF
saito2011socially Saito, M., & Miyake, N. (2011). Socially Constructive Interaction for Fostering Conceptual Change. PDF

Publications with keyword "conceptual change"

smith1994misconceptions Smith III, J. P., diSessa, A. A., & Roschelle, J. (1994). Misconceptions reconceived: A constructivist analysis of knowledge in transition. The journal of the learning sciences, 3(2), 115–163. Taylor \& Francis. PDF
smith2007bootstrapping Smith, C. L. (2007). Bootstrapping processes in the development of students' commonsense matter theories: Using analogical mappings, thought experiments, and learning to measure to promote conceptual restructuring. Cognition and Instruction, 25(4), 337–398. Taylor \& Francis. PDF
chi2008three Chi, M. T. H. (2008). Three types of conceptual change: Belief revision, mental model transformation, and categorical shift. International handbook of research on conceptual change, 61–82. Routledge New York. PDF
muller2008raising Muller, D. A., Sharma, M. D., & Reimann, P. (2008). Raising cognitive load with linear multimedia to promote conceptual change. Science Education, 92(2), 278–296. Wiley Online Library. PDF
vosniadou1994capturing Vosniadou, S. (1994). Capturing and modeling the process of conceptual change. Learning and instruction, 4(1), 45–69. Elsevier. PDF
wiser2002computer Wiser, M., & Amin, T. (2002). Computer-based interactions for conceptual change in science. Reconsidering conceptual change: Issues in theory and practice, 357–387. Springer.
carey2009origin Carey, S. (2009). The origin of concepts. USA Oxford University Press.
saito2011socially Saito, M., & Miyake, N. (2011). Socially Constructive Interaction for Fostering Conceptual Change. PDF
concept.txt · Last modified: 2014/11/26 22:32 by ryan