ARTICLE | doi:10.20944/preprints202208.0124.v1
Subject: Social Sciences, Education Keywords: Digital Systems; Educational Systems; State-space Models; Optimal Control; Long-term learning prediction; Learning Analytics
Online: 5 August 2022 (14:37:36 CEST)
Every month teachers face the dilemma of what exercises should their students practice, and what their consequences are on 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 couldn’t 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 2,386 online fourth-grade mathematic questions designed by teachers and 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 do exercises more carefully or doing 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.