Conceptual Change and Developmental Teaching

I am happy to provide a commentary on Thomas Gennen’s article (this issue) on the relation between conceptual change research and developmental teaching (DT), the latter referring to what might be described as neo-Vygotskian approaches to educational problems largely instigated in Soviet-era Russian psychology and educational work. To begin, I very strongly resonate with the larger effort behind the work. It is too often the case that research traditions that might productively interact with each other are separated by assumed incompatibilities or mere disconnection of the relevant communities. While it is often difficult to bridge such differences, I feel that there are often cross-paradigm commonalities — or productive differences — that can move the whole field forward. Indeed, I spent several years with a group of educational researchers attempting to bridge “knowledge analysis” (which is the generic term for the work of my own research tradition, known as “knowledge in pieces” — KiP), and “interaction analysis,” which focuses on social interaction. The work resulted in a book (diSessa, et al., 2016) in which we not only explored sensible collaboration but also tried to establish good models of the processes and results of productive engagement. In my own research practice, I try hard to be aware of core ideas in different intellectual traditions, mainly to make use of their insights in my own work.The second sentence in the introduction for that book read, “...at some point, sometimes fractious debate between diverse communities with the same overarching goal ...must be replaced by sensible interactions among perspectives and mutual accountability.” I was pleased to see the same phrase, “mutual accountability,” in Gennen’s article. I see Gennen as trying to instigate a similar social movement to connect DT and conceptual change research, without presuming a “fractious” relationship to start with.One of the attractive things I found in his article was a sensible and dispassionate review of the different theoretical strands in conceptual change work. I judge it to be largely fair and free from errors and bias. The world of conceptual change research is fractious and complex, so a sensible review is not a trivial accomplishment. Of course, being a participant in the disputes among points of view on conceptual change (not all “different perspectives” deserve bridging; some need contest and “settling”), I would write the review differently. But Gennen’s “fair and balanced” position is well-suited to his agenda.Aside from my general openness and advocacy of tradition-bridging agendas, I have a slightly special relationship with Vygotskian and neo-Vygotskian approaches. Not intending to evoke a cliché, some of my best friends are in those camps. In particular, I feel I have gotten good personal tutoring on productive, modern uses of those views, somewhat free of some afflictions, such as “the social viewpoint frees us from any obligation to analyze knowledge”; or even (in extreme cases), “sociocultural viewpoints forbid us from considering knowledge.”I feel an affiliation with some particular elements of DT that I find important and also essentially missing from other views of conceptual change – or, indeed, missing from education broadly. So, in essence, with respect to these elements, I feel DT and my own perspective are allies against many other theoretical positions that ignore or devalue these points. Here, to maintain a semblance of simplicity, I will focus on just one point, the idea of “germ cells.” According to Gennen (this issue), germ cells are a result of “delineating the most general and fundamental conceptual interrelation ... out of which a series of objects, phenomena, or events are systematically derived and interconnected in a subject area or problem field.” Germ cells are particular parsings of the top-level, most general framing of the relevant intellectual field. According to Davydov, finding “the best,” most appropriate germ cell organizes instruction in a very particular way that can be most effective, educationally.I call my neighboring concept “reformulation.” It really sits most naturally in a different theoretical framework, so differences may be easy to discern. But, at top level, it is not only similar to the idea of germ cell, but similarly opposed to essentially every other modern view not only of conceptual change, but of theoretically driven approaches to education, broadly. DT and my theoretical community are, I would say, allies in an important battle.The idea of reformulation is, in essence, that there exist fundamental and pervasive differences in approaches to instructed subject matter. I identify two different versions of reformulation. One is “representational” and can be well-exemplified with the shift in the nature of physics before and after the introduction of algebra. Galileo was the bridge, with his workable geometric diagrams facilitating quantitative description, and Newton was most definitely rooted on the “far side” of the representational bridge that algebra and calculus represented. You can read an elaborated version of this story in diSessa, 2018, p. 4ff.The second form of reformulation is conceptual, and I describe it as based on the property of conceptual simplicity. In my own terms, conceptual simplicity means that one has carefully selected the set of pre-instructional ideas that one systematically draws on in instruction. It presumes that the choice of a particular pool of intuitive knowledge that is drawn on instructionally can deeply affect the experience of learners. Not all subjects have such rich and influential core choices, but some do. And, when you get to choose, the choice can be massively important in the quality of learning engendered. The example that Gennen (this issue) cites in his article is the reformulation that I call “momentum flow.” The case is that the ordinary way that Newton’s laws are framed draws pervasively (with both good and bad effects) on intuitions of agentive causality: agents, patients, and “forceful” interactions in which they participate. Momentum flow shifts the intuitive base to a roughly comparable, but very different set of intuitive ideas concerning flow and conservation. Every child comes to understand how liquids are conserved in cases of flow (e.g., water poured from a narrower glass to a wider one), and the momentum flow perspective uses this as a root understanding of force, as a flow of conserved “stuff” (momentum) from one place or object to another.While it is largely irrelevant to this discussion, my considered judgment is that neither the conventional agentive intuitive framing of “force” nor flow/conservation is obviously