Learning the concept of fractions is among the most challenging topics in school mathematics. One of the main sources of difficulties in learning fractions is related to "natural number bias" (Van Hoof, Verschaffel & Van Dooren, 2015). Applying properties of the natural numbers incorrectly in situations involving rational numbers can…

High attrition and dropout rates are common in introductory programming courses. One of the reasons students drop out is loss of motivation due to the lack of feedback and proper assessment of their progress. Hence, a process-oriented approach is needed in assessing programming progress, which entails examining and measuring students' compilation…

This study investigated how population parameters representing heterogeneity of variance, skewness, kurtosis, bimodality, and outlier-proneness, drawn from normal and eleven non-normal distributions, also characterized the ranks corresponding to independent samples of scores. When the parameters of population distributions from which samples were…

A quantum probability model is introduced and used to explain human probability judgment errors including the conjunction and disjunction fallacies, averaging effects, unpacking effects, and order effects on inference. On the one hand, quantum theory is similar to other categorization and memory models of cognition in that it relies on vector…

Florida requires that students who do not meet grade-level reading proficiency standards on the end-of-year state assessment (Florida Comprehensive Assessment Test, FCAT) receive intensive reading intervention. With the stakes so high, teachers and principals are interested in using screening or diagnostic assessments to identify students with a…

This article explores the configural weighted average (CWA) hypothesis suggesting that extension biases, like conjunction and disjunction errors, occur because people estimate compound probabilities by taking a CWA of the constituent probabilities. The hypothesis suggests a process consistent with well-known cognitive constraints, which…

Early efforts to apply knowledge of dialect differences to reading stressed the importance of the distinction between differences in pronunciation and mistakes in reading. This study develops a method of estimating the probability that a given oral reading that deviates from the text is a true reading error by observing the semantic impact of the…

Differential item functioning (DIF) analysis is a statistical technique used for ensuring the equity and fairness of educational assessments. This study formulates a new DIF analysis method using the information similarity index (ISI). ISI compares item information functions when data fits the Rasch model. Through simulations and an international…

This study examined age differences in error processing and reinforcement learning. We were interested in whether the electrophysiological correlates of error processing, the error-related negativity (ERN) and the feedback-related negativity (FRN), reflect learning-related changes in younger and older adults. To do so, we applied a probabilistic…

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…

Previous research has shown that--due to the extensive attention spent to proportional reasoning in mathematics education--many students have a strong tendency to apply linear or proportional models anywhere, even in situations where they are not applicable. This phenomenon is sometimes referred to as the "illusion of linearity". For example, in…

HyperProb is a Hypercard tutoring system designed to help students develop an effective step-by-step schema for solving probability problems. With this program, students are able to select areas they wish to study via hypermedia links and develop an understanding of terminology and procedures at their own pace with continued reinforcement. Nine…

This chapter provides an overview of statistical issues arising in work on educational assessment and school accountability, organized around some of the most consequential misunderstandings. The article proceeds via a series of nine vignettes describing misunderstandings of statistical uncertainty in educational assessment and school…