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Control Theory Forecasts of Optimal Training Dosage to Facilitate Children’s Arithmetic Learning in a Digital Educational Application

Published online by Cambridge University Press:  01 January 2025

Sy-Miin Chow Open the ORCID record for Sy-Miin Chow [Opens in a new window] ,
Jungmin Lee ,
Abe D. Hofman ,
Han L. J. van der Maas ,
Dennis K. Pearl  and
Peter C. M. Molenaar
Sy-Miin Chow*
Affiliation:
The Pennsylvania State University
Jungmin Lee
Affiliation:
The Pennsylvania State University
Abe D. Hofman
Affiliation:
University of Amsterdam
Han L. J. van der Maas
Affiliation:
University of Amsterdam
Dennis K. Pearl
Affiliation:
The Pennsylvania State University
Peter C. M. Molenaar
Affiliation:
The Pennsylvania State University
*
Correspondence should be made to Sy-Miin Chow, The Pennsylvania State University, 119 Health and Human Development Building, University Park, PA 16802, USA. Email: symiin@psu.edu
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Abstract

Education can be viewed as a control theory problem in which students seek ongoing exogenous input—either through traditional classroom teaching or other alternative training resources—to minimize the discrepancies between their actual and target (reference) performance levels. Using illustrative data from n=784\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$n=784$$\end{document} Dutch elementary school students as measured using the Math Garden, a web-based computer adaptive practice and monitoring system, we simulate and evaluate the outcomes of using off-line and finite memory linear quadratic controllers with constraintsto forecast students’ optimal training durations. By integrating population standards with each student’s own latent change information, we demonstrate that adoption of the control theory-guided, person- and time-specific training dosages could yield increased training benefits at reduced costs compared to students’ actual observed training durations, and a fixed-duration training scheme. The control theory approach also outperforms a linear scheme that provides training recommendations based on observed scores under noisy and the presence of missing data. Design-related issues such as ways to determine the penalty cost of input administration and the size of the control horizon window are addressed through a series of illustrative and empirically (Math Garden) motivated simulations.

Keywords

Control theoryArithmetic trainingDigital appState-spaceMath Garden
Type
Application Reviews and Case Studies
Information
Psychometrika , Volume 87 , Issue 2: Special Issue on Forecasting with Intensive Longitudinal Data , June 2022 , pp. 559 - 592
Copyright
copyright © 2022 The Author(s) under exclusive licence to The Psychometric Society

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Footnotes

Supplementary Information The online version contains supplementary material available at https://doi.org/10.1007/s11336-021-09829-3.

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