Misconceptions reconceived

Smith, J. P., diSessa, A. A., & Roschelle, J. (1994). Misconceptions reconceived: A constructivist analysis of knowledge in transition. Journal of the Learning Sciences, 3, 115-163.

Summary:
+ Casting misconceptions as mistakes is too narrow a view of their role in learning
+ Misconceptions are faulty extensions of productive prior knowledge
+ Misconceptions are not always resistant to change; strength is a property of knowledge systems
+ Replacing misconceptions is neither plausible nor always desirable
+ Instruction that confronts misconceptions is misguided and unlikely to succeed
+ It is time to move beyond the identification of misconceptions

Notes:
p115: basic premise of constructivism: that students build more advanced knowledge from prior understandings

p117: The knowledge system framework makes it easier to understand how novice conceptions can play productive roles in evolving expertise, despite their flaws and limitations.

p124: Learning Paradox: How is it possible for our existing cognitive structures to transform themselves into more complex forms? Smith et al. suggest that misconceptions, especially those that are most robust, have their roots in productive and effective knowledge.

p125: If concepts are more like complex clusters of related ideas than separable independent units, then replacement looks less plausible as a learning process (disessa, in press; Smith, 1992).

p128: Smith et al. show that novices can exhibit expert-like behavior in explaining how a complex but familiar physical system works. Specifically, novices are willing to search for appropriate underlying mechanisms that are independent of salient surface representations. The heart of this analysis is that explanation is an everyday activity.

p132: These analyses have generally asserted that the flaws in students' understandings result from overgeneralized applications of prior mathematical knowledge-for example, using only knowledge of whole number order and place value to order decimals. Although many students eventually work through and beyond their flawed conceptualizations, mastery of these elementary mathematical domains is neither easy, rapid, nor uniformly achieved

p137: Smith et al. claim that learning in both of these cases involves shifts in the applicability of strategies more than changes in the content of the strategies themselves. The examples suggest that mastery is achieved, in part, by using what you already know in more general and powerful ways and also by learning where and why pieces of knowledge that are conceptually correct may work only in more restricted contexts.

p139: Larkin's analysis emphasized fundamental differences between novice and expert reasoning. She claimed that her expert and novice subjects used different representations and different concepts. Without disputing that experts' reasoning is different in important ways from that of novices, we emphasize the substantial continuities between them.

p145: Smith et al. have argued that there is often more similarity between expert and novice than meets the eye. Historically, elements of prior knowledge have played essential roles in the development of scientific theory. Prior knowledge has provided new concepts for scientific theory by abstracting objects and processes from everyday experience.

p145: In the final section, Smith et al. identify a set of theoretical principles that represents a step beyond the epistemological premise of constructivism.

+ Knowledge in pieces: A shift toward viewing knowledge as involving numerous elements of different types
+ Continuity: Persistent misconceptions, if studied in an evenhanded way, can be seen as novices' efforts to extend their existing useful conceptions to instructional contexts in which they turn out to be inadequate. p147
+ Functionality: Learning is a process of finding ideas that sensibly and consistently explain some problematic aspect of the learner's world. Conceptions that do not work in this way (or are linked to other conceptions that do) are unlikely to take root, be applied in reasoning, and subsequently defended by students
+ A Systems Perspective: Smith et al. for an analytical shift from single units of knowledge to systems of knowledge with numerous elements and complex substructure that may gradually change, in bits and pieces and in different ways.


Implications:

Discussion rather than confrontation. Classroom discussion, when freed of its confrontation frame, can play an important role in learning, particularly when it concerns problematic situations in which students' ideas are strongly engaged and the impact of reformulation may be most clear. But the purpose of discussion changes when we conceptualize learning in terms of refinement rather than replacement. We still need to have students' knowledge -- much of which may be inarticulate and therefore invisible to them -- accessed, articulated, and considered. Rather than opposing those ideas to the relevant expert view, instruction should help students reflect on their present commitments, find new productive contexts for existing knowledge, and refine parts of their knowledge for specific scientific and mathematical purposes. The instructional goal is to provide a classroom context that is maximally supportive of the processes of knowledge refinement.

Analytic microworlds can foster interactive learning and reflection; Three types: simulation environments, computer-based graphics packages, and knowledge spaces