This study extends past research on students' understanding of slope by analyzing college students' mistakes on routine tasks involving slope. We conduct quantitative and qualitative analysis of students' mistakes to extract information regarding slope conceptualizations described in prior research. Results delineate procedural proficiencies and…

We show that student learning can be accurately modeled using a mixture of learning curves, each of which specifies error probability as a function of time. This approach generalizes Knowledge Tracing [7], which can be viewed as a mixture model in which the learning curves are step functions. We show that this generality yields order-of-magnitude…

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…

User modelling algorithms such as Performance Factors Analysis and Knowledge Tracing seek to determine a student's knowledge state by analyzing (among other features) right and wrong answers. Anyone who has ever graded an assignment by hand knows that some answers are "more wrong" than others; i.e. they display less of an understanding…

To improve mathematics achievement, students' errors should be treated as a source to stimulate their understanding of the conceptual and procedural basis of their errors. The study investigated 20 Chinese and 20 U.S. high school teachers' interpretations and responses to a student's errors in solving a quadratic equation. The teachers' responses…

The purpose of this study was to investigate the effect of integrating blogging into the English as a Foreign Language (EFL) curriculum on students' performance in expressive writing. Previous studies have shown that integrating blogging into EFL learning raises students' motivation and develops their linguistic and social skills as a result of…

Games (1973) criticized the Marascuilo and Levin (1970) "nested" or simple effects design as a poor substitute for the usual logic of a factorial analysis of variance. Marascuilo and Levin's use of "nesting" is completely idiosyncratic and contrary to well-established usage, thus confusing the student. Proper usage is…

The probability of experiment-wise error is explored. Overall, the experiment-wise error rate is directly related to the test-wise error rate--the alpha level set by researchers to curtail the existence of a Type I error. A Type I error occurs when a true null hypothesis is rejected in a given study or experiment. The experiment-wise error rate is…

A multi-faceted Rasch measurement (MFRM) model was used to analyze a clinical skills assessment of 173 fourth-year medical students in a Midwestern medical school to investigate four types of rater errors: leniency, inconsistency, halo, and restriction of range. Each student performed six clinical tasks with six standardized patients (SPs), who…

Three procedures used to control Type I error rate in stepwise regression analysis are forward selection, backward elimination, and true stepwise. In the forward selection method, a model of the dependent variable is formed by choosing the single best predictor; then the second predictor which makes the strongest contribution to the prediction of…

This paper examines the multivariate multiple regression model and explores its applicability to communication research. The first section discusses partitioning of a data matrix, as a heuristic device for distinguishing among alternative regression models. Section two examines various aspects of univariate multiple regression, including the form…

This study introduced a probabilistic model utilizing item response theory (IRT) for dealing with a variety of misconceptions. The model can be used for evaluating the transition behavior of error types, advancement of learning stages, or the stability and persistence of particular misconceptions. Moreover, it apparently can be used for relating…

Suggesting that James Coleman's paper on massive school desegragation reveals methodological flaws of such magnitude that they raise serious questions as to the validity of the conclusions, this paper addresses a full sequence of perceived methodological errors found in the Coleman document, but does not dismiss the conclusions based upon initial…