A central issue in the mathematics curriculum is that we want students to make connections. This issue has been analysed in a series of curricula and instruction design and analysis studies. Moving towards mathematics connections--and away from treating mathematics as a body of isolated concepts and procedures--is an important goal of mathematics…

When data for multiple outcomes are collected in a multilevel design, researchers can select a univariate or multivariate analysis to examine group-mean differences. When correlated outcomes are incomplete, a multivariate multilevel model (MVMM) may provide greater power than univariate multilevel models (MLMs). For a two-group multilevel design…

The impact of retrieval practice on analogical-problem-solving performance was investigated using a complex, educationally relevant task. Participants studied a statistical hypothesis testing scenario and practiced recalling the material or repeatedly studied it. Participants then completed a final test either 5 minutes or 1 week later involving a…

This paper develops the ideas of "The Pedagogical Power of Context: Iterative Calculus Methods and the Epidemiology of Eyam" (French "et al." 2018 "J. Phys. Educ."), where we considered the application of the Euler method to solve epidemiological problems. Our purpose was to convey some examples of school level work…

A successful instructional method is to engage learners with exploratory problem-solving before providing explanations of the canonical solutions and foundational concepts. A key question is whether and what type of guidance will lead learners to explore more productively and how this guidance will affect subsequent learning and transfer. We…

This paper shares how fourth grade students solved a unique type of number line task. Instead of giving students the unit and asking them to locate a fraction on the number line, students were given two points on the number line and asked to either find 1, or another number on the number line. This type of task is called "reconstructing the…

Introduction: The purpose of this study was to gain additional insight on patterns of behavior of three individuals dually diagnosed with intellectual disability (ID) and bipolar disorder as they cycled between elevated and depressed mood states. Methods: Data were collected from weekly, one-hour observations across a period of several months. The…

Students' attitudes and approaches to problem solving are claimed to be related to their ways they learn physics and to their success in solving physics problems. In this study, the Attitudes and Approaches to Problem Solving (AAPS) survey was used to reveal Turkish introductory university students' attitudes and approaches to physics problem…

In this brief article, the author illustrates the flaws of FOIL (multiply the First, Outer, Inner, and Last terms of two binomials) and introduces the box method. Much like FOIL, the box method can become easy to use. Unlike FOIL, however, the box method is a more direct and visible link to using the distributive property to determine area, a…

Researchers have documented many misconceptions students hold about sampling variability. This study takes a different approach--instead of identifying shortcomings, we consider the productive reasoning pieces students construct as they reason about sampling distributions. We interviewed eight undergraduate students newly enrolled in an…

In this article, we open with a discussion of stress and its potential impact on the teaching profession. We then follow with an empirical rationale for and steps in the implementation of potentially promising mindfulness-based stress reduction (MBSR) interventions for teachers, particularly teachers of students with emotional and behavioral…

In children with autism spectrum disorder (ASD), there are often discrepancies between direct assessment and third-party reports. We compared these children with groups with/without difficulties in interpersonal problem-solving skills in order to determine whether these discrepancies appear and if they could be a diagnostic indicator for ASD.…

In theory, STEM (interdisciplinary science, technology, engineering and mathematics) is cross-disciplinary and situated in real-world problem-solving contexts. In practice, STEM disciplines are often implemented separately using contrived contexts. This paper examines theoretical and empirical aspects of Montessori middle school science in the…

The content of research methods courses in tertiary education, as revealed by popular textbooks, tends to focus largely on procedural aspects of research investigations. Although following proper procedures is essential for reaching valid and reliable outcomes, there is another attribute of good quality research that is often missing from research…

The UN declared 2010 the "International Year of Biodiversity" (IYB). A survey was undertaken at the end of this year in the Washington D.C. metro area (n = 180). Thirty-eight point nine percent of the participants had not heard of the term "biodiversity". Only 36.7% could correctly define "biodiversity". Almost no one…