This study is situated in a course designed for both on-campus and online pre-service and in-service teachers, where student-created mathscasts provide a way for university lecturers to assess students' quality of teaching, and understanding of mathematics. Teachers and pre-service teachers, in a university course with 90% online enrolment, were…

In their response to our paper, Nicholson and Ridgway agree with the majority of what we wrote. They echo our concerns about the misuse of inferential statistics and NHST in particular. Very little of their response explicitly challenges the points we made but where it does their defence of the use of inferential techniques does not stand up to…

This article reports on action research that was undertaken while teaching a mathematics education subject to a series of cohorts of final-year primary pre-service teachers at a university in Australia. My aim was to increase the understanding of an assessment task, as well as its intrinsic value. Each action research cycle involved the…

As a self described lesson collector, author Charles Lovett enjoys gathering "interesting" lessons and teasing them apart to find out what makes them "tick", particularly the pedagogy. He often wonders what decisions the teacher made that generated such an interesting and successful learning environment. Here he describes a…

The proliferation of computers, tablets, and internet access has brought the use of virtual manipulatives into the majority of classrooms in the developed world. In responding to the needs of today's students, many of whom are adept at accessing and manipulating technology devices, virtual manipulatives provide a variety of classroom…

We hope to initiate a discussion about various methods for introducing Cauchy's Theorem. Although Cauchy's Theorem is the fundamental theorem upon which complex analysis is based, there is no "standard approach." The appropriate choice depends upon the prerequisites for the course and the level of rigor intended. Common methods include…

In this note, we revisit the problem of polynomial interpolation and explicitly construct two polynomials in n of degree k + 1, P[subscript k](n) and Q[subscript k](n), such that P[subscript k](n) = Q[subscript k](n) = f[subscript k](n) for n = 1, 2,… , k, where f[subscript k](1), f[subscript k](2),… , f[subscript k](k) are k arbitrarily chosen…

Given three planes in space, a complete characterization of their intersection is provided. Special attention is paid to the case when the intersection set does not exist of one point only. Besides the vector cross product, the tool of generalized inverse of a matrix is used extensively.

Around 430 BCE it is reported that a typhoid epidemic carried off about a quarter of the population of Athens in ancient Greece. When the gods were asked what could be done to halt this raging epidemic, they apparently replied that the altar in the Temple of Apollo in Delios would have to be doubled in size. After several attempts to double the…

The mathematics education literature shows that encouraging students to develop multiple solutions for given problems has a positive effect on students' understanding and creativity. In this paper, we present an example of multiple-solution problems in statistics involving a set of non-traditional dice. In particular, we consider the exact…

This paper provides an analysis of a teaching episode of the multidigit algorithm for multiplication, with a focus on the influence of the teacher's mathematical knowledge on their teaching. The theoretical framework uses Mathematical Knowledge for Teaching, mathematical pertinence of the teacher and structuration of the milieu in a descending and…

When teaching the measurement attribute of time, most teachers are aware that just getting students to read a clock is a task with its own challenges, but is developing this skill and understanding enough? What else do teachers need to make sure they cover, in order to give students a chance of developing this important component of being a…

The authors asked a group of students during a classroom research study to analyze data sets containing different amounts of noise. The authors use the word "noise" to refer to statistical variability. The four students in the group were finishing seventh grade and participating in summer mathematics instruction. The authors carefully…

Video is often used in professional development courses to sensitize mathematics teachers to students' thinking and issues of classroom interaction. This article presents an approach that incorporates students' perspectives on mathematics classroom interactions into video-based professional development in order to enhance teachers' reflection on…

Considering the important role played by mathematical derivatives in the study of physical-chemical processes, this paper discusses the different possibilities and formulations of this concept and its application. In particular, in Chemical Thermodynamics, we study exact differentials associated with the so-called state functions and inexact…