more effective than the other: just pervasively different in feel and range of “easy” and “difficult” problems. I argue that teaching both can easily be accomplished and doing so results in more flexible and epistemologically wiser students.The core idea of both germ cells and reformulation (via cognitive simplicity) is just the same: some basic decisions about organization and fundamental structures can make massive differences in the quality of student learning. What is even more striking is the complete absence of this general idea from ordinary instructional design. It is so much easier just to take “current textbooks” to be the arbiter of “what the knowledge to be instructed” should be. People raised on those historical framings are likely not even to consider that another frame could be possible. I can vouch that physicists largely treat the agentive framing (starting with “a force is a push or pull”) as “the way it is or should be” rather than a choice with significant learning and epistemological implications for students. So, we (my KiP community, and Davydov and DT followers) are on the same side, whereas the vast majority of learning researchers and designers – including the non-KiP conceptual change researchers – do not appear to believe such top-level choices exist.So, KiP and DT have, at one level of abstraction, a common goal, which is to advocate for consideration of new, or at least nonstandard “larger frames” for subject matter instruction, based on careful analysis rather than on tradition. It would seem that a relationship of mutual accountability of our different traditions might be profitable.In the sequitur of this commentary, I will pursue preliminary steps in this direction. I have to apologize in advance because my knowledge of DT and germ cells is limited, and some of what I say may be obviated by a better understanding on my part. On the other hand, “getting acquainted” is a very natural aspect of early stages of mutual accountability. What follows is a set of perspectives that helpfully frame the articulation of KiP and DT, taken here to focus on germ cells versus reformulations.KiP is focused on developing modern and better theories of the nature and development of knowledge. So, for example, the KiP-theoretical term, p-prim, is hypothesized to be an essential component of intuitive and experiential knowledge. In briefest terms, p-prims are “small,” flexible knowledge elements that serve as unanalyzable explanations for why some things happen and others do not in the physical world. They are not concepts, theories, principles, or any other standard-form kinds of knowledge. Instead, I have provided a model of p-prims that includes empirically accessible parameters that define the conditions of their activation and use. There are many p-prims, and some can easily become part of a developing understanding of normative science. P-prims were the main initial motivation for the moniker “knowledge in pieces,” although other knowledge ontologies in the larger KiP epistemology show how p-prims and other knowledge elements can be combined and organized into working, normative scientific concepts.“Intuitions of conservation and flow” is the description of a family of p-prims (and likely other knowledge elements and capabilities) that constitute the basis for my momentum flow reformulation of Newtonian mechanics. The reformulation is precisely the systematic use of these ideas in the core conceptualization of Newton’s laws.I do not yet see what replacement DT has for this elaborated epistemology – the stipulation of knowledge types, such as p-prims. The closest that I can see is the Vygotskian distinction between everyday and scientific concepts. I think I understand the intuition behind such categories, but my judgment is that this is far from sufficient to track learning in any detail. One principal issue is that experts use p-prims too, some of them as essential parts of larger knowledge constructions (technical concepts, or theories). So, the either/or of everyday versus scientific is muddled. This is the first of several interesting potential conversations that I cannot pursue in this limited context. In fact, pursuing it probably would not be optimally productive without interaction with DT advocates relevant to establishing mutual accountability. But my entry card in this case is clear: I believe we must develop modern, revised, and careful epistemological theories to improve learning and instructional theory successfully. But I do not yet understand what DT has to offer in that regard. I would be most disappointed if DT advocates responded with, “No, last-century knowledge categories (facts, procedures, theories, etc.) are perfectly sufficient.”KiP has developed empirical methodologies to adapt to its view of knowledge as a complex, evolving system that we need to track at fine grain-sizes. One of them is “microgenetic learning analysis” (Parnafes & diSessa, 2013). In briefest terms, this is an attempt to track learning at nearly real-time scales, analyzing learning events on a second-by-second basis. A recent paper (diSessa, 2017) looks at a group of students who develop a normative model of thermal equilibration (Newton’s Laws of Heating/Cooling) with essentially no instruction. A part of this work tracked, individually and localized-in-time, contributions of a goodly number of previously documented p-prims.Micro-analysis is not just a means of pursuing an understanding of real-time learning. It also provides feedback on preliminary instructional designs and suggestions for improvement. My view is that any particular reformulation (or choice of germ cell) has benefits but also problems that need addressing. The germ cell or core reformulation is simply incapable, by itself, of addressing all these complications. So, we must do “micro-design” around emergent problems to provide optimal instruction. For example, one of the empirically discovered problems in extending the pathway to learning about thermal equilibration in diSessa (2017) to younger and less privileged students was a “pesky” and persistent newly discovered p-prim that seemed almost maliciously to interfere with the learning of younger students, but, for unknown reasons, was far less prominent with older students.So, germ cells and core reformulations are great! But they never do all the work, and we need theoretical views and empirical strategies to do the patching-to-optimal. Micro-design, beyond either a germ cell or the outline of a core reformulation is necessary. In our work, we deal with this all the time. What does DT do about this? I don’t see any equivalent, or even a frame for understanding the necessity of post-initial-design (post “identifying a germ cell”) patchwork.I