This study investigates an exploratory teaching style used in an undergraduate geometry course to help students identify an ellipse. We attempt to probe beneath the surface of exploration to understand how the actions of teachers can contribute to developing students' competence in justifying an ellipse. We analyse the complex interactions between…

This article examines the practice of studying texts in secondary school English lessons as a particular type of reading experience. Through a critical stylistic analysis of a popular edition of John Steinbeck's "Of Mice and Men", the article explores how reading the text is framed by educational editions, and how this might present the…

In this study, we identify ways in which a sample of 18 graduates with mathematics-related first degrees found the nth term for quadratic sequences from the first values of a sequence of data, presented on a computer screen in various formats: tabular, scattered data pairs and sequential. Participants' approaches to identifying the nth term were…

This study seeks to determine whether giving an explicit incentive to students in an upper-division first-semester electromagnetism course (EM1), in the form of partial credit for reworking unit exam problems, will improve their problem-solving skills as measured by performance on identical problems on the final exam. Three problems--a primarily…

In the fall of 2012, Mason County High School implemented a 1:1 iPad program which placed the devices into the hands of every teacher and student. Researchers examined data from student and teacher interviews, program maintenance data and instructional change examples to answer the question, "Did it work?" With digital and blended…

Background: Coach observation studies have been a mainstay of coaching science research for decades, with a major focus on the use of instruction and feedback by coaches. However, relatively few studies have investigated feedback provided in a live competition setting, with a majority focussing on the training environment. As such, little is known…

In this paper, we provide an elaboration of the notion of mathematical structure -- a term agreed upon as valuable but difficult to define. We pull apart the terminology surrounding the notion of structure in mathematics: relationship, generalising/generalisation and properties, and offer an architecture of structure that distinguishes and…

Organizations around the world are forming innovative partnerships to offer virtual learning opportunities to global audiences. This book, part of a series on the impacts of information technology on higher education, focuses on crucial questions higher education leaders are asking about these "learning marketplace" partnerships. The chapters are:…

This article discusses the concepts of "key ideas" and "memorability" and how they relate to the metric "width of a proof" put forward by the Fields medalist Timothy Gowers (2007) in a recent essay entitled "Mathematics, memory and mental arithmetic". The paper looks at the meaning of these concepts and…

As with so many aspects of mathematical enquiry, there is little that is "original", or "brand new", but that does not diminish the outcome of work that borrows from "those who have gone before". In this piece the author "borrows" from the work of Desargues, Monge, Ceva, Menelaus, van Aubel, and Gergonne. This novel approach to providing a proof…

In 2002, the American School Counselor Association (ASCA) presented the ASCA National Model for school counseling programs as a framework for implementing best practices in training counselors to deliver effective evidence-based approaches for K-12 students. Without a unifying theory of practice, school counselors are often uncertain about how to…

We propose that what teachers can say or write about their views of mathematics and about a range of pedagogic strategies and didactic tactics that they use is of minor importance compared to what comes to mind moment by moment when they are planning or leading a lesson. Beginning with a quote from a teacher that provoked a focus on the role and…

Given a family of "p" greater than or equal to 3 points in the plane, some three of them have the property that the smallest circle encompassing them encompasses all "p" points. Similarly, we show that for "p" greater than or equal to 3 circles, there are three of them such that the smallest circle encompassing them…

The well known property of quadratic functions, that the tangents at either end of a chord of a parabola meet in a point aligned vertically with the midpoint of the chord is extended to polynomials of degree d. Given two distinct points on a polynomial of degree d, the Taylor polynomials of degree d - 1 at those points meet in d - 1 points whose…

This single-case meta-analysis is the first to provide a quantitative synthesis of the published literature on mathematics word problem-solving intervention studies for English learners with learning disabilities and mathematics difficulties. A total of ten single-subject studies were included for analysis. The current study investigated the…