National numeracy tests : a graphic tells a thousand words

Mandatory numeracy tests have become commonplace in many countries, heralding a new era in school assessment. New forms of accountability and an increased emphasis on national and international standards (and benchmarks) have the potential to reshape mathematics curricula. It is noteworthy that the mathematics items used in these tests are rich in graphics. Many of the items, for example, require students to have an understanding of information graphics (e.g., maps, charts and graphs) in order to solve the tasks. This investigation classifies mathematics items in Australia’s inaugural national numeracy tests and considers the effect such standardised testing will have on practice. It is argued that the design of mathematics items are more likely to be a reliable indication of student performance if graphical, linguistic and contextual components are considered both in isolation and in integrated ways as essential elements of task design.

Primary students’ spatial visualization and spatial orientation : an evidence base for instruction

This paper reports on the performance of 58 11 to 12-year-olds on a spatial visualization task and a spatial orientation task. The students completed these tasks and explained their thinking during individual interviews. The qualitative data were analysed to inform pedagogical content knowledge for spatial activities. The study revealed that “matching” or “matching and eliminating” were the typical strategies that students employed on these spatial tasks. However, errors in making associations between parts of the same or different shapes were noted. Students also experienced general difficulties with visual memory and language use to explain their thinking. The students’ specific difficulties in spatial visualization related to obscured items, the perspective used, and the placement and orientation of shapes.

Gender effects in orientation on primary students’ performance on items rich in graphics

This study investigated the longitudinal performance of 378 students who completed mathematics items rich in graphics. Specifically, this study explored student performance across axis (e.g., numbers lines), opposed-position (e.g., line and column graphs) and circular (e.g., pie charts) items over a three-year period (ages 9-11 years). The results of the study revealed significant performance differences in the favour of boys on graphics items that were represented in horizontal and vertical displays. There were no gender differences on items that were represented in a circular manner.

Chinese young children’s strategies on basic addition facts

Kindergartens in China offer structured full-day programs for children aged 3-6. Although formal schooling does not commence until age 7, the mathematics program in kindergartens is specifically focused on developing young children’s facility with simple addition and subtraction. This study explored young Chinese children’s strategies for solving basic addition facts as well as their intuitive understanding of addition via interview methods. Results indicate a strong impact that teacher-directed teaching methods have on young children’s cognitions in relation to addition.

Enhancing students' self-concepts and related constructs: A critical longitudinal analysis capitalising on and combining promising enhancement techniques for educational settings

Enhancing children's self-concepts is widely accepted as a critical educational outcome of schooling and is postulated as a mediating variable that facilitates the attainment of other desired outcomes such as improved academic achievement. Despite considerable advances in self-concept research, there has been limited progress in devising teacher-administered enhancement interventions. This is unfortunate as teachers are crucial change agents during important developmental periods when self-concept is formed. The primary aim of the present investigation is to build on the promising features of previous self-concept enhancement studies by: (a) combining two exciting research directions developed by Burnett and Craven to develop a potentially powerful cognitive-based intervention; (b) incorporating recent developments in theory and measurement to ensure that the multidimensionality of self-concept is accounted for in the research design; (c) fully investigating the effects of a potentially strong cognitive intervention on reading, mathematics, school and learning self-concepts by using a large sample size and a sophisticated research design; (d) evaluating the effects of the intervention on affective and cognitive subcomponents of reading, mathematics, school and learning self-concepts over time to test for differential effects of the intervention; (e) modifying and extending current procedures to maximise the successful implementation of a teacher-mediated intervention in a naturalistic setting by incorporating sophisticated teacher training as suggested by Hattie (1992) and including an assessment of the efficacy of implementation; and (f) examining the durability of effects associated with the intervention.

A Malaysian tale : pre-service teacher education and ICT integration for a better world

The use of Information and Communication Technologies (ICT) in education is often a topic of much discussion within all sectors of education with educators and educational researchers continually looking for innovative ways of using these technologies to support and enhance student outcomes in education. Consequently, Malaysia is no exception to this and as the Ministry of Education (MOE), Malaysia strives to meet its government’s Vision 2020, educational reform across all educational sectors has become imperative. ICT will play an integral role in the educational reform process and teacher education programs are no exception to this. ICT and capacity building will play an important role in the re-conceptualisation of teacher education programs. This paper reports on how a collaborative capacity building project between two Malaysian teacher education Institutes and an Australian University has given lecturers and pre-service teachers an opportunity to redefine their use of ICT in their prospective teaching areas of science, mathematics and design and technology. It also highlights the positive capacity building programs that occurred between both Australian university lecturers and Malaysian Institute lecturers and how this contributed to the effective integration and use of ICT.

Bubble geometry and chaotic pricing behaviour

This paper is a deductive theoretical enquiry into the flow of effects from the geometry of price bubbles/busts, to price indices, to pricing behaviours of sellers and buyers, and back to price bubbles/busts. The intent of the analysis is to suggest analytical approaches to identify the presence, maturity, and/or sustainability of a price bubble. We present a pricing model to emulate market behaviour, including numeric examples and charts of the interaction of supply and demand. The model extends into dynamic market solutions myopic (single- and multi-period) backward looking rational expectations to demonstrate how buyers and sellers interact to affect supply and demand and to show how capital gain expectations can be a destabilising influence – i.e. the lagged effects of past price gains can drive the market price away from long-run market-worth. Investing based on the outputs of past price-based valuation models appear to be more of a game-of-chance than a sound investment strategy.

Mixing colours: An ICT tool based on a semiotic framework for mathematical meaning-makng about ratio and fractions

This paper reports on the research and development of an ICT tool to facilitate the learning of ratio and fractions by adult prisoners. The design of the ICT tool was informed by a semiotic framework for mathematical meaning-making. The ICT tool thus employed multiple semiotic resources including topological, typological, and social-actional resources. The results showed that individual semiotic resource could only represent part of the mathematical concept, while at the same time it might signify something else to create a misconception. When multiple semiotic resources were utilised the mathematical ideas could be better learnt.

Numerical simulation for the 3D seepage flow with fractional derivatives in porous media

In this paper, the numerical simulation of the 3D seepage flow with fractional derivatives in porous media is considered under two special cases: non-continued seepage flow in uniform media (NCSFUM) and continued seepage flow in non-uniform media (CSF-NUM). A fractional alternating direction implicit scheme (FADIS) for the NCSF-UM and a modified Douglas scheme (MDS) for the CSF-NUM are proposed. The stability, consistency and convergence of both FADIS and MDS in a bounded domain are discussed. A method for improving the speed of convergence by Richardson extrapolation for the MDS is also presented. Finally, numerical results are presented to support our theoretical analysis.

Mixing colours : an ICT tool based on a semiotic framework for mathematical meaning-making about ratio and fractions

This paper reports on the research and development of an ICT tool to facilitate the learning of ratio and fractions by adult prisoners. The design of the ICT tool was informed by a semiotic framework for mathematical meaning-making. The ICT tool thus employed multiple semiotic resources including topological, typological, and social-actional resources. The results showed that individual semiotic resource could only represent part of the mathematical concept, while at the same time it might signify something else to create a misconception. When multiple semiotic resources were utilised the mathematical ideas could be better learnt.