Representational change and strategy use in children's number line estimation during the first years of primary school

Background: The objective of this study was to scrutinize number line estimation behaviors displayed by children in mathematics classrooms during the first three years of schooling. We extend existing research by not only mapping potential logarithmic-linear shifts but also provide a new perspective by studying in detail the estimation strategies of individual target digits within a number range familiar to children. Methods: Typically developing children (n = 67) from Years 1 – 3 completed a number-to-position numerical estimation task (0-20 number line). Estimation behaviors were first analyzed via logarithmic and linear regression modeling. Subsequently, using an analysis of variance we compared the estimation accuracy of each digit, thus identifying target digits that were estimated with the assistance of arithmetic strategy. Results: Our results further confirm a developmental logarithmic-linear shift when utilizing regression modeling; however, uniquely we have identified that children employ variable strategies when completing numerical estimation, with levels of strategy advancing with development. Conclusion: In terms of the existing cognitive research, this strategy factor highlights the limitations of any regression modeling approach, or alternatively, it could underpin the developmental time course of the logarithmic-linear shift. Future studies need to systematically investigate this relationship and also consider the implications for educational practice.

Stepping Stones A world-Class Mathematics program for the Australian Curriculum Year 1 (Student Journal)

ORIGO Stepping Stones gives mathematics teachers the best of both worlds by delivering lessons and teacher guides on a digital platform blended with the more traditional printed student journals. This uniquely interactive program allows students to participate in exciting learning activites whilst still allowing the teacher to maintain control of learning outcomes. It is the first program in Australia to give teachers activities to differentiate instruction within each lesson and across school years. Written by a team of Australia's leading mathematics educators, this program integrates key research findings in a practical sequence of modules and lessons providing schools with a step-by-step approach to the new curriculum. Click links on the right to explore the program.

The world of adolescence and the world of STEM : are they irrevocably separated?

Adolescents are indeed bothered by the complexities of the present and future and are concerned with making sense out of the multiple demands of parents, teachers, and peers while trying to develop identities as autonomous individuals. In this confused world, contemporary school science does not fit their view of desirable world as evident in the findings of the ROSE study. However, there are bright spots where teachers, community, parents and youth do engage with STEM. This paper will report on initiatives drawn from a decade of research in schools that have attempted to reconcile the interests of youth and the contemporary world of science. The aim is to identify those factors that do stimulate student interest. These case studies were conducted generally using both qualitative and quantitative data and findings analysed in terms of program outcomes and student engagement. The key finding is that the formation of relationships and partnerships in which students have high degree of autonomy and sense of responsibility is paramount to positive dispositions towards STEM. The findings raise some hope that innovative schools and partnerships can foster innovation and connect youth with the real world.

Meeting under the “Omei” Tree in the Torres Strait Islands : networks and funds of knowledge of mathematical ideas

This paper focuses on the turning point experiences that worked to transform the researcher during a preliminary consultation process to seek permission to conduct of a small pilot project on one Torres Strait Island. The project aimed to learn from parents how they support their children in their mathematics learning. Drawing on a community research design, a consultative meeting was held with one Torres Strait Islander community to discuss the possibility of piloting a small project that focused on working with parents and children to learn about early mathematics processes. Preliminary data indicated that parents use networks in their community. It highlighted the funds of knowledge of mathematics that exist in the community and which are used to teach their children. Such knowledges are situated within a community’s unique histories, culture and the voices of the people. “Omei” tree means the Tree of Wisdom in the Island community.

Visualising mathematical knowledge and understanding

Contemporary mathematics education attempts to instil within learners the conceptualization of mathematics as a highly organized and inter-connected set of ideas. To support this, a means to graphically represent this organization of ideas is presented which reflects the cognitive mechanisms that shape a learner’s understanding. This organisation of information may then be analysed, with the view to informing the design of mathematics instruction in face-to-face and/or computer-mediated learning environments. However, this analysis requires significant work to develop both theory and practice.

Funds of knowledge of sorting and patterning : networks of exchange in a Torres Strait Island community

The purpose of this article is to describe a project with one Torres Strait Islander Community. It provides some insights into parents’ funds of knowledge that are mathematical in nature, such as sorting shells and giving fish. The idea of funds of knowledge is based the premise that people are competent and have knowledge that has been historically and culturally accumulated into a body of knowledge and skills essential for their functioning and well-being. This knowledge is then practised throughout their lives and passed onto the next generation of children. Through using a community research approach, funds of knowledge that can be used to validate the community’s identities as knowledgeable people, can be used as foundations for future learnings for teachers, parents and children in the early years of school. They can be the bridge that joins a community’s funds of knowledge with schools validating that knowledge.

