An important concept in mathematics, yet one that is often elusive for students, is the concept of rate. For many real-life situations--those involving work, distance and speed, interest, and density--reasoning by using rate can be an efficient strategy for problem solving. Students struggle with the concept of rate, despite the many possible…

The title is that of a course with the same name, designed for teachers of mathematics. The rational for a course specifically on geometry was that "many of those currently teaching mathematics in school had little geometrical education". Teachers on the course experience geometry through problem solving, and learning to pose geometrical problems.…

Many delegates at "conference" relish the opportunity, and the space, to "do some mathematics". Opportunity and space help to make the experience memorable, but how often is the quality of the starting point, or question acknowledged? Here is a set of starting points or problems that invite the reader to "do some mathematics". Deliberately, no…

This dissertation examines the problem-solving processes of seven graduate student novices enrolled in a course in educational assessment and ten educational assessment experts. Using Jonassen's (1997) ill- and well-structured problem-solving frameworks, I analyze think-aloud protocols of experts and novices as they examine ill-structured…

Although students' difficulties in developing and understanding proofs in mathematics is well documented, less is known about how students' example use may support their proof practices, particularly at the middle school level. Research on example use suggests that strategic thinking with examples could play an important role in exploring…

This is a study about the didactical organization of a research based group of activities designed using APOS theory to help university students make constructions, needed to understand and graph two-variable functions, but found to be lacking in previous studies. The model of the "moments of study" of the Anthropological Theory of…

In this paper, the RBC+C framework (Hershkowitz, Schwartz, & Dreyfus, 2001) is used to analyse and describe construction and consolidation of mathematical knowledge by primary pupils in a whole-class setting. I describe a lesson that concerned what is commonly termed the Handshakes problem. One pupil spontaneously established a connection with…

Although history of science is a potential resource for instructional materials, teachers do not have a tendency to use historical materials in their lessons. Studies showed that instructional materials should be adaptable and consistent with curriculum. This study purports to examine the alignment between history of science and the curriculum in…

This paper is concerned with how research ethics is evolving along with emerging online research methods and settings. In particular, it focuses on ethics issues implied in a hypothetical virtual ethnography study aiming to gain insights on participants' experience in an emergent context of networked learning, namely a MOOC--Massive Online Open…

Terms to be familiar with before you start to solve the test: transcription, pre-mRNA, RNA processing, RNA transport, RNA polymerase II, direct and indirect immunofluorescence staining, cell fractionation by centrifugation, oligo(dT)-cellulose chromatography, washing and elution of the column, ribonuclease, SDS-polyacrylamide gel electrophoresis,…

This article focuses on a simple trigonometric problem that generates a strange phenomenon when different methods are applied to tackling it. A series of problem-solving activities are discussed, so that students can be alerted that the precision of diagrams is important when solving geometric problems. In addition, the problem-solving plan was…

The current debate over whether to choose just one universal human performance technology (HPT) model, in particular Langdon's language of work (LOW) model, promises a shared understanding among HPT professionals, credibility for the HPT profession, and a return on investment of time and effort in developing performance models over more than 70…

In this article we explore the theoretical and experimental field of sharing and of partitive and quotitive division problems, as illustrated by recent studies in this field. The purpose was to explain and justify the utility of presenting quotitive division problems, accompanied by graphical representations, to young children. The current study…

This article points out a simple connection between related rates and differential equations. The connection can be used for in-class examples or homework exercises, and it is accessible to students who are familiar with separation of variables.

Applying a previously learned concept to a novel problem is an important but difficult process called transfer. It is suggested that a commonsense analogy aids in transfer by linking novel concepts to familiar ones. How the context of practice affects transfer when learning using analogies is still unclear. This study investigated the effect of a…