Torres Strait Islander parents’ involvement in their children’s mathematics learning : a discussion paper

This paper is a beginning point for discussing what the literature states about parents’ involvement in their children’s mathematics education. Where possible it will focus on Torres Strait Islander Peoples. Little is known about how Torres Strait Islander parents approach their children’s learning of mathematics and how important early mathematics is to mothers. What is known is that is they are keen for their children to receive an education that provides them with opportunities for their present and future lives. However, gaining access to education is challenging given that the language of instruction in schools is written to English conventions, decontextualised and disconnected from the students’ culture, community and home language. This paper discusses some of the issues raised in the literature about what parents are confronted with when making decisions about their children’s education.

Torres Strait Island parents' involvement in their children's mathematics learning : a discussion paper

This paper is a beginning point for discussing what the literature states about parents’ involvement in their children’s mathematics education. Where possible it will focus on Torres Strait Islander Peoples. Little is known about how Torres Strait Islander parents approach their children’s learning of mathematics and how important early mathematics is to mothers. What is known is that is they are keen for their children to receive an education that provides them with opportunities for their present and future lives. However, gaining access to education is challenging given that the language of instruction in schools is written to English conventions, decontextualised and disconnected from the students’ culture, community and home language. This paper discusses some of the issues raised in the literature about what parents are confronted with when making decisions about their children’s education.

The role of fluency in a mathematics item with an embedded graphic: Interpreting a pie chart.

The purpose of this study was to identify the pedagogical knowledge relevant to the successful completion of a pie chart item. This purpose was achieved through the identification of the essential fluencies that 12–13-year-olds required for the successful solution of a pie chart item. Fluency relates to ease of solution and is particularly important in mathematics because it impacts on performance. Although the majority of students were successful on this multiple choice item, there was considerable divergence in the strategies they employed. Approximately two-thirds of the students employed efficient multiplicative strategies, which recognised and capitalised on the pie chart as a proportional representation. In contrast, the remaining one-third of students used a less efficient additive strategy that failed to capitalise on the representation of the pie chart. The results of our investigation of students’ performance on the pie chart item during individual interviews revealed that five distinct fluencies were involved in the solution process: conceptual (understanding the question), linguistic (keywords), retrieval (strategy selection), perceptual (orientation of a segment of the pie chart) and graphical (recognising the pie chart as a proportional representation). In addition, some students exhibited mild disfluencies corresponding to the five fluencies identified above. Three major outcomes emerged from the study. First, a model of knowledge of content and students for pie charts was developed. This model can be used to inform instruction about the pie chart and guide strategic support for students. Second, perceptual and graphical fluency were identified as two aspects of the curriculum, which should receive a greater emphasis in the primary years, due to their importance in interpreting pie charts. Finally, a working definition of fluency in mathematics was derived from students’ responses to the pie chart item.

Students as decoders of graphics in mathematics

This paper reports on students’ ability to decode mathematical graphics. The findings were: (a) some items showed an insignificant improvement over time; (b) success involves identifying critical perceptual elements in the graphic and incorporating these elements into a solution strategy; and (c) the optimal strategy capitalises on how information is encoded in the graphic. Implications include a need for teachers to be proactive in supporting students’ to develop their graphical knowledge and an awareness that knowledge varies substantially across students.

Implementing a Pattern and Structure Mathematics Awareness Program (PASMAP) in kindergarten

This paper provides an interim report of a large empirical evaluation study in progress. An intervention was implemented to evaluate the effectiveness of the Pattern and Structure Mathematical Awareness Program (PASMAP) on Kindergarten students’ mathematical development. Four large schools (two from Sydney and two from Brisbane), 16 teachers and their 316 students participated in the first phase of a 2-year longitudinal study. Eight of 16 classes implemented the PASMAP program over three school terms. This paper provides an overview of key aspects of the intervention, and preliminary analysis of the impact of PASMAP on students’ representation, abstraction and generalisation of mathematical ideas.

Culture-fair assessment : challenging Indigenous students through effortful mathematics teaching

This paper reports on a mathematics education research project centred on teachers’ pedagogical practices and capacity to assess Indigenous Australian students in a culture-fair manner. The project has been funded by the Australian Research Council Linkage program and is being conducted in seven Catholic and Independent primary schools in north Queensland. Our Industry Partners are Catholic Education and the Association of Independent Schools, Queensland. The study aims to provide greater understanding about how to build more equitable assessment practices to address the issue of underperforming Aboriginal and Torres Strait Islander (ATSI) students in regional and remote Australia. The goal is to identify ways forward by attending to culture-fair assessment practice. The research is exploring the attitudes, beliefs and responses of Indigenous students to assessment in the context of mathematics learning with particular focus on teacher knowledge in these educational settings in relation to the design of assessment tasks that are authentic and engaging for these students in an accountability context. This approach highlights how teachers need to distinguish the ‘funds of knowledge’ (González, Moll, Floyd Tenery, Rivera, Rendón, Gonzales & Amanti, 2008) that Indigenous students draw on and how teachers need to be culturally responsive in their pedagogy to open up curriculum and assessment practice to allow for different ways of knowing and being

