How Should I Teach from This Month Onward? A State-Space Model That Helps Drive Whole Classes to Achieve End-of-Year National Standardized Test Learning Targets

Abstract

Every month, teachers face the dilemma of what exercises their students should practice, and what their consequences are regarding long-term learning. Since teachers prefer to pose their own exercises, this generates a large number of questions, each one attempted by a small number of students. Thus, we could not use models based on big data, such as deep learning. Instead, we developed a simple-to-understand state-space model that predicts end-of-year national test scores. We used 2386 online fourth-grade mathematics questions designed by teachers, each attempted by some of the 500 students in 24 low socioeconomic schools. We found that the state-space model predictions improved month by month and that in most months, it outperformed linear regression models. Moreover, the state-space estimator provides for each month a direct mechanism to simulate different practice strategies and compute their impact on the end-of-year standardized national test. We built iso-impact curves based on two critical variables: the number of questions solved correctly in the first attempt and the total number of exercises attempted. This allows the teacher to visualize the trade-off between asking students to perform exercises more carefully or perform more exercises. To the best of our knowledge, this model is the first of its kind in education. It is a novel tool that supports teachers drive whole classes to achieve long-term learning targets.

Keywords

• digital systems
• educational systems
• state-space models
• optimal control
• long-term learning prediction
• learning analytics