We derive the additive property of Poisson random variables directly from the probability mass function. An important application of the additive property to quality testing of computer chips is presented.

Algebraic structures are a necessary aspect of algebraic thinking for K-12 students and teachers. An approach for introducing the algebraic structure of groups and fields through the arithmetic properties required for solving simple equations is summarized; the collective (not individual) importance of these axioms as a foundation for algebraic…

A polytomous item is one for which the responses are scored according to three or more categories. Given the increasing use of polytomous items in assessment practices, item response theory (IRT) models specialized for polytomous items are becoming increasingly common. The purpose of this ITEMS module is to provide an accessible overview of…

An equation published by Loftin, Waddell, Robinson, and Owens (2010) was cross-validated using ten normal-weight walkers, ten overweight walkers, and ten distance runners. Energy expenditure was measured at preferred walking (normal-weight walker and overweight walkers) or running pace (distance runners) for 5 min and corrected to a mile. Energy…

Researchers have consistently demonstrated that multiple examples are better than one example in facilitating learning because the comparison evoked by multiple examples supports learning and transfer. However, research outcomes are unclear regarding the effects of example variability and prior knowledge on learning from comparing multiple…

According to national mathematics standards, algebra instruction should begin at kindergarten and continue through elementary school. Most often, teachers address algebra in the elementary grades with problems related to solving equations or understanding functions. With 789 second-grade students, we administered: (1) measures of calculations and…

Developing expertise in physics problem solving requires the ability to use mathematics effectively in physical scenarios. Novices and experts often perceive the use of mathematics in physics differently. Students' perceptions and how they frame the use of mathematics in physics play an important role in their physics problem solving. In this…

Eighth grade students in Australia (N = 60) participated in an experiment on learning how to solve percentage change problems in a regular classroom in three conditions: unitary, pictorial, and equation approaches. The procedure involved a pre-test, an acquisition phase, and a post-test. The main goal was to test the relative merits of the three…

The sequential probability ratio test (SPRT) is a common method for terminating item response theory (IRT)-based adaptive classification tests. To decide whether a classification test should stop, the SPRT compares a simple log-likelihood ratio, based on the classification bound separating two categories, to prespecified critical values. As has…

Due to its fundamental role for the consolidation of Maxwell's equations, the displacement current is one of the most important topics of any introductory course on electromagnetism. Moreover, this episode is widely used by historians and philosophers of science as a case study to investigate several issues (e.g. the theory-experiment…

Newer statistical procedures are typically introduced to help address the limitations of those already in practice or to deal with emerging research needs. Quantile regression (QR) is introduced in this paper as a relatively new methodology, which is intended to overcome some of the limitations of least squares mean regression (LMR). QR is more…

Although there is no consensus in regard to a unique meaning for abstraction, there is a recognition of the existence of several theories of abstraction, and that the ability to abstract is imperative to learning and doing meaningful mathematics. The theory of "reducing abstraction" maps the abstract nature of mathematics to the nature…

This paper provides a method for analysing undergraduate teaching of proof-based courses using Toulmin's model (1969) of argumentation. It presents a case study of one instructor's presentation of proofs. The analysis shows that the instructor presents different levels of detail in different proofs; thus, the students have an…

The study aimed to investigate students' conceptions on the notion of absolute value and their abilities in applying the specific notion in routine and non-routine situations. A questionnaire was constructed and administered to 17-year-old students. Data were analysed using the hierarchical clustering of variables and the implicative method,…

The assessment of the achievement of students and the quality of schools has drawn increasing attention from educational researchers, policy makers, and practitioners. Various test-based accountability and feedback systems involving the use of value-added techniques have been developed for evaluating the effectiveness of individual teaching…