Randomized evaluations of educational technology produce log data as a bi-product: highly granular data on student and teacher usage. These datasets could shed light on causal mechanisms, effect heterogeneity, or optimal use. However, there are methodological challenges: implementation is not randomized and is only defined for the treatment group,…

Recent methods have sought to improve precision in randomized controlled trials (RCTs) by utilizing data from large observational datasets for covariate adjustment. For example, consider an RCT aimed at evaluating a new algebra curriculum, in which a few dozen schools are randomly assigned to treatment (new curriculum) or control (standard…

Latent interaction models have motivated a great deal of methodological research, mainly in the area of estimating such models. Product-indicator methods have been shown to be competitive with other methods of estimation in terms of parameter bias and standard error accuracy, and their continued popularity in empirical studies is due, in part, to…

This study explored a diagnostic assessment method that emphasized the cognitive process of algebra learning. The study utilized a design and a theory-driven model to examine the content knowledge. Using the theory driven model, the thinking skills of algebra learning was also examined. A Bayesian network model was applied to represent the theory…

Molenaar (2003, 2011) showed that a common factor model could be transformed into an equivalent model without factors, involving only observed variables and residual errors. He called this invertible transformation the Houdini transformation. His derivation involved concepts from time series and state space theory. This article verifies the…

The purpose of this study was to compare students' performances in a freshmen level quantitative reasoning course (QR) under three different instructional models. A cohort of 155 freshmen students was placed in one of the three models: needing a prerequisite course, corequisite (students enroll simultaneously in QR course and a course that…

Learning analysts often consider whether learning processes across time are related (1) to one another or (2) to learning outcomes at higher levels. For example, are a group's temporal sequences of talk (e.g., correct evaluation [right arrow] correct, new idea) during its problem solving related to its group solution? I show how to address these…

This article focuses on four-parameter logistic (4PL) model as an extension of the usual three-parameter logistic (3PL) model with an upper asymptote possibly different from 1. For a given item with fixed item parameters, Lord derived the value of the latent ability level that maximizes the item information function under the 3PL model. The…

A growing body of research suggests that accounting for student specific variability in educational data can improve modeling accuracy and may have implications for individualizing instruction. The Additive Factors Model (AFM), a logistic regression model used to fit educational data and discover/refine skill models of learning, contains a…

The residuals obtained from fitting a structural equation model are crucial ingredients in obtaining chi-square goodness-of-fit statistics for the model. The authors present a didactic discussion of the residuals, obtaining a geometrical interpretation by recognizing the residuals as the result of oblique projections. This sheds light on the…

The use of multiple forms of collaborative instruction to teach integrated algebra makes it difficult for teachers to determine which collaborative form is best suited for the curriculum. An inconsistent approach to integrated algebra instruction at the study school needed to be addressed for the benefit of teacher effectiveness and student…

In response to pedagogical challenges in higher education, blended learning has become a prevalent practice in colleges and universities. Flipped learning (FL) represents a newly emerging form of blended learning, where students individually watch online lectures prior to class and then engage in classroom learning activities interacting with…

There are usually limited user evaluation of resources on a recommender system, which caused an extremely sparse user rating matrix, and this greatly reduce the accuracy of personalized recommendation, especially for new users or new items. This paper presents a recommendation method based on rating prediction using causal association rules.…

The use of handheld CAS technology in undergraduate mathematics courses in Australia is paradoxically shrinking under sustained disapproval or disdain from the professional mathematics community. Mathematics education specialists argue with their mathematics colleagues over a range of issues in course development and this use of CAS or even…

The authors used a mixed-methods research design to evaluate a multi-tiered system of supports model to address the disturbing failure rates of underprepared college students placed in developmental mathematics at a small state university. While qualitative data gathered from using Participatory Action Research methods directed the two-year…