Students living in disadvantaged contexts and whose second language is English (ESL) are at risk of not succeeding in school mathematics. It has been internationally recognised that students' socioeconomic background and their achievements in mathematics is more pronounced for Australian students (Thomson et al. 2011). This gap is even more…

This study investigated whether a four-week intensive professional development workshop for math teachers was effective in improving their knowledge and skills of mathematics concepts and technology, as well as improving their attitudes toward integrating technology into teaching math. Instruments for data collection included a pre- and post- test…

Researches carried out all around the world showed that students learn more effectively if they are able to make connections between subjects. This case reports based on an investigation of how mathematics concepts were connected to science concepts by a science teacher in an elementary science classroom, and on the science teacher's views about…

The following is a report of an exploration of what mathematical reasoning might look like in classrooms. Focusing on just one lesson in one classroom, data are presented that indicate that upper primary students are willing and able to reason for themselves, especially in classrooms in which the culture for such reasoning has been established. It…

This paper focuses on an inferential view on introducing new concepts in mathematics classrooms. A theoretical framework is presented which helps to analyse and reflect on the processes of teaching and learning mathematical concepts. The framework is based on the philosophies by Ludwig Wittgenstein and Robert Brandom. Wittgenstein's language-game…

Profound Understanding of Emergent Mathematics has been recently proposed as a means of conceptualizing the mathematics knowing of teachers as an open disposition that extends well-defined and fixed categories of knowledge proposed in the literature. The purpose of this paper is to explore how this disposition may be assessed through the…

This study gives insights into how Logo-like microworlds can affect cognitive development related to mathematics education of students with math learning difficulties. In particular, we analyse the case of a 15-year-old student with dyslexia and severe dyscalculia. Among the various cognitive aspects involved, here we delve into the development of…

The "Monty Hall" problem or "Three Door" problem--where a person chooses one of three doors in hope of winning a valuable prize but is subsequently offered the choice of changing his or her selection--is a well known and often discussed probability problem. In this paper, the structure, history, and ultimate solution of the…

Two common examples of one-dimensional maps (the tent map and the logistic map) are generalized to cases where they have more than one control parameter. In the case of the tent map, this still allows the global Lyapunov exponent to be found analytically, and permits various properties of the resulting global Lyapunov exponents to be investigated…

Archimedes, the famous Greek mathematician, lived from 287 BCE until approximately 212 BCE. He thought that the figure of two semi-circles on a straight line enclosed by a larger semi-circle resembled a shoemaker's knife. Archimedes called this figure an "arbelos" since arbelos is the Greek word for a shoemaker's knife. The author describes the…

"Lord Brouncker's continued fraction for pi" is a well-known result. In this article, we show that Brouncker found not only this one continued fraction, but an entire infinite sequence of related continued fractions for pi. These were recorded in the "Arithmetica Infinitorum" by John Wallis, but appear to have been ignored and forgotten by modern…

In this article we study a specific lattice classification of converse quadrilaterals, based on the relations between diagonals. This lattice contains 16 = 2[superscript 4] elements, which form a hypercube, and therefore it is a Boolean lattice. "Complementary" species of quadrilaterals thus appear and may be related in the lattice diagram. We…

In this article we present an exploratory tool for extracting systematic patterns from multivariate data. The technique, hierarchical segmentation (HS), can be used to group multivariate time series into segments with similar discrete-state recurrence patterns and it is not restricted by the stationarity assumption. We use a simulation study to…

By rhotrix we understand an object that lies in some way between (n x n)-dimensional matrices and (2n - 1) x (2n - 1)-dimensional matrices. Representation of vectors in rhotrices is different from the representation of vectors in matrices. A number of vector spaces in matrices and their properties are known. On the other hand, little seems to be…

This research is aimed to determine the role of Indonesian folklore context namely the Legend of Kemaro Island in supporting average learning on 6 grade students with Pendidikan Matematika Realistik Indonesia (PMRI) approach. The method used is a design research that contains three stage namely preliminary design, teaching experiment, and…