Optimized Screening for At-Risk Students in Mathematics: A Machine Learning Approach
Abstract
:1. Introduction
1.1. Gated Screening Approaches
1.2. Classification Accuracy
1.3. Current Study
- What is the difference in classification accuracy outcomes between single-measure and multi-measure (e.g., gated) screening frameworks?
- To what extent does the cut-score parameter influence the classification accuracy of the screening approach used to identify at-risk students?
2. Methods
2.1. Sample
2.2. Measures
2.2.1. Star Early Literacy
2.2.2. Star Reading
2.2.3. Star Math
2.3. Data Analysis
2.3.1. Single-Stage Screening
2.3.2. Gated Screening
2.3.3. Evaluation Criteria
3. Results
4. Discussion
4.1. Screening for Mathematics Difficulties
4.1.1. Single vs. Gated Screening Approaches
4.1.2. Weighing Evaluation Metrics
4.1.3. The Influence of Cut-Score Parameters
4.2. Limitations and Future Directions
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
FN | False negative classifications |
FP | False positive classifications |
MCC | Matthews correlation coefficient |
RF | Random Forest algorithm |
TN | True negative classifications |
TP | True positive classifications |
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Screening Method | Algorithm | Prediction Model | Sampling | Sensitivity | Specificity | Accuracy |
---|---|---|---|---|---|---|
Single-Stage | RF | Model 0 (SM) | Oversampling | 0.797 | 0.717 | 0.731 |
Single-Stage | RF | Model 1 (SM + SR + SEL) | Oversampling | 0.685 | 0.839 | 0.812 |
Single-Stage | LogitBoost | Model 0 (SM) | Oversampling | 0.713 | 0.790 | 0.777 |
Single-Stage | LogitBoost | Model 1 (SM + SR + SEL) | Oversampling | 0.835 | 0.726 | 0.744 |
Single-Stage | RF | Model 0 (SM) | Undersampling | 0.799 | 0.706 | 0.722 |
Single-Stage | RF | Model 1 (SM + SR + SEL) | Undersampling | 0.829 | 0.737 | 0.753 |
Single-Stage | LogitBoost | Model 0 (SM) | Undersampling | 0.711 | 0.792 | 0.778 |
Single-Stage | LogitBoost | Model 1 (SM + SR + SEL) | Undersampling | 0.788 | 0.781 | 0.782 |
Single-Stage | RF | Model 0 (SM) | ROSE | 0.635 | 0.793 | 0.766 |
Single-Stage | RF | Model 1 (SM + SR + SEL) | ROSE | 0.882 | 0.667 | 0.704 |
Single-Stage | LogitBoost | Model 0 (SM) | ROSE | 0.856 | 0.690 | 0.719 |
Single-Stage | LogitBoost | Model 1 (SM + SR + SEL) | ROSE | 0.866 | 0.665 | 0.699 |
Gated (Standard) | - | 30% Threshold | - | 0.468 | 0.923 | 0.844 |
Gated (Standard) | - | 40% Threshold | - | 0.624 | 0.863 | 0.822 |
Gated (Standard) | - | 50% Threshold | - | 0.778 | 0.781 | 0.780 |
Gated (Mixed) | RF | 30% Threshold | Oversampling | 0.698 | 0.788 | 0.773 |
Gated (Mixed) | RF | 40% Threshold | Oversampling | 0.781 | 0.739 | 0.746 |
Gated (Mixed) | RF | 50% Threshold | Oversampling | 0.863 | 0.670 | 0.703 |
Gated (Mixed) | LogitBoost | 30% Threshold | Oversampling | 0.570 | 0.868 | 0.816 |
Gated (Mixed) | LogitBoost | 40% Threshold | Oversampling | 0.892 | 0.568 | 0.624 |
Gated (Mixed) | LogitBoost | 50% Threshold | Oversampling | 0.896 | 0.594 | 0.646 |
Gated (Mixed) | RF | 30% Threshold | Undersampling | 0.703 | 0.787 | 0.773 |
Gated (Mixed) | RF | 40% Threshold | Undersampling | 0.784 | 0.736 | 0.744 |
Gated (Mixed) | RF | 50% Threshold | Undersampling | 0.876 | 0.663 | 0.699 |
Gated (Mixed) | LogitBoost | 30% Threshold | Undersampling | 0.627 | 0.848 | 0.810 |
Gated (Mixed) | LogitBoost | 40% Threshold | Undersampling | 0.704 | 0.804 | 0.787 |
