Robots are used in all kinds of industrial settings. They are used to rivet bolts to cars, to move items from one conveyor belt to another, to gather information from other planets, and even to perform some very delicate types of surgery. Anyone who has watched a robot perform its tasks cannot help but be impressed by how it works. This article…

An earlier paper discussed the case of a flexible but inextensible membrane filled to capacity with incompressible fluid. It was found that the resulting shape satisfies a set of three simultaneous partial differential equations. This article gives a more general derivation of these equations and shows their form in an interesting special case.

Several mathematicians struggled to solve cubic equations, and in 1515 Scipione del Ferro reportedly solved the cubic while participating in a local mathematical contest, but did not bother to publish his method. Then it was Cardano (1539) who first published the solution to the general cubic equation in his book "The Great Art, or, The Rules of…

The purpose of this study was to describe the mathematics ability of preservice agricultural education teachers related to each of the National Council of Teachers of Mathematics (NCTM) content/process areas and their corresponding sub-standards that are cross-referenced with the National Agriculture, Food and Natural Resources Career Cluster…

Anne Roche and Doug Clarke discuss the importance of developing students' persistence in relation to problem solving during the use of challenging tasks. They provide a useful list of strategies that teachers can use to encourage persistence amongst their students.

This study investigates prospective secondary mathematics teachers' visual representations of polynomial and rational inequalities, and graphs of exponential and logarithmic functions with GeoGebra Dynamic Software. Five prospective teachers in a university in the United States participated in this research study, which was situated within a…

Engaging learners in exploratory problem-solving activities prior to receiving instruction (i.e., explore-instruct approach) has been endorsed as an effective learning approach. However, it remains unclear whether this approach is feasible for elementary-school children in a classroom context. In two experiments, second-graders solved mathematical…

This study combines the Japanese lesson study approach and mathematics teachers' professional development. The first year of a 4-year project in which 3 Dutch secondary school teachers worked cooperatively on introducing making sense of the calculus is reported. The analysis focusses on instrumental and relational student understanding of…

This paper contains a discussion of how the concept of critical aspects and the principle of compositionality can provide a powerful tool to analyse and understand the communications that occur in the classroom. It is grounded in data collected in a longitudinal study. The content chosen is algebra. It is argued that the critical aspects and the…

In this article, the authors introduce a scenario identifying an elementary school special education teacher and interventionist (Mr. Powers) and his concerns in meeting the Common Core State Standards in Mathematics (CCSS-M). Like many teachers, Powers uses a response-to-intervention (RTI) framework to provide supports for students who require…

The Mat-Rix-Toe project utilizes a matrix-based game to deepen students' understanding of linear algebra concepts and strengthen students' ability to express themselves mathematically. The project was administered in three classes using slightly different approaches, each of which included some editing component to encourage the…

The purpose of this exploratory study was to assess the effect of a novel approach to mathematics instruction on gifted high school students' engagement, motivation, and metacognition. Participants in this study included gifted students who were enrolled in a 3-year, residential, specialized mathematics and science high school. Rather than respond…

Understanding how students translate between mathematical representations is of both practical and theoretical importance. This study examined students' processes in their generation of symbolic and graphic representations of given polynomial functions. The purpose was to investigate how students perform these translations. The result of the study…

The general goal of this paper is to explore the potential of computer environments for the teaching and learning of functions. To address this, different theoretical frameworks and corresponding research traditions are available. In this study, we aim to network different frameworks by following a "double analysis" method to analyse two…

This study aims to determine how primary school eighth grade (14 years old) gifted students use knowledge types while solving problems. In the context, the data were collected through clinical interviews conducted with three gifted students. The students' voice recordings during problem solving and the solutions they wrote on the paper formed the…