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.

Scaffolding techniques : a teacher training for cooperative learning in Thailand primary education

Using cooperative learning in classrooms promotes academic achievement, communication skills, problem-solving, social skills and student motivation. Yet it is reported that cooperative learning as a Western educational concept may be ineffective in Asian cultural contexts. The study aims to investigate the utilisation of scaffolding techniques for cooperative learning in Thailand primary mathematics classes. A teacher training program was designed to foster Thai primary school teachers’ cooperative learning implementation. Two teachers participated in this experimental program for one and a half weeks and then implemented cooperative learning strategies in their mathematics classes for six weeks. The data collected from teacher interviews and classroom observations indicates that the difficulty or failure of implementing cooperative learning in Thailand education may not be directly derived from cultural differences. Instead, it does indicate that Thai culture can be constructively merged with cooperative learning through a teacher training program and practices of scaffolding techniques.

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.

The influence of school science teachers : the differential importance attributed by males and females to encouragement from science teachers

Research on the achievement and retention of female students in science and mathematics is located within a context of falling levels of participation in physical science and mathematics courses in Australian schools, and underrepresentation of females in some science, technology, engineering and mathematics (STEM) courses. The Interests and Recruitment in Science (IRIS) project is an international project that aims to contribute to understanding and improving recruitment, retention and gender equity in STEM higher education. Nearly 3500 first year students in 30 Australian universities responded to the IRIS survey of 5-point Likert items and open responses. This paper explores gender differences in first year university students’ responses to three questions about important influences on their course choice. The IRIS study found good teachers were rated highly by both males and females as influential in choosing STEM courses, and significantly higher numbers of females rated personal encouragement from senior high school science teacher as very important. In suggestions for addressing sex disparities in male-dominated STEM courses, more females indicated the importance of good teaching/encouragement and more females said (unspecified) encouragement. This study relates to the influence of school science teachers and results are discussed in relation to implications for science education.

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.

Maximum loadability achievement in SWER networks using optimal sizing and locating of batteries

This paper presents an optimisation algorithm to maximize the loadability of single wire earth return (SWER) by minimizing the cost of batteries and regulators considering the voltage constraints and thermal limits. This algorithm, that finds the optimum location of batteries and regulators, uses hybrid discrete particle swarm optimization and mutation (DPSO + Mutation). The simulation results on realistic highly loaded SWER network show the effectiveness of using battery to improve the loadability of SWER network in a cost-effective way. In this case, while only 61% of peak load can be supplied without violating the constraints by existing network, the loadability of the network is increased to peak load by utilizing two battery sites which are located optimally. That is, in a SWER system like the studied one, each installed kVA of batteries, optimally located, supports a loadability increase as 2 kVA.

Bridging the gap in school achievement through the arts : summary report

Educational Transformations Pty Ltd was commissioned by The Song Room (TSR) to conduct a study of the impact of TSR programs in government schools in relatively disadvantaged communities in New South Wales (NSW) on indicators of student performance that have been identified in previous research as related to potential engagement in juvenile crime. Students in Grades 5 and 6 were the subjects of study. TSR is a not-for-profit organisation in receipt of grants from public and private sources that conducts free programs in the performing arts in schools where these are not currently offered. These programs are conducted by mutual agreement between TSR and participating schools. Across Australia, approximately 200 schools and 40,000 students are engaged for a minimum of six months each year. Students typically participate for approximately one hour per week in each class. Instruction is provided by a Teaching Artist (TA), contracted to TSR and working in partnership with the classroom teacher at the school of placement. TSR received a three-year grant from the Macquarie Group Foundation to investigate the efficacy of its interventions in improving social and education outcomes for children in a range of high need target group areas participating in its program...

Does improving school level attendance lead to improved school level achievement? An empirical study of indigenous educational policy in Australia

Current federal government policy initiatives in Aboriginal education and social welfare reform are based on assumptions about the relationship between increased attendance and increased student performance on standardized tests. There are empirical assumptions underlying these policy interventions and their accompanying public debates. Our aim here is to empirically explore the relationships between patterns of student attendance and patterns of student achievement in schools with significant cohorts of Aboriginal and/or Torres Strait Islander students at the school level. Based on an analysis of the publicly available data reported on the ‘MySchool’ website, we find that reforms and policies around attendance have not and are unlikely to generate patterns of improved achievement. Questions about the rationale and rhetoric of government policy focused at the school level as opposed to the need to focus on pedagogy and curriculum are discussed.

Physical activity, self-regulation, and early academic achievement in preschool children

Research Findings The present study investigated whether active play during recess was associated with self-regulation and academic achievement in a prekindergarten sample. A total of 51 children in classes containing approximately half Head Start children were assessed on self-regulation, active play, and early academic achievement. Path analyses indicated that higher active play was associated with better self-regulation, which in turn was associated with higher scores on early reading and math assessments. Practice or Policy Results point to the benefits of active play for promoting self-regulation and offer insight into possible interventions designed to promote self-regulation and academic achievement.

ORIGO stepping stones common core mathematics Grade 5 practice book

ORIGO Stepping Stones is written and developed by a team of experts to provide teachers with a world-class elementary math program. Our expert team of authors and consultants are utilizing all available educational research to create a unique program that has never before been available to teachers. The full color Student Practice Book provides practice pages that support previous and current lessons.