YuMi deadly maths program : efficacy and collaboration

Historically, perceptions about mathematics and how it is taught and learned in schools have been mixed and as a consequence have an influence on self efficacy. There are those of us who see mathematics as logical and an enjoyable subject to learn, whilst others see mathematics as irrelevant, difficult and contributing to their school failure. Research has shown that over-represented in the latter are Aboriginal and Torres Strait Islander, low SES and ESL students. These students are the focus of YuMi Deadly Centre (YDC) professional learning and research work at the Queensland University of Technology in Brisbane.

A Summative Evaluation of the Stronger Smarter Learning Communities Project : Vol 1 and Vol 2

This is a summative evaluation of the Stronger Smarter Learning Communities (SSLC) project that examines whether and how the SSLC project had an impact on Australian state schools which adopted its models and approaches. Drawing from qualitative and quantitative data sets, it also presents the largest scale and most comprehensive analysis of Indigenous education practices and outcomes to date. It includes empirical findings on: success in changing school ethos and community engagement; challenges in progress at closure of the 'gap' in conventionally measured achievement and performance; schools' and principals' choices in curriculum and instruction; profiles of teachers' and principals' training and views on teacher education; and a strong emphasis on community and school Indigenoous voices and views on Indigenous education.

Rich and purposeful mathematical knowledge of mothers and children in a Torres Strait Islander community

This paper focuses on a pilot study that explored the situated mathematical knowledge of mothers and children in one Torres Strait Islander community in Australia. The community encouraged parental involvement in their children’s learning and schooling. The study explored parents’ understandings of mathematics and how their children came to learn about it on the island. A funds of knowledge approach was used in the study. This approach is based on the premise that people are competent and have knowledge that has been historically and culturally accumulated into a body of knowledge and skills essential for their functioning and well-being (Moll, 1992). The participants, three adults and one child are featured in this paper. Three separate events are described with epiphanic or illuminative moments analysed to ascertain the features that enabled an understanding of the nature of the mathematical events. The study found that Indigenous ways of knowing of mathematics were deeply embedded in rich cultural practices that were tied to the community. This finding has implications for teachers of children in the early years. Where school mathematics is often presented as disembodied and isolated facts with children seeing little relevance, learning a different perspective of mathematics that is tied to the resources and practices of children’s lives and facilitated through social relationships, may go a long way to improving the engagement of children and their parents in learning and schooling.

Constructing a frame of cube : connecting 3D shapes with direction, location and movement

With the advancement of new technologies, this author has in 2010 started to engineer an online learning environment for investigating the nature and development of spatial abilities, and the teaching and learning of geometry. This paper documents how this new digital learning environment can afford the opportunity to integrate the learning about 3D shapes with direction, location and movement, and how young children can mentally and visually construct virtual 3D shapes using movements in both egocentric and fixed frames of reference (FOR). Findings suggest that year 4 (aged 9) children can develop the capacity to construct a cube using egocentric FOR only, fixed FOR only or a combination of both FOR. However, these young participants were unable to articulate the effect of individual or combined FOR movements. Directions for future research are proposed.

Teaching fractions to adult learners enrolled in a civil construction course : knowledge, action and materials action in tandem

This paper investigates the teaching and learning of fractions to Indigenous adult learners in a Civil Construction Certificate Course. More specifically it explores why the use of materials is critical to building knowledge and understanding. This focus is important for two reasons. First, it allows for considerations of a trainer’s approach for teaching fractions and, second it provides insights into how adult learners can be supported with representing their practical experiences of fractions to make generalisation thus building on their knowledge and learning experiences. The paper draws on teaching episodes from an Australian Research Council funded Linkage project that investigates how mathematics is taught and learned in Certificate Courses, here, Certificate 11 in Civil Construction. Action research and decolonising methods (Smith, 1999) were used to conduct the research. Video excerpts which feature one trainer and three students are analysed and described. Findings from the data indicate that adult learners need to be supported with materials to assist with building their capacity to know and apply understandings of fractions in a range of contexts, besides construction. Without materials and where fractions are taught via pen and paper tasks, students are less likely to retain and apply fraction ideas to their Certificate Course. Further they are less likely to understand decimals because of limited understanding of fractions.

Use of genetic decompositions to scaffold the development of a structurally sequenced curriculum for mathematics acceleration

The authors have collaboratively used a graphical language to describe their shared knowledge of a small domain of mathematics, which has in turn scaffolded their re-development of a related curriculum for mathematics acceleration. This collaborative use of the graphical language is reported as a simple descriptive case study. This leads to an evaluation of the graphical language’s usefulness as a tool to support the articulation of the structure of mathematics knowledge. In turn, implications are drawn for how the graphical language may be utilised as the detail of the curriculum is further elaborated and communicated to teachers.