Early years teachers’ attitudes towards mathematics

Worldwide, there is considerable attention to providing a supportive mathematics learning environment for young children because attitude formation and achievement in these early years of schooling have a lifelong impact. Key influences on young children during these early years are their teachers. Practising early years teachers‟ attitudes towards mathematics influence the teaching methods they employ, which in turn, affects young students‟ attitudes towards mathematics, and ultimately, their achievement. However, little is known about practising early years teachers‟ attitudes to mathematics or how these attitudes form, which is the focus of this study. The research questions were: 1. What attitudes do practising early years teachers hold towards mathematics? 2. How did the teachers‟ mathematics attitudes form? This study adopted an explanatory case study design (Yin, 2003) to investigate practising early years teachers‟ attitudes towards mathematics and the formation of these attitudes. The research took place in a Brisbane southside school situated in a middle socio-economic area. The site was chosen due to its accessibility to the researcher. The participant group consisted of 20 early years teachers. They each completed the Attitude Towards Mathematics Inventory (ATMI) (Schackow, 2005), which is a 40 item instrument that measures attitudes across the four dimensions of attitude, namely value, enjoyment, self-confidence and motivation. The teachers‟ total ATMI scores were classified according to five quintiles: strongly negative, negative, neutral, positive and strongly positive. The results of the survey revealed that these teachers‟ attitudes ranged across only three categories with one teacher classified as strongly positive, twelve teachers classified as positive and seven teachers classified as neutral. No teachers were identified as having negative or strongly negative attitudes. Subsequent to the surveys, six teachers with a breadth of attitudes were selected from the original cohort to participate in open-ended interviews to investigate the formation of their attitudes. The interview data were analysed according to the four dimensions of attitudes (value, enjoyment, self-confidence, motivation) and three stages of education (primary, secondary, tertiary). Highlighted in the findings is the critical impact of schooling experiences on the formation of student attitudes towards mathematics. Findings suggest that primary school experiences are a critical influence on the attitudes of adults who become early years teachers. These findings also indicate the vital role tertiary institutions play in altering the attitudes of preservice teachers who have had negative schooling experiences. Experiences that teachers indicated contributed to the formation of positive attitudes in their own education were games, group work, hands-on activities, positive feedback and perceived relevance. In contrast, negative experiences that teachers stated influenced their attitudes were insufficient help, rushed teaching, negative feedback and a lack of relevance of the content. These findings together with the literature on teachers‟ attitudes and mathematics education were synthesized in a model titled a Cycle of Early Years Teachers’ Attitudes Towards Mathematics. This model explains positive and negative influences on attitudes towards mathematics and how the attitudes of adults are passed on to children, who then as adults themselves, repeat the cycle by passing on attitudes to a new generation. The model can provide guidance for practising teachers and for preservice and inservice education about ways to foster positive influences to attitude formation in mathematics and inhibit negative influences. Two avenues for future research arise from the findings of this study both relating to attitudes and secondary school experiences. The first question relates to the resilience of attitudes, in particular, how an individual can maintain positive attitudes towards mathematics developed in primary school, despite secondary school experiences that typically have a negative influence on attitude. The second question relates to the relationship between attitudes and achievement, specifically, why secondary students achieve good grades in mathematics despite a lack of enjoyment, which is one of the dimensions of attitude.

An evaluation of the pattern and structure mathematics awareness program in the early school years

This paper reports a 2-year longitudinal study on the effectiveness of the Pattern and Structure Mathematical Awareness Program (PASMAP) on students’ mathematical development. The study involved 316 Kindergarten students in 17 classes from four schools in Sydney and Brisbane. The development of the PASA assessment interview and scale are presented. The intervention program provided explicit instruction in mathematical pattern and structure that enhanced the development of students’ spatial structuring, multiplicative reasoning, and emergent generalisations. This paper presents the initial findings of the impact of the PASMAP and illustrates students’ structural development.

Developing the Pattern and Structure Assessment (PASA) interview to inform early mathematics learning

The Pattern and Structure Mathematical Awareness Program(PASMAP) stems from a 2-year longitudinal study on students’ early mathematical development. The paper outlines the interview assessment the Pattern and Structure Assessment(PASA) designed to describe students’ awareness of mathematical pattern and structure across a range of concepts. An overview of students’ performance across items and descriptions of their structural development are described.

Mathematics and complex learning

There is unprecedented worldwide demand for mathematical solutions to complex problems. That demand has generated a further call to update mathematics education in a way that develops students’ abilities to deal with complex systems.

