Three Diagnoses of Why Transfer Across Disciplines Can Fail and Their Implications for Interdisciplinary Education

One goal of interdisciplinary educational efforts is to increase students’ ability to transfer knowledge from one disciplinary context to another. The approach taken to foster this transfer depends on the diagnosis of why this transfer can fail in the first place. Although a common diagnosis focuses on content knowledge and problem features as explanatory, there exist other, less prevalent diagnoses for why transfer across disciplines fails. In this paper, we show how one student responds differently to two similar problems set in physics and calculus problem contexts. We argue that beyond a content knowledge diagnosis, an epistemology diagnosis and an accountability diagnosis can also plausibly contribute to an explanation of why this student approaches these two similar problems differently, presenting additional considerations in fostering interdisciplinary transfer. How Approaches to Interdisciplinary Education Imply Diagnoses of Why Transfer Fails The transfer of content knowledge across different disciplines is one goal of a multidisciplinary education system. A typical curriculum for an undergraduate STEM major is designed with the expectation that students can and will, in any particular course, apply knowledge and skills learned in other disciplinary courses – for example, the typical undergraduate physics curriculum is designed expecting that students can and will transfer knowledge learned in prerequisite math courses into those physics courses; similarly, engineering courses expect students can transfer-in knowledge from math and physics courses. Although these various courses are largely designed independently from one another, some interdisciplinary course reform efforts have developed, aiming to bolster transfer across the disciplines. The most common interdisciplinary approach is to align the content between two courses in order to construct content connections across the disciplines (e.g. Al-Holou et al., 1999; Dunn & Barbanel, 2000; Plomer, Jessen, Rangelov, & Meyer, 2010). Common goals of these efforts include avoiding haphazard coverage of related content across disciplinary courses as well as highlighting content connections between disciplines to decrease compartmentalization of knowledge and encourage future transfer to different disciplinary problem contexts. Approaches such as these reveal (either explicit or implicit) views that poor content knowledge generalization and problem-specific surface features are explanatory in understanding why transfer across disciplines can fail. This content knowledge diagnosis is aligned with classical views of transfer that found reduced spontaneous transfer of a learned problem solution when the surface features of transfer problems were made more dissimilar from the initial training cases (Gick & Holyoak, 1980; Reed, Ernst, & Banerji, 1974). Such transfer is improved when multiple training cases were used, supporting the development of a more general solution schema not tied to the surface features of any one particular case (Gick & Holyoak, 1983; Reeves & Weisberg, 1994). In the same way, the alignment and co-presentation of content in interdisciplinary efforts aims, in part, to prevent the content knowledge from being tied to any one disciplinary context while also providing practice in applying that content knowledge in multiple disciplinary problem contexts. We argue that there exist other possible diagnoses for why transfer across disciplines fails, which are not as prevalent as the content knowledge diagnosis. In this paper, we present one student, Will, who reasons differently on two similar problems set in physics and calculus disciplinary contexts. Investigating why his reasoning differs on these problems leads to two additional diagnoses of why he applies different ideas and approaches in each case: an epistemology diagnosis and an accountability diagnosis. We conclude with the possible implications of these alternative diagnoses for interdisciplinary education efforts. Two Problems Asking “What Counts as a Good Approximation? ” As part of a larger study, we designed a set of problems to investigate how students might reason with similar mathematical content in different disciplinary problem contexts. This paper will include an in-depth discussion of one student’s reasoning on two of these problems. The two problems, PENDULUM and ARCTAN, ask about approximations and infinite series in physics and calculus problem contexts, respectively: PENDULUM (includes a figure of a pendulum with angle, length, and mass labeled): You have a pendulum made of a metal ball on a string. The string is 1 meter long and the metal ball has a mass of 1 kg. You might know that the approximation for the period of a pendulum ICLS 2014 Proceedings 62 © ISLS for small oscillations is: ! = 2! , where T is the period of the pendulum, l is the length of the pendulum, and g is acceleration due to gravity (9.81 m/s 2 ). This equation only holds for small angle oscillations of the pendulum. For larger angles, the period of a pendulum can be found with the following equation: ! = 2!