In any meta-analysis, it is critically important to report the dispersion in effects as well as the mean effect. If an intervention has a moderate clinical impact "on average" we also need to know if the impact is moderate for all relevant populations, or if it varies from trivial in some to major in others. Or indeed, if the…

This paper is a critical exposition on three major issues related to 'interpretive research conducted by researchers who claim they engaged in mixed methods' research. First, to provide context, we demonstrate that the term 'mixed' is inappropriate for the research practices usually adopted by its exponents. Secondly, we argue, expositions in…

In the context of problem behavior, treatment integrity refers to the extent to which a behavioral intervention is implemented as intended. Treatment-integrity errors may lead to relapse of problem behavior. For example, omitting reinforcers can lead to increases in problem behavior called resurgence. Researchers have previously described the…

Taylor series play a ubiquitous role in calculus courses, and their applications as approximants to functions are widely taught and used everywhere. However, it is not common to present the students with other types of approximations besides Taylor polynomials. These notes show that polynomials construed to satisfy certain boundary conditions at…

Functions and formulas in spreadsheets provide an instructional opportunity to help students build their skills in identifying errors in their own work and identifying a path to go about correcting the errors. This paper provides examples of functions and equations used to create two approaches to calculating the solution to one problem, such as a…

Barlow et al. (2018) discussed three types of mistakes worthy of inspection: procedural errors, inappropriate solution processes, and misconceptions. Here, the authors focus on procedural errors, as these often led the teachers in their professional development project to limit their inspection of mistakes to correcting. Despite this narrow focus,…

This paper aims to broaden the scope of the construct concept image by addressing the mathematically oriented notion of "solution of an algebraic equation." The notion solution of an algebraic equation is not mathematical per se, but it is most prevalent in mathematical communications and in mathematics education. The paper describes…

The determination of the speed of sound in air is a classical experiment, usually performed with a resonance tube apparatus. The measured value can be checked against Eq. (1), which describes the temperature dependence of the speed of sound in dry air. A modern implementation of this speed of sound investigation uses an Arduino Uno microcontroller…

The present study describes an R function that implements six corrective procedures developed by Bartlett, Swain, and Yuan in the correction of 21 statistics associated with the omnibus Chi-square test, the residuals, or fit indices in confirmatory factor analysis (CFA) and structural equation modeling (SEM).

COVID-19 pandemic policies requiring disease testing provide a rich context to build insights on true positives versus false positives. Our main contribution to the pedagogy of data analytics and statistics is to propose a method for teaching updating of probabilities using Bayes' rule reasoning to build understanding that true positives and false…

It is generally agreed that proper pre-lineup instructions can reduce the rate of mistaken identifications of innocent suspects. However, the exact nature of these instructions has not been empirically established. We compared the effects of the detailed pre-lineup instructions recommended by the US Department of Justice to a simple instruction…

Uncertainty in education, both general and special, has long troubled educational researchers, reformers, and practitioners. Responding to students with special (atypical) educational needs is an example of decisions that are prone to error. Although some efforts to reduce uncertainty in education are reasonable and helpful, efforts to eliminate…

Background: The content presents a conceptually powerful and attractive framework for understanding the proposal development process to capture the complexity of the steps that contribute to successful grant writing. Based on experiences from 15 years in research administration and using real-life examples, the author juxtaposes the diverse roles…

Errors are essential for emergent literacy learning because they reveal the gaps in young children's knowledge. The ways in which teachers respond to these errors can have important implications for children's knowledge building; yet, there is limited information for teachers about how to effectively respond to children's errors in emergent…

This article describes "Build It!--The Rectangle Game" task that uses the context of a game to develop mathematical generalizations based on strategy. The underlying mathematics in this game-based task is for students to discover factors and prime and composite numbers through 100. The playful use of "The Rectangle Game"…