The following study shows how reparameterizations and constraints of the general linear model can serve to parse quantitative and qualitative aspects of predictors. We demonstrate three different approaches. The study uses data from the High School Longitudinal Study of 2009 on mathematics course-taking and achievement as an example. Results show…

This article proposes a flexible extension of the Fay--Herriot model for making inferences from coarsened, group-level achievement data, for example, school-level data consisting of numbers of students falling into various ordinal performance categories. The model builds on the heteroskedastic ordered probit (HETOP) framework advocated by Reardon,…

Following previous research which showed the significance of learners' self-efficacy and dispositions towards progression in school and university transition, we developed and validated similar measures for use in modelling undergraduate students' Learning Gain (LG). We validated three dimensions of confidence using data from a sample of (mainly…

Considering the general problem of integrating mathematical modelling into current educational systems, this paper focuses on the "ecological dimension" of this problem--the institutional constraints that hinder the development of mathematical modelling as a normalised teaching activity--and the inevitable step of the professional…

Many aspects of the geometry of linear statistical models and least squares estimation are well known. Discussions of the geometry may be found in many sources. Some aspects of the geometry relating to the partitioning of variation that can be explained using a little-known theorem of Pappus and have not been discussed previously are the topic of…

Data analysis techniques can be used to analyze the pattern of data in different fields. Based on the analysis' results, it is recommended that suggestions be provided to decision making authorities. The data mining techniques can be used in educational domain to improve the outcome of the educational sectors. The authors carried out this research…

Peer play provides ample opportunities for the use and development of self-regulatory and mathematical skills. This study aimed at examining whether children's engagement in solitary low-level play, interactive play and competent play influences their self-regulatory and number sense skills. The effect of demographic variables and children's…

Randomized experiments are commonly used to evaluate the effectiveness of educational interventions. The goal of the present investigation is to develop small-sample corrections for multiple contrast hypothesis tests (i.e., F-tests) such as the omnibus test of meta-regression fit or a test for equality of three or more levels of a categorical…

The study used earliest available student data from a flagship university in the southeast United States to build data mining models like logistic regression with different variable selection methods, decision trees, and neural networks to explore important student characteristics associated with retention leading to graduation. The decision tree…

Computational experiment approach considers models as the fundamental instructional units of Inquiry Based Science and Mathematics Education (IBSE) and STEM Education, where the model take the place of the "classical" experimental set-up and simulation replaces the experiment. Argumentation in IBSE and STEM education is related to the…

Propensity score analysis (PSA) is a methodological technique which may correct for selection bias in a quasi-experiment by modeling the selection process using observed covariates. Because logistic regression is well understood by researchers in a variety of fields and easy to implement in a number of popular software packages, it has…

Critical to many science, technology, engineering, and mathematics (STEM) career paths is mathematical modeling--specifically, the creation and adaptation of mathematical models to solve problems in complex settings. Conventional standardized measures of mathematics achievement are not structured to directly assess this type of mathematical…

Children (N = 157) 4 to 8 years old participated 1 time (single) or 4 times (repeated) in an interactive event. Across each condition, half were questioned a week later about the only or a specific occurrence of the event ("depth first") and then about what usually happens. Half were prompted in the reverse order ("breadth first"). Children with…

This study evaluates the effects of an intervention aimed at improving representational flexibility in linear-function problems. Forty-nine students aged 13-16 participated in the study. A pretest-intervention-posttest design with an experimental and control group was used. At pretest, both groups solved a choice test, where they could freely…

Past studies have suggested that in light of recent curriculum standards, many US teachers make limited use of drawn models in their mathematics instruction. To gain insight into this phenomenon, we investigated relationships between US teachers' opportunities to learn about, knowledge of, motivation for, and instructional use of drawn models for…