Making "Direct Instruction" and "Discovery Learning" Play Along: Restoring the Historical Educational Role of Practice

• In Event: Discovery-Based STEM Learning 2.0: Are We There Yet?

Abstract

Objective
Dewey (1916) remarked that learning naturally results from doing. We concur and turn our attention to the role of practice. Specifically, heeding von Glaserfeld’s (1983) call to investigate the pedagogical approaches in the physical disciplines, we first turn our attention to how practice and learning are conceived in certain Chinese martial arts, then attend to parallels in our own design.

Theoretical Approach
Drawing on a multiyear ethnographic study of taiji and yiquan instruction, we outline a pedagogical approach centered on learning from doing. This approach, we offer, does away with the oft-heard tension of “direct instruction” versus “discovery.” Namely, students are directly instructed on the practice, even as discovery is explicitly understood as the purpose of practice.

In making sense of this pedagogical approach, we turn to the work of Soviet neurophysiologist Nikolai Bernstein (1996). Bernstein provides an original and pragmatic framework, wherein teachers provide what he labels outer aspects of knowing—i.e., hands go there, elbows here…—yet inner aspects of knowing must be experientially felt and thus arrive only as personal discovery.

The fact that the ‘secrets’ of swimming or cycling are not in some special body movements but in special sensations and corrections explains why these secrets are impossible to teach by demonstration” (p. 187).

On this account we agree with Freudenthal, who famously remarked that learning mathematics is like learning to swim (1971). Inspired by this perspective, we strive to design contemporary mathematics learning environments.

Methods & Design
Next, we present a contemporary mathematics-education motion-sensor learning environment. In our target design, students literally inscribe mathematical proportion with their hand movements (see, e.g., Authors, 2015b; see Figure 16). Specifically, students engage an educational activity they perceive as a game, yet the goal of which—unbeknownst to them—is to move their hands at proportional rates from some given baseline (e.g., the table). Once students become proficient at this practice, they begin using standard mathematical notations (e.g., numerals, grids) to reflect on and enhance their actions. We draw on microgenetic analysis of video data as well as records of participants’ gaze (i.e., eye tracking; see Figure 17) to illustrate how students in our study discover and coordinate various meanings of proportion through their practice.

Significance
In both traditional Chinese martial arts classes and our own design for mathematical proportion, the student is first given a practice and then, through this practice, discovers disciplinary meanings. While we cannot directly tell “the secrets” (Freudenthal, 1971) of our disciplines, we can and should provide students, as clearly as possible, with the sorts of practices that lead to meaningful personal discovery. Hence, “direct instruction” and “discovery” are not opposite (also see Taber, 2010) but complementary. Conceived thus, “direct instruction” is not used to tell the disciplinary meanings (because this would be a waste of time), but rather to instruct practices that lead to discovery and meaning-making, that is to say, that lead to learning.

Authors

• Dragan Trninic, University of California - Berkeley

• Dor Abrahamson, University of California - Berkeley