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Coherence vs. fragmentation

October 12, 2012

diSessa, Gillespie, & Esterly (2004), Coherence versus fragmentation in the development of the concept of force, Cogn. Sci. 28, 843.

This paper is a response to a paper by Ioannides & Vosniadou that claimed that childrens’ naive ideas concerning force are coherent and can be classified as belonging to one of a small number of theories. A quasi-replication study was carried out in which the majority of students failed to align with any of I&V’s coherent theories. In addition, extension questions (questions comparing situations experts would consider equivalent but novices often consider disparate) showed further fragmentation in students’ ideas regarding force.

A lengthy theoretical section introduces two new terms in an to attempt to provide a more nuanced distinction between theories of knowledge than is provided by “coherent” and “fragmented”.

Contextuality – The range of contexts over which a certain mental model or naive idea is applied. I&V consider novices to have mental models that cover a large domain of applicability. A domain comparable to the domain covered by an experts mental model (novice and expert mental models may yield different predictions but their ranges of applicability are comparable). diSessa et al. consider novices to have a network of smaller-scale knowledge elements which collectively cover a domain comparable to the domain of the expert’s theory. Contextuality refers not just to the number of knowledge elements needed to cover the domain but also the fuzziness & stability of the domain boundaries of knowledge elements and the possible overlap of knowledge elements.

Specification – How much a researcher must specify in order to present a complete picture of a learner’s mental model or naive idea. diSessa et al. propose five aspects of specification that they believe apply to any mental model relating to physical phenomena. Each aspects represents a possible point of distinction between novices and experts:

  • Existential aspect – When does a force exist?
  • Course quantitative aspect – Two forces can balance or one can be greater.
  • Ontological aspect – What is the character of force? Is it conserved, transferred, a thing, a process?
  • Compositional aspect – How does one deal with multiple forces acting at once?
  • Causal aspect – What are the consequences of a force?

P-prims exist at a level below these aspects of specification hence these aspects cannot be applied to an individual p-prim however they could be applied to a mental model or a tightly linked network of p-prims.

I’m bothered by the fact that diSessa et al. seem to be taking language at face-value in their quasi-replication study. They code student responses to a test during an interview but do not code their explanations. They claim the explanations were confusing and difficult to interpret accurately but it seems like without the explanation they are left simply coding words not ideas. It seems very possible to me that a student could use the word “force” in some answer when in fact the student is not actually thinking about force. Perhaps the student would have chosen a different word had their been a different word available. I&V note that they observe some increased “fragmentation” amongst the older students. This could be due to older students being more articulate in their ideas but still lacking the scientific vocabulary to use other words in place of force (e.g. the older student can now articulate the difference between something being exerted and something being transferred but does not have the  word momentum available and so uses the word force in each instance).

Ozdemir & Clark (2007), An overview of conceptual change theories, Eurasia J. Math Sci. & Tech. Ed. 3, 351.

This is a nice, short overview of knowledge-as-theory and knowledge-as-elements views of naive knowledge. In addition to summarizing the main characteristics of views like diSessa’s compared to views like Vosniadou’s, this article also gives brief descriptions of some of the other highly cited works. I was particularly happy to read short descriptions of the work by Carey and by Strike & Posner which I have seen heavily cited but have not yet read. This article also talks about conceptual change whereas the diSessa and Vosniadou articles I’ve been reading have focused primarily on describing the state of naive knowledge and have included little discussion of the actual learning process.


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