Modeling as a bridge between real world problems and school mathematics

This article argues for an interdisciplinary approach to mathematical problem solving at the elementary school, one that draws upon the engineering domain. A modeling approach, using engineering model eliciting activities, might provide a rich source of meaningful situations that capitalize on and extend students’ existing mathematical learning. The study reports on the developments of 48 twelve-year old students who worked on the Bridge Design activity. Results revealed that young students, even before formal instruction, have the capacity to deal with complex interdisciplinary problems. A number of students created quite appropriate models by developing the necessary mathematical constructs to solve the problem. Students’ difficulties in mathematizing the problem, and in revising and documenting their models are presented and analysed, followed by a discussion on the appropriateness of a modeling approach as a means for introducing complex problems to elementary school students.

A comparison of Chinese and Australian early childhood mathematics

In the 21st century mathematics proficiency is synonymous with a numerate citizenry. In the past few decades young children’s ability to reason mathematically and develop mathematical proficiencies has been recognised. This paper explores the history of early childhood mathematics (ECME) that may explicate differences in Chinese and Australian contexts. Results of this review established that China and Australia are diametrically positioned in ECME. Influencing each countries philosophies and practices are their cultural beliefs. ECME in China and Australia must be culturally sustainable to achieve excellent outcomes for young children. Ongoing critique and review is necessary to ensure that ECME is meeting the needs of all teachers and children in their particular context. China and Australia with their rich contrasting philosophies can assist each other in their journeys to create exemplary ECME for the 21st century.

Mathematics learning in prep

Most teachers recognise the importance of mathematics teaching and learning in early years but there is not consensus on how and when this learning should occur. Young-Loveridge (cited in de Vries, Thomas, and Warren, 2010) suggests that quality early mathematical experiences are a key determinant to later achievement.

Combinatorial design of key distribution mechanisms for wireless sensor networks

Key distribution is one of the most challenging security issues in wireless sensor networks where sensor nodes are randomly scattered over a hostile territory. In such a sensor deployment scenario, there will be no prior knowledge of post deployment configuration. For security solutions requiring pair wise keys, it is impossible to decide how to distribute key pairs to sensor nodes before the deployment. Existing approaches to this problem are to assign more than one key, namely a key-chain, to each node. Key-chains are randomly drawn from a key-pool. Either two neighbouring nodes have a key in common in their key-chains, or there is a path, called key-path, among these two nodes where each pair of neighbouring nodes on this path has a key in common. Problem in such a solution is to decide on the key-chain size and key-pool size so that every pair of nodes can establish a session key directly or through a path with high probability. The size of the key-path is the key factor for the efficiency of the design. This paper presents novel, deterministic and hybrid approaches based on Combinatorial Design for key distribution. In particular, several block design techniques are considered for generating the key-chains and the key-pools. Comparison to probabilistic schemes shows that our combinatorial approach produces better connectivity with smaller key-chain sizes.

Assessing the potential of mathematics textbooks to promote deep learning

Curriculum documents for mathematics emphasise the importance of promoting depth of knowledge rather than shallow coverage of the curriculum. In this paper, we report on a study that explored the analysis of junior secondary mathematics textbooks to assess their potential to assist in teaching and learning aimed at building and applying deep mathematical knowledge. The method of analysis involved the establishment of a set of specific curriculum goals and associated indicators, based on research into the teaching and learning of a particular field within the mathematics curriculum, namely proportion and proportional reasoning. Topic selection was due to its pervasive nature throughout the school mathematics curriculum at this level. As a result of this study, it was found that the five textbook series examined provided limited support for the development of multiplicative structures required for proportional reasoning, and hence would not serve well the development of deep learning of mathematics. The study demonstrated a method that could be applied to the analysis of junior secondary mathematics in many parts of the world.

Data and measurement in Year 4 of the national curriculum : Mathematics

The activities introduced here were used in association with a research project in four Year 4 classrooms and are suggested as a motivating way to address several criteria for Measurement and Data in the Australian Curriculum: Mathematics. The activities involve measuring the arm span of one student in a class many times and then of all students once.

Perspectives on Reconceptualizing Early Mathematics Learning

This introductory section provides an overview of the different perspectives on reconceptualizing early mathematics learning. The chapters provide a broad scope in their topics and approaches to advancing young children’s mathematical learning. They incorporate studies that highlight the importance of pattern and structure across the curriculum, studies that target particular content such as statistics, early algebra, and beginning number, and studies that consider how technology and other tools can facilitate early mathematical development. Reconceptualizing the professional learning of teachers in promoting young children’s mathematics, including a consideration of the role of play, is also addressed. Although these themes are diffused throughout the chapters, we restrict our introduction to the core focus of each of the chapters.

