How to Avoid Inert Knowledge

• In Event: The Form and Function of Transfer in Diverse Contexts

Abstract

The phenomenon that students know abstract principles (e.g., mathematical theorems) but cannot, or at least do not, apply them when solving related problems is called inert knowledge. The goal of this contribution is to present and substantiate three theses directed toward avoiding inert knowledge. These theses are based on converging evidence from three thematically related, but typically unconnected research areas: example-based learning, analogical reasoning, and abstract modeling vis-a-vis Bandura’s (1986) socio-cognitive learning theory.

Thesis 1: Interconnected cognitive representations of abstract principles and concrete cases allow for transfer. Learners can apply abstract principles to new problems if they have knowledge structures representing abstract principles as well as concrete problem cases, and above all, the interconnections between them (Renkl, 2011). Representing just the principles and the problem cases (without tight interconnections) is not sufficient. In more colloquial terms, students should have knowledge on how to apply abstract principles to a variety of problem cases.

Thesis 2: Several instructional approaches can be used to effectively induce such interconnected knowledge structures. Several learning methods can foster interconnected knowledge structures addressed in thesis 1. In particular, many empirical studies have shown that self-explaining example cases (example-based learning; e.g., Schworm & Renkl, 2007), comparing example cases (analogical reasoning; e.g., Gentner, Loewenstein, & Thompson, 2003), and observing as well as actively encoding so-called “abstract models” (i.e., models that show the application of abstract principles; e.g., Braaksma, Rijlaarsdam, & van den Bergh, 2002) are suitable methods for fostering transferable (i.e., non-inert) knowledge. It is not the learning methods’ superficial features in terms of their exact procedures that are crucial, but instead their deep features in terms of the learning processes they elicit (Renkl, 2009). All these methods can elicit learning processes that interconnect abstract principles and problem cases.

Thesis 3: It is not the type of instructional method that interconnects principles and cases that is crucial to transfer; rather it is the quality of their implementation. Many studies show that a specific learning method’s effects strongly depend on the quality of its implementation. For example, providing students with several example cases for comparison is typically not sufficient when the learners should abstract a common solution principle behind the different examples. Example comparison has to be prompted and, best, even be guided (e.g., Gentner et al., 2003). Similarly, the potential of example-based learning is only fully exploited when self-explanation prompts encourage the learners to interconnect the solution steps of an example case with the underlying principles (Renkl, 2011). To sum up, the extent to which transfer is fostered is only marginally influenced by the type of learning method. Instead, it is crucial how well the chosen learning method is implemented (Renkl, 2008).
The present theses are a contribution toward solving the inert knowledge problem. On a more general level, the present position also casts doubts on theoretical discussions on the general superiority of certain learning methods and on corresponding meta-analyses. Finally, new hypotheses can be derived from the present theses that can extend the research literature on cognitive transfer.

Author

• Alexander Renkl, University of Freiburg