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Re: Can Education Research Be "Scientific"? What's "Scientific"? (was "in Defense of. . . .")
Posted:
Nov 1, 2012 6:10 PM


On Nov 1, 2012, at 3:44 PM, Richard Hake wrote:
> Some subscribers to MathEdCC might be interested in a recent post > "Can Education Research Be 'Scientific'? What's 'Scientific'? (was > 'in Defense of. . . .') " [Hake (2012)].
Because I think highly of Hake but do not understand at all his position with respect to research in mathematics education, I read his <http://bit.ly/Ujaogk> in toto. Not easy reading but here are my reactions.
(1) First a disclosure: I am not a physicist but, in a first life, was an All But Dissertation in (Fluid) Mechanics and, in a second life, an All But Dissertation in CategoryTopoi Theory. As such, I would say that the difference between Physics and Mathematics, as subject matters, is immense which in turn goes a long way towards explaining why Research in Physics Education exists and produces results (E.g. Hestenes) while Research in Mathematics Education does not and cannot:
(i) Physics HAS an experimental component which needs to be part of the learning of Physics. That experimental component in turn has to be taken care of by Physics Education. Moreover, the experimental component MUST be reconciled with the theoretical component, both by Physics Researchers and Physics Educators.
Mathematics on the other hand does NOT have an experimental component. Mathematics is all on paper even if it is ABOUT the real worldbut not much in the way Physics is. Mathematics Education then can only deal with what happens on paper.
(ii) Another major difference is that the learning of Mathematics starts at the Piaget preoperational stage, roughly somewhere around 5even if it often has to restart at the age of 18 or later in Developmental Mathematics courseswhile Physics starts much later, roughly at the Piaget Concrete Operational Stage. So while the learning of Mathematics, a logic based discipline, starts way before the students have reached the Formal Operationalaka hypothetico deductivestage, the learning of Physics, at least its experimental component, starts when the students are at a stage where experimentation makes complete sense.
(2) What I find striking is that, in all this discussion, not a single example has been examined, or even advanced or even mentioned. The only one is BOX 55 Elementary School Students and Ratio and Proportion which I quoted from the NRC on October 27, 2012 11:45:37 AM EDT.
So let me take an example. Let us say we are trying to decide which of "lecture" or "reading pencil in hand with access to a mathematically enabled person" works better in a given situation. Do we need a lot of experimentation and then statistics or can we decide on just the basis of an argument as in the case of the elephants and the eagles? I would claim the latter, arguing that students in a lecture are essentially passive which therefore leaves them with memorization as only means while extracting information and understanding from a mathematical text pencil in hand is extremely active and enables the students to reconstruct things whenever memory does not serve.
And here is where the first of the above mentioned difference comes in: Physics cannot be, and I think never has been, taught as lecture only, the reason being that its "experimental component" cannot be ignored. Mathematics on the other hand can very well be, and is still overwhelmingly, taught excathedra. Consider, for instance, how research mathematicians learn (more) mathematics. Yes, they go to meetings and attend lectures. But, as any working mathematician will tell you, that is not where the action is and very few are still awake after the first five or ten minutes of a talk.
In fact, to my mind, a great part of the "developmental math" disaster originates in that, one way or the other, we mostly lectureeven if with occasional pseudo discussions.
I would be curious to see specific examples being discussed in the context of mathematics education research but I think that they will be hard to find.
(3) I have only "speedread" Hake's <http://www.physics.indiana.edu/~sdi/ajpv3i.pdf > but it seems quite convincing to me if only because it does not seem to cover up anything, e.g. does not use educando jargon. (Disclosure: I am statisticschallenged.)
My conclusion then is that, while Hake seems well aware of the educational problems in Physics and familiar with the research dealing with these problems, this is not quite the case when it comes to Mathematics where he seems to think that the issue remains, at least roughly, the same. Which is probably why he disagreed with Greeno so ... intensely.
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