Pavlik and Koedinger - Generalizing the Assistance Formula

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Generalizing the Assistance Formula across multiple dimensions of instructional assistance


To foster more robust student learning, when should instruction provide information and assistance to students and when should it request students to generate information, ideas, and solutions? In different forms, this dilemma for instructors has been a part of debates on education since Plato. However, it is fair to say that we remain far from a precise and sound scientific response. We believe this “Assistance Dilemma” is one of the fundamental unsolved problems in the cognitive and learning sciences. To address this dilemma, we suggest a four step strategy for more clearly articulating the problem and tackling it with computational models that can be used to make precise, replicable, and testable predictions about when instructional assistance should be given vs. withheld. We illustrate these steps on two different dimensions of instructional assistance. On the “problem spacing” dimension, we present a computational model that generates precise predictions of the kind we call for. On the more complex “example-problem” dimension, we illustrate how the field is at a point where such a precise computational model may be possible.

Project Description

We will use DataShop log data to make progress on the Assistance Dilemma by targeting dimensions of assistance one at a time and creating parameterized mathematical models that predict the optimal level of assistance to enhance robust learning (cf., Koedinger et al., 2008). Such a mathematical model has been achieved for the practice-interval dimension (changing the amount of time between practice trials), and progress is being made on study-test dimension (changing the ratio of study trials to test trials) and the example-problem dimension (changing the ratio of examples to problems). These models generate the inverted-U shaped curve characteristic of the Assistance Dilemma as a function of particular parameter values that describe the instructional context. This function has a general form (L = [P*Sb+(1-P)Fb]/[P*Sc+(1-P)Fc]), which we call the “Assistance Formula”. We hypothesize that the Assistance Formula can be effectively instantiated for many other dimensions of assistance. These models address limitations of current instructional theory (e.g., Cognitive Load Theory) by generating a priori predictions of what forms of assistance or difficulty will enhance learning. Further, these models will provide the basis for on-line algorithms that adapt to individual student differences and changes over time, optimizing the assistance provided to each student for each knowledge component at each time in their learning trajectory. The benefits of such student-adapted optimization have already been demonstrated in PSLC projects on optimized practice scheduling (Pavlik & Anderson, 2008) and adaptive fading of worked examples (Salden, Renkl, Aleven et al. 2008). Similar efforts are needed for the many other dimensions of instructional assistance (e.g., study time, study-test, concrete-abstract, feedback timing, etc.).

Further Information

Annotated Bibliography

  • Koedinger, K. R., Pavlik, P., McLaren, B. M., & Aleven, V. (2008). Is it Better to Give than to Receive? The assistance dilemma as a fundamental unsolved problem in the cognitive science of learning and instruction. In V. Sloutsky, B. Love & K. McRae (Eds.), Proceedings of the 30th Conference of the Cognitive Science Society. Washington, D.C.


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Future Plans

Year 6 Project Deliverable: Journal publication on the Assistance Dilemma. 6th Month Milestone: Submission of journal article on the Assistance Dilemma.