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Machine learning (ML) provides a powerful framework for the analysis of high-dimensional datasets by modelling complex relationships, often encountered in modern data with many variables, cases and potentially non-linear effects. The impact of ML methods on research and practical applications in the educational sciences is still limited, but continuously grows, as larger and more complex datasets become available through massive open online courses (MOOCs) and large-scale investigations. The educational sciences are at a crucial pivot point, because of the anticipated impact ML methods hold for the field. To provide educational researchers with an elaborate introduction to the topic, we provide an instructional summary of the opportunities and challenges of ML for the educational sciences, show how a look at related disciplines can help learning from their experiences, and argue for a philosophical shift in model evaluation. We demonstrate how the overall quality of data analysis in educational research can benefit from these methods and show how ML can play a decisive role in the validation of empirical models. Specifically, we (1) provide an overview of the types of data suitable for ML and (2) give practical advice for the application of ML methods. In each section, we provide analytical examples and reproducible R code. Also, we provide an extensive Appendix on ML-based applications for education. This instructional summary will help educational scientists and practitioners to prepare for the promises and threats that come with the shift towards digitisation and large-scale assessment in education.

When physicians are asked to determine the positive predictive value from the a priori probability of a disease and the sensitivity and false positive rate of a medical test (Bayesian reasoning), it often comes to misjudgments with serious consequences. In daily clinical practice, however, it is not only important that doctors receive a tool with which they can "correctly" judge--the "speed" of these judgments is also a crucial factor. In this study, we analyzed accuracy and efficiency in medical Bayesian inferences. In an empirical study we varied information format (probabilities vs. natural frequencies) and visualization (text only vs. tree only) for four contexts. 111 medical students participated in this study by working on four Bayesian tasks with common medical problems. The correctness of their answers was coded and the time spent on task was recorded. The median time for a correct Bayesian inference is fastest in the version with a frequency tree (2:55 min) compared to the version with a probability tree (5:47 min) or to the text only versions based on natural frequencies (4:13 min) or probabilities (9:59 min). The score "diagnostic efficiency" (calculated by: median time divided by percentage of correct inferences) is best in the version with a frequency tree (4:53 min). Frequency trees allow more accurate "and" faster judgments. Improving correctness and efficiency in Bayesian tasks might help to decrease overdiagnosis in daily clinical practice, which on the one hand cause cost and on the other hand might endanger patients' safety.

In the present study, the relationship between the mathematics grade and the three basic cognitive abilities (inhibition, working memory, and reasoning) was analyzed regarding possible alterations during elementary school. In a sample of N = 244 children, the mathematics grade was best predicted by working memory performance in the second grade and by reasoning in the third and fourth grades. Differentiation of these abilities during elementary school was considered as a cause for this pattern but discarded after the analysis of structural equation models. Thus, with respect to output-orientated curricula, scholastic standards, and a large inter-individual heterogeneity of students, it is implied for teachers to account for different cognitive strengths and weaknesses of their students, using adequate tasks and teaching strategies like self-differentiating tasks and adaptive explorative learning.