This article presents an e-mail conversation between two teachers discussing how to have a "rich task" lesson in which they get to the heart of mathematical modeling and in which students are motivated into working on mathematics. One teacher emphasizes that the power of maths is in developing mathematical descriptions of situations by…

The transition process to advanced mathematical thinking is experienced as traumatic by many students. Experiences that students had of school mathematics differ greatly to what is expected from them at university. Success in school mathematics meant application of different methods to get an answer. Students are not familiar with logical…

Many approaches to the transfer problem argue that transfer depends on the recognition of the same or similar abstract "structure" in 2 different situations. However, mainstream cognitive perspectives and contrasting Piagetian constructivist accounts differ in their conceptualizations of structure. These differences, not clearly articulated in the…

Biology is well suited for mathematical description, from the perfect geometry of viruses, to equations that describe the flux of ions across cellular membranes, to computationally intensive models for protein folding. For this short Web review, however, the author focuses on how mathematics helps biologists sort, evaluate, and draw conclusions…

An important component of intermediate and college algebra courses involves teaching students methods to factor a trinomial with integer coefficients over the integers. The aim of this article is to present a theoretical justification of that which is often taught, but really never explained as to why it works. The theory is presented, and a…

In the years since the Third International Mathematics and Science Study (TIMSS) focused on the success of Japanese students, much has been written about Japanese lesson study and its possible benefits for mathematics classrooms in America. Lesson study is a professional development process used in Japanese schools that brings teachers (and other…

In this paper, 28 mathematics majors who completed a transition-to-proof course were given 10 mathematical arguments. For each argument, they were asked to judge how convincing they found the argument and whether they thought the argument constituted a mathematical proof. The key findings from this data were (a) most participants did not find the…

In the context of a teaching experiment in elementary group theory, interesting difficulties arose as undergraduate students struggled to make sense of the meaning of the associative property as they reinvented the group concept. A subsequent exploration of the research literature revealed similar difficulties have been observed in research with…

Current reform efforts call for an emphasis on the use of representation in the mathematics classroom across levels and topics. The aim of the study was to examine teachers' conceptions of representation as a process in doing mathematics, and their perspectives on the role of representations in the teaching and learning of mathematics at the…

Mathematics may be inconceivable without its diagrams and symbols--its representations. Mathematical representations help individuals organize their thinking; they bring a visual component to abstract ideas and serve as templates for computation with understanding. But the inevitability of representations is no guarantee that they are used…

People often have difficulties in understanding situations that involve non-linear processes. Also, the topic of non-linear functions is introduced relatively late in the curriculum. Previous research has nevertheless shown that already children aged 6 years and older are able to discriminate non-linear from linear processes. Within the present…

The solution to the Euler-Lagrange equation is an extremal functional. To understand that the functional is stationary at local extrema (maxima or minima), we propose a physics experiment that involves using a soap film to form a catenoid. A catenoid is a surface that is formed between two coaxial circular rings and is classified mathematically as…

The authors observed preschoolers engaged at the sand and water table to determine if math could be found within their play. Wanting to understand how children interact with provided materials and what kinds of math ideas they explore during these interactions, the authors offer practical examples of how such play can promote mathematical…

This paper details the outcomes of a qualitative in-depth investigation into teacher education mathematics preparation. This research is grounded in the notion that mathematics teacher education students (as "degree seeking candidates") need to develop strong foundations of mathematical practice as defined by the Common Core State…

Lorraine Day reports on some of the findings of the Teaching Teachers for the Future Project. The Australian Curriculum constantly makes reference to digital technologies so we believe our readers will be interested to see how teachers are making use of technology in classrooms across Western Australia. The results may be used to…