Gated (Mixed) | LogitBoost | 50% Threshold | Undersampling | 0.885 | 0.609 | 0.657 |
Gated (Mixed) | RF | 30% Threshold | ROSE | 0.737 | 0.767 | 0.762 |
Gated (Mixed) | RF | 40% Threshold | ROSE | 0.791 | 0.712 | 0.726 |
Gated (Mixed) | RF | 50% Threshold | ROSE | 0.879 | 0.641 | 0.682 |
Gated (Mixed) | LogitBoost | 30% Threshold | ROSE | 0.909 | 0.504 | 0.574 |
Gated (Mixed) | LogitBoost | 40% Threshold | ROSE | 0.679 | 0.808 | 0.786 |
Gated (Mixed) | LogitBoost | 50% Threshold | ROSE | 0.930 | 0.529 | 0.598 |
Screening Method | Algorithm | Prediction Model | Sampling | Sensitivity | Specificity | Accuracy |
---|---|---|---|---|---|---|
Single-Stage | RF | Model 0 (SM) | Oversampling | 0.784 | 0.714 | 0.727 |
Single-Stage | RF | Model 1 (SM + SR + SEL) | Oversampling | 0.678 | 0.831 | 0.803 |
Single-Stage | LogitBoost | Model 0 (SM) | Oversampling | 0.731 | 0.775 | 0.767 |
Single-Stage | LogitBoost | Model 1 (SM + SR + SEL) | Oversampling | 0.843 | 0.710 | 0.734 |
Single-Stage | RF | Model 0 (SM) | Undersampling | 0.779 | 0.715 | 0.727 |
Single-Stage | RF | Model 1 (SM + SR + SEL) | Undersampling | 0.838 | 0.722 | 0.743 |
Single-Stage | LogitBoost | Model 0 (SM) | Undersampling | 0.701 | 0.790 | 0.774 |
Single-Stage | LogitBoost | Model 1 (SM + SR + SEL) | Undersampling | 0.842 | 0.670 | 0.701 |
Single-Stage | RF | Model 0 (SM) | ROSE | 0.683 | 0.738 | 0.728 |
Single-Stage | RF | Model 1 (SM + SR + SEL) | ROSE | 0.873 | 0.664 | 0.702 |
Single-Stage | LogitBoost | Model 0 (SM) | ROSE | 0.847 | 0.678 | 0.708 |
Single-Stage | LogitBoost | Model 1 (SM + SR + SEL) | ROSE | 0.898 | 0.607 | 0.659 |
Gated (Standard) | - | 30% Threshold | - | 0.461 | 0.914 | 0.832 |
Gated (Standard) | - | 40% Threshold | - | 0.622 | 0.851 | 0.809 |
Gated (Standard) | - | 50% Threshold | - | 0.758 | 0.764 | 0.763 |
Gated (Mixed) | RF | 30% Threshold | Oversampling | 0.713 | 0.776 | 0.764 |
Gated (Mixed) | RF | 40% Threshold | Oversampling | 0.779 | 0.728 | 0.737 |
Gated (Mixed) | RF | 50% Threshold | Oversampling | 0.849 | 0.661 | 0.695 |
Gated (Mixed) | LogitBoost | 30% Threshold | Oversampling | 0.729 | 0.682 | 0.690 |
Gated (Mixed) | LogitBoost | 40% Threshold | Oversampling | 0.717 | 0.776 | 0.765 |
Gated (Mixed) | LogitBoost | 50% Threshold | Oversampling | 0.824 | 0.679 | 0.705 |
Gated (Mixed) | RF | 30% Threshold | Undersampling | 0.710 | 0.776 | 0.764 |
Gated (Mixed) | RF | 40% Threshold | Undersampling | 0.783 | 0.720 | 0.731 |
Gated (Mixed) | RF | 50% Threshold | Undersampling | 0.858 | 0.651 | 0.688 |
Gated (Mixed) | LogitBoost | 30% Threshold | Undersampling | 0.615 | 0.831 | 0.792 |
Gated (Mixed) | LogitBoost | 40% Threshold | Undersampling | 0.736 | 0.763 | 0.758 |
Gated (Mixed) | LogitBoost | 50% Threshold | Undersampling | 0.821 | 0.694 | 0.717 |
Gated (Mixed) | RF | 30% Threshold | ROSE | 0.716 | 0.762 | 0.753 |
Gated (Mixed) | RF | 40% Threshold | ROSE | 0.808 | 0.690 | 0.711 |
Gated (Mixed) | RF | 50% Threshold | ROSE | 0.864 | 0.637 | 0.678 |
Gated (Mixed) | LogitBoost | 30% Threshold | ROSE | 0.698 | 0.793 | 0.776 |
Gated (Mixed) | LogitBoost | 40% Threshold | ROSE | 0.678 | 0.803 | 0.780 |
Gated (Mixed) | LogitBoost | 50% Threshold | ROSE | 0.867 | 0.619 | 0.664 |
Screening Method | Algorithm | Prediction Model | Sampling | 2016–2017 | 2017–2018 | ||
---|---|---|---|---|---|---|---|
MCC | MCC | ||||||
Single-Stage | RF | Model 0 (SM) | Oversampling | 0.755 | 0.414 | 0.747 | 0.418 |
