Correct specifications of hierarchical attribute structures in analyses using diagnostic classification models (DCMs) are pivotal because misspecifications can lead to biased parameter estimations and inaccurate classification profiles. This research is aimed to demonstrate DCM analyses with various hierarchical attribute structures via Bayesian…

Completion of remedial mathematics has been identified as one of the keys to college success. However, completion rates in remedial mathematics have been low and are of much debate across America. This study leverages machine learning techniques in trying to predict and understand completion rates in remedial mathematics. The purpose of this study…

Hybrid learning implementation is closely related with technology. In designing hybrid lessons, lecturers need to have both the pedagogical and content-related skills that make the best use of technology so that it also improves the students' skills, including their computational thinking skills. The purpose of this research is to examine whether…

There is strong evidence from research conducted in the United States that fraction magnitude understanding supports mathematics achievement. Unfortunately, there has been little research that examines if this relation is present across educational contexts with different approaches to teaching fractions. The current study compared fourth and…

Panel or grouped data are often used to allow for unobserved individual heterogeneity in econometric models via fixed effects. In this paper, we discuss identification of a panel data model in which the unobserved heterogeneity both enters additively and interacts with treatment variables. We present identification and estimation methods for…

Knowledge tracing is a fundamental area of educational data modeling that aims at gaining a better understanding of the learning occurring in tutoring systems. Knowledge tracing models fit various parameters on observed student performance and are evaluated through several goodness of fit metrics. Fitted parameter values are of crucial interest in…

Students need to construct strong knowledge of angles as well as relationships between angles and side lengths in a triangle to succeed in geometry. Although many researchers pointed out the importance of angles and angle-related concepts, students and teachers have had limited knowledge of these concepts. This study is a part of a larger study,…

A primary purpose of cognitive diagnosis models (CDMs) is to classify examinees based on their attribute patterns. The Q-matrix (Tatsuoka, 1985), a common component of all CDMs, specifies the relationship between the set of required dichotomous attributes and the test items. Since a Q-matrix is often developed by content-knowledge experts and can…

Representations of numerical value have been assessed by using bounded (e.g., 0-1,000) and unbounded (e.g., 0-?) number-line tasks, with considerable debate regarding whether 1 or both tasks elicit unique cognitive strategies (e.g., addition or subtraction) and require unique cognitive models. To test this, we examined how well a mixed log-linear…

Math fluency, which refers to the ability to solve single digit arithmetic problems quickly and accurately, is a foundational mathematical skill. Recent research has examined the role of phonological processing, executive control, and number sense in explaining differences in math fluency performance in school-aged children. Identifying the links…

This technical report is one of a series of four technical reports that describe the results of a study comparing eight alternative models for estimating school academic achievement using data from the Arizona, North Carolina, Oregon, and Pennsylvania accountability systems. The purpose of these reports was to evaluate a broad range of models…

This technical report is one of a series of four technical reports that describe the results of a study comparing eight alternative models for estimating school academic achievement using data from the Arizona, North Carolina, Oregon, and Pennsylvania accountability systems. The purpose of these reports was to evaluate a broad range of models…

Item response models typically assume that the item characteristic (step) curves follow a logistic or normal cumulative distribution function, which are strictly monotone functions of person test ability. Such assumptions can be overly-restrictive for real item response data. We propose a simple and more flexible Bayesian nonparametric IRT model…

This technical report is one of a series of four technical reports that describe the results of a study comparing eight alternative models for estimating school academic achievement using data from the Arizona, North Carolina, Oregon, and Pennsylvania accountability systems. The purpose of these reports was to evaluate a broad range of models…

This technical report is one of a series of four technical reports that describe the results of a study comparing eight alternative models for estimating school academic achievement using data from the Arizona, North Carolina, Oregon, and Pennsylvania accountability systems. The purpose of these reports was to evaluate a broad range of models…