In a post on my precision principle, I made a fairly humdrum observation about a typical elementary-level geometry question:
Why can we so easily figure out the logics that lead to the incorrect answers? It seems like a silly question, but I mean it to be a serious one. At some level, this should be a bizarre ability, shouldn't it? . . . . The answer is that we can easily switch back and forth between different "versions" of the truth.
What happened next of course is that researchers Potvin, Masson, Lafortune, and Cyr, having read my blog post, decided to go do actual serious academic work to test my observation. And they seem to agree--non-normative 'un-scientific' conceptions about the world do not go away. They share space in our minds with "different versions of the truth." (I may be misrepresenting the authors' inspirations and goals for their research somewhat.)
Participants in the study were 128 14- and 15-year-olds. They were given several trials involving deciding which of two objects "will have the strongest tendency to sink if it were put in a water tank." The choices for the objects were pictures of balls (on a computer), each made of one of 3 different materials: lead, wood, or "polystyrene (synthetic foam material)" and having one of 3 different sizes: small, medium, or large. The trials were categorized from "very intuitive" to "very counter-intuitive" as shown in the figure from the paper at the right.
Instead of concerning themselves with whether answers were correct or incorrect, however (most of the students got above 90% correct), the authors were interested in the time it took students to complete trials in the different categories. The theory behind this is simple: if students took longer to complete the "counter-intuitive" trials than the "intuitive" ones, it may be because the greater-size-greater-sinkability misconception was still present.
Not only did counterintuitive trials take longer, trials that were more counterintuitive took longer than those that were less counterintuitive. The mean reaction times in milliseconds for trials in the 5 categories from "very intuitive" to "very counter-intuitive" were 716, 724, 756, 784, and 804. This spectrum of results is healthy evidence in favor of the continued presence of the misconception(s).
So why doesn't the sheer force of the counterintuitive idea overwhelm students into answering incorrectly? The answer might be inhibition—i.e., being able to suppress "intuitive interference" (their "gut reaction"):
[Lafortune, Masson, & Potvin (2012)] concluded that inhibition is most likely involved in the explanation of the improvement of answers as children grow older (ages 8–14). Other studies that considered accuracy, reaction times, or fMRI data . . . . concluded that inhibition could play an important role in the production of correct answers when anterior knowledge could potentially interfere. The idea that there is a role for the function of inhibition in the production of correct answers is, in our opinion, consistent with the idea of persistence of misconceptions because it necessarily raises the question of what it is that is inhibited.
Further analysis in this study, which cites literature on "negative priming," shows that inhibition is a good explanation for the increased cognitive effort that led to higher reaction times in the more counterintuitive trials.
So, What's the Takeaway?
In my post on the precision principle, my answer wasn't all that helpful: "accuracy within information environments should be maximized." The authors of this study are much better:
There are multiple perspectives within this research field. Among them, many could be associated with the idea that when conceptual change occurs, initial conceptions ". . . cannot be left intact."
Ohlsson (2009) might call this category "transformation-of-previous-knowledge" (p.20), and many of the models that belong to it can also be associated to the "classical tradition" of conceptual change, where cognitive conflict is seen as an inevitable and preliminary step. We believe that the main contribution of our study is that it challenges some aspects of these models. Indeed, if initial conceptions survive learning, then the idea of "change", as it is understood in these models, might have to be reconsidered. Since modifications in the quality of answers appear to be possible, and if initial conceptions persist and coexist with new ones, then learning might be better explained in terms of "reversal of prevalence" then [sic] in terms of change (Potvin, 2013).
This speaks strongly to the idea of exposing students' false intuitions so that their prevalence may be reversed (a "20%" idea, in my opinion). But it also carries the warning—which the researchers acknowledge—that we should be careful about what we establish as "prevalent" in the first place (an "80%" idea):
Knowing how difficult conceptual change can sometimes be, combined with knowing that conceptions often persist even after instruction, we believe our research informs educators of the crucial importance of good early instruction. The quote "Be very, very careful what you put in that head because you will never, ever get it out" by Thomas Woolsey (1471–1530) seems to be rather timely in this case, even though it was written long ago. Indeed, there is no need to go through the difficult process of "conceptual changes" if there is nothing to change.
This was closer to my meaning when I wrote about maximizing accuracy within information environments. There is no reason I can see to simply resign ourselves to the notion that students must have misconceptions about mathematics. What this study tells us is that once those nasty interfering intuitions are present, they can live somewhat peacefully alongside our "scientific" conceptions. It does not say that we must develop a pedagogy centered around an inevitability of false intuitions.
What's your takeaway?
Potvin, P., Masson, S., Lafortune, S., & Cyr, G. (2014). Persistence of the Intuitive Conception that Heavier Objects Sink More: A Reaction Time Study with Different Levels of Interference International Journal of Science and Mathematics Education, 13 (1), 21-43 DOI: 10.1007/s10763-014-9520-6