Harnessing what you know

Harnessing what you know: The role of analogy in robust learning

Robert Hausmann and Timothy J. Nokes

Abstract. Knowledge transfer is a core assumption built into the pedagogy of most educational programs from K-12 to college. It is assumed that the material learned in the fourth week of the course is retained and transfers to material taught in the eighth week of the course. This is particularly true for highly structured courses such as physics; however, the empirical literature on learning suggests that far transfer is much more difficult than traditional pedagogy assumes (for reviews, see Bransford, Brown, & Cocking, 2000; Bransford & Schwartz, 1999; Gick & Holyoak, 1983). The goal of the present paper is to reconcile these apparently incompatible beliefs. Toward that end, we will use a repository of data, taken from the Physics LearnLab, to argue that the level of granularity of the constituent knowledge components affects the detection of to transfer from one domain to another.

Introduction

In well-structured domains, such as math or science, teachers often presume that the contents of one unit will transfer to units taught later in the semester; however, the learning literature is replete with evidence suggesting that transfer, especially far transfer, is difficult to achieve (Detterman, 1993). Do teachers have unrealistic expectations of their students, or are scientists looking in the wrong places to find evidence of far transfer? The primary goal of the present paper is to seek a resolution to this potential contradiction. Toward that end, we will define learning at multiple levels of granularity and show how different levels of knowledge disaggregation reveal different conclusions about the existence or non-existence of far transfer.

Knowledge decomposition and learning curves

Many domains, such as math, science, and computer programming, assume that knowledge can be decomposed into a partially ordered set of skills or knowledge components. This assumption has been formalized in computational models of human cognition, including production rules in the ACT-R architecture (Anderson & Lebiere, 1998) and chunks in the SOAR architecture (Newell, 1990).
Evidence for the psychological plausibility for knowledge components can be found in the shape of the curve when an individual's performance, which is typically measured as an error rate or the elapsed time, plotted against the opportunities to apply that particular piece of knowledge. These graphs are often referred to as learning curves, and an idealized learning curve monotonically decreases over time. Classic examples of learning curves include memorizing non-sense syllables (Ebbinghaus, 1913), learning how to roll a cigar (Crossman, 1959), and transmitting Morse code (Bryan & Harter, 1897).
A more contemporary example of a learning curve can be found in the domain of electrodynamics (Hausmann & VanLehn, under review). Students enrolled in a second-semester physic course were asked to solve problems with the Andes Physics Tutor (VanLehn et al., 2005). During an in vivo experiment (Hausmann & VanLehn, 2007), students were asked to solve four electrodynamics problems, which included calculating the magnitude of an electric force (F) that a charged particle (q) experiences when it is located in a region with an electric field (E). The relationship between these three quantities is summarized by the following equation: F = E

Introduction

In well-structured domains, such as math or science, teachers often presume that the contents of one unit will transfer to units taught later in the semester; however, the learning literature is replete with evidence suggesting that transfer, especially far transfer, is difficult to achieve (Detterman, 1993). Do teachers have unrealistic expectations of their students, or are scientists looking in the wrong places to find evidence of far transfer? The primary goal of the present paper is to seek a resolution to this potential contradiction. Toward that end, we will define learning at multiple levels of granularity and show how different levels of knowledge disaggregation reveal different conclusions about the existence or non-existence of far transfer.

Knowledge decomposition and learning curves

Many domains, such as math, science, and computer programming, assume that knowledge can be decomposed into a partially ordered set of skills or knowledge components. This assumption has been formalized in computational models of human cognition, including production rules in the ACT-R architecture (Anderson & Lebiere, 1998) and chunks in the SOAR architecture (Newell, 1990).
Evidence for the psychological plausibility for knowledge components can be found in the shape of the curve when an individual's performance, which is typically measured as an error rate or the elapsed time, plotted against the opportunities to apply that particular piece of knowledge. These graphs are often referred to as learning curves, and an idealized learning curve monotonically decreases over time. Classic examples of learning curves include memorizing non-sense syllables (Ebbinghaus, 1913), learning how to roll a cigar (Crossman, 1959), and transmitting Morse code (Bryan & Harter, 1897).
A more contemporary example of a learning curve can be found in the domain of electrodynamics (Hausmann & VanLehn, under review). Students enrolled in a second-semester physic course were asked to solve problems with the Andes Physics Tutor (VanLehn et al., 2005). During an in vivo experiment (Hausmann & VanLehn, 2007), students were asked to solve four electrodynamics problems, which included calculating the magnitude of an electric force (F) that a charged particle (q) experiences when it is located in a region with an electric field (E). The relationship between these three quantities is summarized by the following equation: F = E