# Optimizing the practice schedule

## Contents

### Optimizing the practice schedule project

### Abstract

This project plan extends dissertation work of Pavlik. In this initial work, a model-based algorithm was described to maximize the rate of learning for simple facts using flashcard like practice by determining the best schedule of presentation for a set of facts. The goal of this project plan is to develop this initial work to allow this tutor with optimized scheduling to handle more complex information and different types of learning in more natural settings (like LearnLabs). Specifically, this project plan describes extensions to the theory in two main areas.

- 1. Specification of a theory of refined encoding
- a. Generalization practice (multimodal and bidirectional training)
- b. Discrimination practice (detailed error remediation)

- 2. Specification of a theory of co-training
- a. Effect of declarative memory chunk sequence during learning
- b. Effect of declarative memory chunks on production rule learning

These theoretical directions are intended to enhance the optimization tutor by greatly extending its capabilities.

A secondary goal of the project is to link the optimization algorithm used in this project with the larger CTAT project. In this linkage the optimization algorithm would be integrated onto the current CTAT system as a curriculum management system that could select or generate problems according to the algorithm, but using CTAT interfaces. This integration will make it easier for people to use the optimal learning system and therefore increase its impact and usefulness.

### Glossary

### Research question

How can the optimal sequence of learning be computed?

### Background and significance

Since the early 60's researchers in learning theory have been describing models of practice which attempt to capture the effect of practice on performance at a later time. These models are applicable to describing many types of learning situations, but are easier to apply where information to be learned can be broken up into small chunks that can be learned independently. For instance, Atkinson (1972) applied a Markov model of learning to schedule drill of German vocabulary.

More recently there has been a renewed emphasis on repeated practice. For instance, the National Council of Teachers of Mathematics new report WSJ article emphasizes the importance of this type of learning for simple math skills.

More information and demonstrations of tutors in this project can be found at Lab Website

### Dependent variables

Current performance -- These measures are usually taken as the student drills in the tutor.

Long-term performance -- These measures are usually taken in the tutor after at least one day of retention (longer intervals occur in the most recent studies).

Transfer -- Many of the studies in this project will look at how learning in the tutor transfers to situations where that knowledge can be applied in a different configuration.

Accelerated future learning -- Some studies in this project will investigate the effect of tutor practice on the learning of items that depend upon the tutor practice.

### Independent variables

Alternative structures of instructional schedule for knowledge component training based on the predictions of an ACT-R based cognitive model. Further independent variables include how the material is presented for each learning event and the assumptions of the model used to presents schedule the learning. The assumptions of the model include alternative analyses of task demands, the structure of relevant knowledge components, and learner background.

### Hypothesis

Robust learning occurs more quickly when practice is scheudled efficiently. In this case efficiently means according to a complex model of the gain and cost of possible scheudling decisions.

### Explanation

The algorithm for scheduling practice uses a mathematical model of learning to predict when new practice should occur for recall to be optimal later. This model accounts for:

When prior practice occurred

- How many prior practices occurred
- Spacing between prior practice was
- Whether prior practice occurred as testing or passive study
- Duration of prior practices
- An individuals history of success or failure with tests
- What type of practice occurs (phonological, orthographic, English to Foreign or Foreign to English)

Optimal scheudules are mainly controlled by the benefit of wide spacing, which results in better long-term learning and the benefit of short spacing, which results faster learning.

### Descendents

- Understanding paired asociate transfer effects based on shared stimulus components (Pavlik, MacWhinney, Bolster, Koedinger)

- Applying optimal scheduling of practice in the Chinese Learnlab (Pavlik, MacWhinney, Sue-mei Wu, Koedinger)

### Annotated bibliography

Atkinson, R. (1972) Optimizing the learning of a second language vocabulary. Journal of Experimental Psychology, 96, 124- 129.

Pavlik Jr., P. I., & Anderson, J. R. (2005). Practice and Forgetting Effects on Vocabulary Memory: An Activation-Based Model of the Spacing Effect. Cognitive Science, 29, 559-586 (Article).

Pavlik Jr., P. I. (in press). Timing is an order: Modeling order effects in the learning of information. In F. E. Ritter, J. Nerb, T. O'Shea & E. Lehtinen (Eds.), In order to learn: How the sequences of topics affect learning. New York, NY: Oxford University Press.