BuchananWWSept22

Response to Putnam, Lampert, and Peterson (1990)

Psychologists try to tell compelling stories to explain learning. Different perspectives in psychology can be used to tell different stories about the same learning scenario. For example, consider a child playing a computer game. A cognitive psychologist might explain that the child is constructing a mental model of the game, including the algorithms for successfully overcoming challenges. A behaviorist might be less ambitious in his story, and only explain what can be observed: operating the controls, and external signs of concentration, anxiety, rumination, and satisfaction. If the child succeeds at the game, the behaviorist might say the game effectively conditioned the child, while the cognitivist might say the child mastered the game. Thus, in behaviorist stories a learner can seem passive. Since this alleged passivity is a common criticism of behaviorism, it's important to consider how learners are "active" from the behaviorist and cognitive perspectives.

Neither the behaviorist nor cognitivist views the learner as truly passive. From both perspectives, a child playing a computer game is actively manipulating the controls and exhibiting experimentation and discrimination. However, the behaviorist story is more succinct (or perhaps parsimonious). If the child tries a certain strategy in the game and loses, the child is simply less likely to try that strategy again. Such a story is largely a clash between arrays of stimuli and arrays of responses, and the child is an impressionable "tablet" for etching or erasing algorithmic behaviors. The cognitivist perspective include such a tablet, but adds an additional layer of complexity. An "executive layer" can mitigate the effects of rewards and punishments, and in other ways influence the etching or erasing of algorithms. Such an executive layer, or metacognitive agency, is why learners are considered more "active" in cognitive stories.

Putnam, Lampert, and Peterson (1990) argue for the existence and utility of an executive layer. For example, they explain that the way that math is taught and practiced in schools differs greatly from the way math is understood and practiced by professional mathematicians. (p. 60) This implies that mathematicians excel at math in spite of classroom instruction. An executive layer is an attractive explanation to this phenomenon: perhaps mathematicians construct their own necessary understanding of math. According to Putnam et al., the National Council of Teachers of Mathematics (NCTM) also argues for an executive layer, when they "deemphasize the view that knowledge consists of distinct parts." (p. 63) The existence of an executive layer is further used to tell stories about a mental "problem space." A learner uses his problem space to manipulate representations and apply rules. (p. 79)

A factory metaphor can help clarify ideas like problem space, and further distinguish the behaviorist and cognitive perspectives. From both perspectives, the factory floor teems with adaptive activity (i.e. algorithms are etched and erased). But only the cognitive perspective posits a factory manager, watching from an upper office window, planning and troubleshooting, acting as "the control structure." (p. 84) He can see his problem space: the factory floor. Like a manager monitoring and modifying the processes on the factory floor, a learner "plays an active role in interpreting and structuring the environmental stimuli." (p. 87) In other words, the learner is assumed to be accurately witnessing and influencing her information processing. The behaviorist doesn't depend on that assumption, nor refute it. Instead, the behaviorist relies on causal descriptions of stimuli and responses, effectively skipping any intervening contemplation. To a behaviorist, accounts of such contemplation are suspect because it's not directly observable. Also, effective behaviorist interventions allegedly make such contemplation irrelevant. Knowledge has distinct parts, and there is no determinant global oversight, no factory manager.

The executive layer makes the cognitive perspective appealing, especially since it's supported by our intuition and experiences. However, Greeno, Collins, and Resnick (1996) have cautioned psychologists against orthodox adherence to any single perspective. For example, instead of behaviorist or cognitive stories, researchers like Putnam et al. may profit from applying a situative perspective. For example, a major impetus for reforming math instruction is the changing nature of math in society, so reforms are driven by situative analyses. The NCTM argues that "math has become 'a critical filter for employment and full participation in our society,'" so learners must be able to apply their understanding in real-world context. (p. 62) As a further impetus to apply a situative perspective, math uses a shared symbol system (p. 70). This shared system may be purely a situative construct, if there is "no mathematical reality 'out there' to be learned or discovered." (p. 90)

In my preservice teacher training program, we were asked whether we saw teaching as a science, an art, or a craft. This choice is analogous to selecting from a behaviorist, cognitive, or situative perspective. A science of teaching would thrive on programmed instruction perfected through experimentation. Choosing the art perspective empowers a teacher to build a unique set of practices, and to celebrate the individuality of learners. Teaching as a craft emphasizes apprenticeship models and the perpetuation of traditions. Ultimately, however, this is a misleading choice. Each approach to teaching has merits and flaws, just as each perspective in psychology affords new understanding while incurring new risks. Good teaching and good research are hybrid approaches based on eclecticism, not orthodoxy. Reading Putnam et al. reinforced my belief in this hybrid, pluralist perspective. Learning and teaching math is too complex and too poorly understood to preemptively settle on any single perspective.