This paper examines the existence and impact of theoretical mathematical foundations on the teaching and learning of whole numbers in elementary school in France. It shows that the study of the New Math reform--which was eventually itself replaced in the longer term--provides some keys to understanding the influence of mathematical theories on…

In this article, we report the results of research that explores the intra-mathematical connections that high school students make when they solve Calculus tasks, in particular those involving the derivative and the integral. We consider mathematical connections as a cognitive process through which a person relates or associates two or more ideas,…

Background: Physical activity is an important component of everyday life. Strong foundational skills of gross motor coordination are typically developed informally in young learners, providing a strong foundational base for movement skills. Research stipulates that there has been a decline in physical activity amongst preschool learners.…

Experience-Language-Pictorial-Symbolic-Application [ELPSA] is a learning framework that presents mathematical ideas through a cyclic design. The ELPSA framework which can be used to develop mathematics lessons and units of work that build students' concept understanding is described here.

This project describes a way to help students recognise that the expressions on both sides of the equals sign are the same. It was developed to support teachers in disadvantaged communities to help their students make sense of mathematics.

The sudden perception of a connection between ideas is exhilarating. We might call these moments 'Aha!' moments. The purpose of this paper is to demonstrate how several different ideas can come together in Year 12 mathematics. The subject Further Mathematics in the Victorian Certificate of Education (VCE) is the Victorian adaptation of General…

Making patterning the basis of mathematics investigations for an entire year produced unexpected results for Bruce Ferrington. A Year 2 class used the spatial tasks from the Pattern and Structure Mathematics Awareness Program (PASMAP) with a specific emphasis on patterning, to develop their thinking mathematically skills. The result was students…

Knowledge that teachers bring to the teaching context is one of the key factors in discussions about mathematics teaching. This study aimed to explore in-service primary teachers' knowledge of fraction division using division tasks. The first phase of the study examined fifty-one primary in-service teachers' written responses to division items.…

The purpose of this research was to develop a valid, practice and effective a bilingual scientific-worksheet of the indefinite integrals. This research is development research with 1) Preliminary investigation phase, 2) Prototyping phase, 3) Assessment phase. Data were collected from test and questionnaire and analyzed to examine validity,…

The purpose of this study was to investigate pre-service teachers' views about the history of mathematics course in which GeoGebra was used. The qualitative research design was used in this study. The participants of the study consisted of 23 pre-service mathematics teachers studying at a state university in Turkey. An open-ended questionnaire was…

How do students cope with and make sense of polysemy in mathematics? Zazkis (1998) tackled these questions in the case of 'divisor' and 'quotient'. When requested to determine the quotient in the division of 12 by 5, some of her pre-service teachers operated in the domain of integers and argued for 2, while others adhered to rational numbers and…

Zero-order systems provide an interesting opportunity for students to think about the underlying mechanism behind the physical phenomena being modeled. The work reported here is part of a larger study that seeks to characterize how students integrate chemistry and mathematics in the context of chemical kinetics. Thirty-six general chemistry…

While it is widely believed that Specialized Content Knowledge (SCK) is essential to effective and quality mathematics teaching, the specific constructs that compose SCK remain underspecified. This paper describes the development and use of a new framework that extends the notion of SCK. The framework was trialled with a cohort of 90 first year…

One way to recognize how mathematical lessons can be stimulating for children is to interpret them as stories. If mathematical lessons follow a structure similar to that of a story, they can build anticipation, create surprise, and even generate intrigue (Egan 1988). To support the design of mathematical lessons with these types of aesthetic…

The importance of mathematical reasoning is unquestioned and providing opportunities for students to become involved in mathematical reasoning is paramount. The open-ended tasks presented incorporate mathematical content explored through the contexts of problem solving and reasoning. This article presents a number of simple tasks that may be…