Reconceptualizing Early Mathematics Learning : The Fundamental Role of Pattern and Structure

The Pattern and Structure Mathematics Awareness Program (PASMAP) was developed concurrently with the studies of AMPS and the development of the Pattern and Structure Assessment (PASA) interview. We summarize some early classroom-based teaching studies and describe the PASMAP that resulted. A large-scale two-year longitudinal study, Reconceptualizing Early Mathematics Learning (REML) resulted. We provide an overview of the REML study and discuss the consequences for our view of early mathematics learning. A purposive sample of four large primary schools, two in Sydney and two in Brisbane, representing 316 students from diverse socio-economic and cultural contexts, participated in an evaluation of the PASMAP intervention throughout the 2009 school year and a follow-up assessment in 2010. Two different mathematics programs were implemented: in each school, two Kindergarten teachers implemented the PASMAP and another two implemented their regular program. The study shows that both groups of students made substantial gains on the ‘I Can Do Maths’ standardized assessment and the PASA interview, but highly significant differences were found on the latter with PASMAP students outperforming the regular group on PASA scores. Qualitative analysis of students’ responses for structural development showed increased levels for the PASMAP students. Implications for pedagogy and curriculum are discussed.

Accelerating the Mathematics Learning of Low Socio-Economic Status Junior Secondary Students : an early report

The Accelerating the Mathematics Learning of Low Socio-Economic Status Junior Secondary Students project aims to address the issues faced by very underperforming mathematics students as they enter high school. Its aim is to accelerate learning of mathematics through a vertical curriculum to enable students to access Year 10 mathematics subjects, thus improving life chances. This paper reports upon the theory underpinning this project and illustrates it with examples of the curriculum that has been designed to achieve acceleration.

A conceptual framework for the cultural integration of cooperative learning : a Thai primary mathematics education perspective

The Thailand education reform adopted cooperative learning to improve the quality of education. However, it has been reported that the introduction and maintenance of cooperative learning has been difficult and uncertain because of the cultural differences. The study proposed a conceptual framework developed based on making a connection between Thai cultures and cooperative learning elements, and implemented a small-scale research project in a Thai primary mathematics class with a teacher and thirty-two Grade 4 students. The results uncovered that the three components including preparation of teachers, instructional strategies and preparation of students can be vehicles for the culture integration in cooperative learning.

Modelling as a vehicle for philosophical inquiry in the mathematics curriculum

Philosophical inquiry in the teaching and learning of mathematics has received continued, albeit limited, attention over many years (e.g., Daniel, 2000; English, 1994; Lafortune, Daniel, Fallascio, & Schleider, 2000; Kennedy, 2012a). The rich contributions these communities can offer school mathematics, however, have not received the deserved recognition, especially from the mathematics education community. This is a perplexing situation given the close relationship between the two disciplines and their shared values for empowering students to solve a range of challenging problems, often unanticipated, and often requiring broadened reasoning. In this article, I first present my understanding of philosophical inquiry as it pertains to the mathematics classroom, taking into consideration the significant work that has been undertaken on socio-political contexts in mathematics education (e.g., Skovsmose & Greer, 2012). I then consider one approach to advancing philosophical inquiry in the mathematics classroom, namely, through modelling activities that require interpretation, questioning, and multiple approaches to solution. The design of these problem activities, set within life-based contexts, provides an ideal vehicle for stimulating philosophical inquiry.

An evaluation of the Australian ‘reconceptualising early mathematics learning’ project : key findings and implications

The Pattern and Structure Mathematics Awareness Project (PASMAP) has investigated the development of patterning and early algebraic reasoning among 4 to 8 year olds over a series of related studies. We assert that an awareness of mathematical pattern and structure (AMPS) enables mathematical thinking and simple forms of generalization from an early age. This paper provides an overview of key findings of the Reconceptualizing Early Mathematics Learning empirical evaluation study involving 316 Kindergarten students from 4 schools. The study found highly significant differences on PASA scores for PASMAP students. Analysis of structural development showed increased levels for the PASMAP students; those categorised as low ability developed improved structural responses over a short period of time.

Starting out in STEM : a study of young men and women in first year science, technology, engineering and mathematics courses

In late 2011, first year university students in science, technology, engineering and mathematics (STEM) courses across Australia were invited to participate in the international Interests and Recruitment in Science (IRIS) study. IRIS investigates the influences on young people's decisions to choose university STEM courses and their subsequent experiences of these courses. The study also has a particular focus on the motivations and experiences of young women in courses such as physics, IT and engineering given the low rates of female participation in these fields. Around 3500 students from 30 Australian universities contributed their views on the relative importance of various school and non-school influences on their decisions, as well as insights into their experiences of university STEM courses so far. It is hoped that their contributions will help improve recruitment, retention and gender equity in STEM higher education and careers.