believe that germ cells (in DT) are ontologically different than reformulations (in KiP). In KiP, reformulations are based on pools of resources in the naïve conceptual ecology that can be drawn on productively in instruction. In DT, it seems that germ cells are more narrowly focused and integrated conceptions and are determined by merely regarding expert understanding in a certain way. I can give a telling example. In Gennen’s paper (this issue), Hedegaard determined the relevant germ cell for biological evolution significantly by consulting expert opinion. “Hedegaard collaborated with academic specialists to delineate the germ cell of animal evolution...” In contrast, my momentum flow view began by noticing surprising insights young students had about forces, which would be generally categorically characterized as misconceptions by most physicists (e.g., that force, itself, is sub-stance-like); the fact is that force is a flow of substance-like stuff, momentum, which turns out to be an instructional manageable transformation in thinking.The momentum flow view is unfamiliar enough to expert physicists that some very high-profile physicists declared it to be incorrect physics. It is not (Herrmann and Pohlig, 2014, provide an early report on this shocking professional judgment.). Evidently, frames for reformulations on the basis of cognitive simplicity depend on the science of knowledge and learning, and not on the opinions of a experts, steeped as they are in views of subject matter. This strongly the and of things reformulations and germ other of reformulation that I identify is that by pervasive in representational this is a of and to intellectual So, it is that it to have no in DT least that I of or can see in Gennen’s example, in his of to Newton’s Gennen assumed that a is the only way to describe a position for every of To this is another case of being by and tradition, and not being to In our work teaching similar ideas to students, we two students could easily and their own of So, in particular, are not the only way of Newtonian This turns out to be a of approaches that as early as (or even much can and really do and their own This is a but for or science. call it introduction can be found in diSessa So, KiP can identify that are missing from the They might even be considered or merely “the of experts, of this – new, and – are a form of reformulation. might it as a reformulation of the a second out of this work is that of attractive and for students. them systematically to the of and even versions of these Newton’s laws this (diSessa, 2018, provides an In representational can reformulations as as cognitive is a issue here of potential A subject of debate the fact that are and the might be experience was that students and our their own and their In essence, they not treat the as but as a of results concerning were to but if they were I would be much more likely to accountability can the of science in of might be a to the but I found the of student knowledge in experience in Gennen’s report on the of My from our early experience with educational experts in their of in instruction. were as and by or, indeed, of in any way what in the world. early paper of with these (diSessa, is a example of on world as a privileged of learning. I will treat the example first and to a larger field of Gennen of of and as of are learning that either of physical or their which must in either case the core conceptual and without and on the to be a version of a of how in experience described as and in in from to of It might just be an but I missing the potential of – and only with – as a in of finding and of indeed, what about In fact, this experiential for learning – for developing p-prims, if you One is that we can far more out of our own educational than the of the not that these are as much or more in than in the world. This basic idea of instruction in with as the of instruction, of rather of relevant the book that I with et al., on The essential is with in geometric phenomena, we can develop an which is not a or of as In fact, I believe that far better knowledge on one it on the other with a of modern geometric (e.g., general or than the KiP intellectual framework, this is and flexible can develop rich pools of intuitive knowledge that will them in a different and better of learning into important and of far as I can this version of developing with different “germ and and different conceptual is missing from DT and its theoretical this the of an focus on educational experts about the germ cells of or might it be an that the theoretical were before the experiential and for learning science and it might be the fact that the DT traditions simply do not in either experiential intuitive pools of or in expert knowledge might by new, frame also of good of conceptual I don’t think KiP can provide any – indeed, a of modern approaches to provide of – for this probably does not and may essentially be of in experts be experts, of at what is the basis for at early experience with and or in any But can we use those ideas in In KiP terms, use things p-prims, which are of from their A different of research on that conceptions of significant and the of is similarly early in tried to understand the and in conceptual change that we have at a the many of learning to a paper previously diSessa might be a good place for the to start their own my analysis was I could not make any at all between stages and the that we have found for both and also the we have had in instructional a more the instructional was but relation to There were two representational each with their own and empirical The was not I think the of the learning any to the I very much Gennen’s what I call which I would of the I would the idea of germ cell, in to the idea of as a good focus for and mutual accountability. I would not model as a good I think conceptual change at and DT are very far would also this as a social and not to only by Instead, one should just try to work on the of researchers they and in their everyday work. if elements of one of the bridge become on the other will researchers feel the in and mutual accountability. In and to in our to knowledge and interaction analysis we found that researchers were the best to researchers seem not to have the to far from their and very researchers may become too and to one particular of this commentary, I on of work by and my research for and from at and the at The work on learning and conceptual change was mainly by the of the work was and contributions by students and are for can be found in the I am also for Thomas Gennen’s work, and for the by to on was for the of this as no or animal subjects were has no of to was for this

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