1 Why Direct Instruction Earns a C- in Transfer Dan Schwartz, Stanford Univ. http://AAALab.stanford.edu/ Most teachers have experienced the frustration of students doing well on chapter tests but forgetting in other contexts. Many times, students did not forget; they were confused. They could not figure out which of their concepts applied to the new situations. Whitehead coined the expression “inert knowledge” to describe peoples’ failure to apply their learning when they should. In behavioral research, it is known as the transfer problem. The transfer problem raises three questions: Why does it happen? Should we care? What can we do? Why Direct Instruction Fails to Transfer Successful transfer depends on learning at least two things: the relevant concepts or skills, and the situations to which they apply (2). In one study, advanced psychology students demonstrated solid memory of clinical theories, but once they met patients, they could not determine which theories applied (3). There are many good instructional techniques for improving memory, but teaching the situations that call for those memories is a different matter. When teaching about situations, students need to learn the deep structures that exist across many instances (4). Experts recognize deep structures. Physicists, for example, categorize both spring and inclined plane problems as cases of energy conservation, whereas novices see them as problems about different devices (5). A prevailing cognitive explanation for failed transfer is that students cannot get past the surface or incidental features of instructional instances. For example, if students learn about density by studying gold, they may not spontaneously transfer the concept of density to water.2 Research has found that students are more likely to transfer if instructional examples are abstract and relatively free of surface details (6, 7, 8). For instance, students who learned to compound quantities using abstract math transferred the formula to physics, but students who learned the same formula through applied physics did not transfer to math (9). Despite this evidence, the surface details of instructional examples are not the primary cause of failed transfer. Instead, the clash between surface features and transfer is an inadvertent outcome of direct instruction. Typical instructional methods for science and math give students the formula first, and then have students complete practice problems. The strength of such “tell-and-practice” methods is that students quickly memorize the formula. The pitfall is that students focus on the formula and never attend to the generalizable structure of the problem situations (10). They are only left with memories for the formula and the obvious surface features of the problems. A study with 8th-grade students demonstrates the negative effects of tell-and-practice for learning deep structure (11). The lessons focused on density and speed. A shared deep feature is their ratio structure (D=m/V, S = d/t). In the first lesson, students in the Tell-and-Practice treatment were directly taught about density and the formula. Afterwards, they received three paired cases. For each pair, they had to apply the density formula. Figure 1a shows that each pair represented a company that had two busses with the same clown density. In the Invent treatment, the students were not told about density. Instead, they were asked to invent a quantitative index for the crowdedness of the clowns. [Figure 1 about here – Clown Task and Memory Results]3 A day later, students redrew the cases from memory. Students in both treatments remembered similar numbers of surface features. However, the Tell-and-Practice students did not reproduce the ratio structure as often as the Invent students (Figs 1b-c). For the Tell-and-Practice students, direct instruction deflected attention from the deep structure, so only easy-to-notice surface features were encoded. For the Invent students, the surface features did not interfere with encoding the deep structure. These differences affected subsequent transfer. Over the next few days, students completed three more pictorial activities on density and speed, maintaining their instructional treatments. The Tell-and-Practice students further received a lecture on the importance of ratio for density, speed, and other topics in physics. Afterwards, all students took a transfer test that depicted springs pressing against plates of different sizes. Their task was to describe the surface pressure. This was a new topic for the students, but it also involves a ratio structure (springs over area). Tell-and-Practice students used a ratio to describ the surface pressure at 41% the rate of the Invent students (Fig 2a). This limited transfer is notable given that these students had completed four tasks that analogously used ratios to describe physical phenomena (12); and, they had been explicitly told that ratios were the common structure and are important more generally in describing physical situations. [Figure 2 about here – Transfer Results] The poor transfer was not due to direct instruction per se, but rather because the direct instruction pre-empted processing the deep structure. After completing the first transfer test, the Invent students also received direct instruction on the formulas and ratio, and both treatments practiced on word problems. Two weeks later, all students completed a delayed transfer test on4 the spring constant – determining the stiffness of trampoline fabrics. The Tell-and-Practice transfer rate was 36% of the Invent rate (Fig. 2b). Direct instruction did not interfere with transfer for the Invent students. Direct instruction is important, because it delivers the explanations and efficient solutions invented by experts. To gain this benefit without undermining transfer, direct instruction can happen after students have engaged the deep structure, per the Invent condition. Figure 2c shows that the Invent students performed just as well on a subsequent test of word problems about density and speed. Direct instruction becomes problematic when it shortcuts the appreciation of deep structure. Across conditions, students who encoded the deep structure of the clown problems were twice as likely to transfer. It is just that fewer students in the Tell-and-Practice condition encoded the deep structure, because they had received direct instruction too soon. A