The goal of this paper is to examine single variable real inequalities that arise as tutorial problems and to examine the extent to which current computer algebra systems (CAS) can (1) automatically solve such problems and (2) determine whether students' own answers to such problems are correct. We review how inequalities arise in contemporary…

Statistical tasks that can be solved in a variety of ways provide rich sites for classroom discourse. Orchestrating such discourse requires careful planning and execution. Five specific practices can help teachers do so. The five practices can be used to structure conversations so that coherent classroom narratives about solutions to tasks may be…

The purpose of the present study was to examine direct and indirect relationships among personality, selfesteem and social problem-solving, as well as the mediating role of self-esteem in the link between personality and social problem-solving among Turkish youth. The study utilized a cross-sectional design comprising several self-reports. Data…

The compound microscope is an important tool in biology, and mastering it requires repetition. Unfortunately, introductory activities for students can be formulaic, and consequently, students are often unengaged and fail to develop the required experience to become proficient in microscopy. To engage students, increase repetition, and develop…

Finding and designing tasks that allow for students to make connections among mathematical ideas is important for mathematics educators. One such task, which affords students the opportunity to make connections and engage with significant mathematical ideas through a variety of problem-solving approaches, is described in this article. Three…

We used event-related potentials (ERPs) to determine the time course of mechanisms underlying strategy selection. Participants had to select the better strategy on multiplication problems (i.e., 51 × 27) to find approximate products. They could choose between rounding up and rounding down both operands to their nearest decades. Two types of…

Gesturally controlled information and communication technologies, such as tablet devices, are becoming increasingly popular tools for teaching and learning. Based on the theoretical frameworks of cognitive load and embodied cognition, this study investigated the impact of explicit instructions to trace out elements of tablet-based worked examples…

In this article, the authors discuss a special type of multiplication-and-division-of-fractions problem that elementary school teachers can use to promote children's understanding of fractional quantities and their relationships. These problems are accessible to students working at different levels of fraction understanding, and they can be solved…

"Collective argumentation" occurs when a group works together to arrive at a conclusion (supporting it with evidence). Simplistically, this occurs when students give answers to questions and tell how they arrived at the answer, perhaps prompted by a teacher. But collective argumentation can be much richer, with a focus on the process of…

This article describes the development of a problem-solving instrument intended for classroom use that addresses the Common Core State Standards for Mathematics. In this study, 137 students completed the assessment, and their responses were analyzed. Evidence for validity was collected and examined using the current standards for educational and…

The purpose of this study was to determine the effectiveness of a point-of-view video modeling intervention to teach mathematics problem-solving when working on word problems involving subtracting mixed fractions with uncommon denominators. Using a multiple-probe across students design of single-case methodology, three high school students with…

Prompting students to construct multiple solutions for modelling problems with vague conditions has been found to be an effective way to improve students' performance on interest-oriented measures. In the current study, we investigated the influence of this teaching element on students' performance. To assess the impact of prompting multiple…

How can physics teachers help students develop consistent problem solving techniques for both simple and complicated physics problems, such as those that encompass objects undergoing multiple forces (mechanical or electrical) as individually portrayed in free-body diagrams and/or phenomenon involving multiple objects, such as Doppler effect…

Nanotechnology allows the synthesis of nanoscale catalysts, which offer an efficient alternative for fuel cell applications. In this laboratory experiment, the student selects a cost-effective anode for fuel cells by comparing three different working electrodes. These are commercially available palladium (Pd) and glassy carbon (GC) electrodes, and…

Issues surrounding the contextual environment in which strategic decisions are made are difficult concepts to grasp, particularly for undergraduate students with little business experience. They are also problematic for graduate students that have not been called on to make such decisions within their career. The authors propose an exercise that…