Single-Stage | RF | Model 1 (SM + SR + SEL) | Oversampling | 0.754 | 0.450 | 0.747 | 0.437 |
Single-Stage | LogitBoost | Model 0 (SM) | Oversampling | 0.750 | 0.417 | 0.752 | 0.418 |
Single-Stage | LogitBoost | Model 1 (SM + SR + SEL) | Oversampling | 0.777 | 0.438 | 0.771 | 0.453 |
Single-Stage | RF | Model 0 (SM) | Undersampling | 0.750 | 0.393 | 0.746 | 0.413 |
Single-Stage | RF | Model 1 (SM + SR + SEL) | Undersampling | 0.780 | 0.445 | 0.776 | 0.439 |
Single-Stage | LogitBoost | Model 0 (SM) | Undersampling | 0.749 | 0.416 | 0.743 | 0.412 |
Single-Stage | LogitBoost | Model 1 (SM + SR + SEL) | Undersampling | 0.784 | 0.462 | 0.746 | 0.399 |
Single-Stage | RF | Model 0 (SM) | ROSE | 0.705 | 0.343 | 0.709 | 0.355 |
Single-Stage | RF | Model 1 (SM + SR + SEL) | ROSE | 0.760 | 0.432 | 0.754 | 0.414 |
Single-Stage | LogitBoost | Model 0 (SM) | ROSE | 0.764 | 0.411 | 0.753 | 0.410 |
Single-Stage | LogitBoost | Model 1 (SM + SR + SEL) | ROSE | 0.752 | 0.442 | 0.724 | 0.388 |
Gated (Standard) | - | 30% Threshold | - | 0.621 | 0.420 | 0.613 | 0.399 |
Gated (Standard) | - | 40% Threshold | - | 0.724 | 0.444 | 0.719 | 0.428 |
Gated (Standard) | - | 50% Threshold | - | 0.779 | 0.448 | 0.761 | 0.429 |
Gated (Mixed) | RF | 30% Threshold | Oversampling | 0.740 | 0.401 | 0.743 | 0.403 |
Gated (Mixed) | RF | 40% Threshold | Oversampling | 0.756 | 0.413 | 0.753 | 0.406 |
Gated (Mixed) | RF | 50% Threshold | Oversampling | 0.754 | 0.415 | 0.743 | 0.400 |
Gated (Mixed) | LogitBoost | 30% Threshold | Oversampling | 0.688 | 0.405 | 0.705 | 0.397 |
Gated (Mixed) | LogitBoost | 40% Threshold | Oversampling | 0.694 | 0.438 | 0.745 | 0.409 |
Gated (Mixed) | LogitBoost | 50% Threshold | Oversampling | 0.714 | 0.427 | 0.745 | 0.402 |
Gated (Mixed) | RF | 30% Threshold | Undersampling | 0.743 | 0.406 | 0.742 | 0.404 |
Gated (Mixed) | RF | 40% Threshold | Undersampling | 0.759 | 0.411 | 0.750 | 0.400 |
Gated (Mixed) | RF | 50% Threshold | Undersampling | 0.755 | 0.411 | 0.740 | 0.395 |
Gated (Mixed) | LogitBoost | 30% Threshold | Undersampling | 0.721 | 0.424 | 0.707 | 0.397 |
Gated (Mixed) | LogitBoost | 40% Threshold | Undersampling | 0.751 | 0.426 | 0.749 | 0.417 |
Gated (Mixed) | LogitBoost | 50% Threshold | Undersampling | 0.722 | 0.374 | 0.752 | 0.401 |
Gated (Mixed) | RF | 30% Threshold | ROSE | 0.752 | 0.406 | 0.738 | 0.404 |
Gated (Mixed) | RF | 40% Threshold | ROSE | 0.749 | 0.418 | 0.744 | 0.400 |
Gated (Mixed) | RF | 50% Threshold | ROSE | 0.741 | 0.405 | 0.733 | 0.395 |
Gated (Mixed) | LogitBoost | 30% Threshold | ROSE | 0.648 | 0.417 | 0.742 | 0.397 |
Gated (Mixed) | LogitBoost | 40% Threshold | ROSE | 0.738 | 0.376 | 0.735 | 0.417 |
Gated (Mixed) | LogitBoost | 50% Threshold | ROSE | 0.674 | 0.423 | 0.722 | 0.401 |
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Bulut, O.; Cormier, D.C.; Yildirim-Erbasli, S.N. Optimized Screening for At-Risk Students in Mathematics: A Machine Learning Approach. Information 2022, 13, 400. https://doi.org/10.3390/info13080400
Bulut O, Cormier DC, Yildirim-Erbasli SN. Optimized Screening for At-Risk Students in Mathematics: A Machine Learning Approach. Information. 2022; 13(8):400. https://doi.org/10.3390/info13080400
Chicago/Turabian StyleBulut, Okan, Damien C. Cormier, and Seyma Nur Yildirim-Erbasli. 2022. "Optimized Screening for At-Risk Students in Mathematics: A Machine Learning Approach" Information 13, no. 8: 400. https://doi.org/10.3390/info13080400