Professional growth through working together : a study of reciprocal benefits for teacher and education advisor through classroom based professional development

Teacher professional development provided by education advisors as one-off, centrally offered sessions does not always result in change in teacher knowledge, beliefs, attitudes or practice in the classroom. As the mathematics education advisor in this study, I set out to investigate a particular method of professional development so as to influence change in a practising classroom teacher’s knowledge and practices. The particular method of professional development utilised in this study was based on several principles of effective teacher professional development and saw me working regularly in a classroom with the classroom teacher as well as providing ongoing support for her for a full school year. The intention was to document the effects of this particular method of professional development in terms of the classroom teacher’s and my professional growth to provide insights for others working as education advisors. The professional development for the classroom teacher consisted of two components. The first was the co-operative development and implementation of a mental computation instructional program for the Year 3 class. The second component was the provision of ongoing support for the classroom teacher by the education advisor. The design of the professional development and the mental computation instructional program were progressively refined throughout the year. The education advisor fulfilled multiple roles in the study as teacher in the classroom, teacher educator working with the classroom teacher and researcher. Examples of the professional growth of the classroom teacher and the education advisor which occurred as sequences of changes (growth networks, Hollingsworth, 1999) in the domains of the professional world of the classroom teacher and education advisor were drawn from the large body of data collected through regular face-to-face and email communications between the classroom teacher and the education advisor as well as from transcripts of a structured interview. The Interconnected Model of Professional Growth (Clarke & Hollingsworth, 2002; Hollingsworth, 1999) was used to summarise and represent each example of the classroom teacher’s professional growth. A modified version of this model was used to summarise and represent the professional growth of the education advisor. This study confirmed that the method of professional development utilised could lead to significant teacher professional growth related directly to her work in the classroom. Using the Interconnected Model of Professional Growth to summarise and represent the classroom teacher’s professional growth and the modified version for my professional growth assisted with the recognition of examples of how we both changed. This model has potential to be used more widely by education advisors when preparing, implementing, evaluating and following-up on planned teacher professional development activities. The mental computation instructional program developed and trialled in the study was shown to be a successful way of sequencing and managing the teaching of mental computation strategies and related number sense understandings to Year 3 students. This study was conducted in one classroom, with one teacher in one school. The strength of this study was the depth of teacher support provided made possible by the particular method of the professional development, and the depth of analysis of the process. In another school, or with another teacher, this might not have been as successful. While I set out to change my practice as an education advisor I did not expect the depth of learning I experienced in terms of my knowledge, beliefs, attitudes and practices as an educator of teachers. This study has changed the way in which I plan to work as an education advisor in the future.

Get Into Vocational Education (GIVE) Gladstone Pilot Project : Final Report to Rio Tinto Alcan Community Fund

This report describes the Get Into Vocational Education (GIVE) pilot project run at Gladstone Central State School from September to December 2010. The report describes the aims, budget, and timeline of the project and its findings in relation to each of the three major objectives of the project, namely (a) build awareness of, interest in, and familiarity with trades as a future vocation and opportunity for advancement; (b) enhance literacy, numeracy and science knowledge and performance; and (c) provide motivation and engagement to stay on at school and build towards a productive future. The clear findings of the GIVE Gladstone Year 4 pilot project are that, for students at risk in terms of school attendance, engagement and learning: (1) awareness of trades, literacy, mathematics and science knowledge, and motivation and engagement all improve and, in most cases, dramatically improve, in the GIVE structure; (2) this improvement involves transfer to situations and concepts not directly addressed in the project; and (3) the crucial factor in the GIVE structure that gives the improvement is the integration of classroom work with trades experiences and not the classroom and trades experiences themselves (although it is better if these are good).

Get Into Vocational Education (GIVE) Rockhampton Region Pilot Project : Final Report to The John Villiers Trust

This report describes the Get Into Vocational Education (GIVE) pilot project run in the Rockhampton Region at two schools in 2011. The report includes a description of the project, including its aims, budget, and timeline; and the findings in relation to each of the three major objectives of the project, namely (a) build awareness of, interest in, and familiarity with, trades as a future vocation and opportunity for advancement; (b) enhance literacy, numeracy and science knowledge and performance; and (c) provide motivation and engagement to stay on at school and build towards a productive future. The clear findings of the GIVE Rockhampton Region pilot project are that, for students at risk in terms of school attendance, engagement and learning: (1) awareness of trade practices in horticulture, hospitality, retail, and design and engineering, literacy, mathematics and science knowledge, and motivation and engagement all improve and, in most cases, dramatically improve, in the GIVE structure; and (2) the crucial factor in the GIVE structure that gives the improvement is the integration of classroom work with trades experiences and not the classroom and trades experiences themselves (although it is better if these are good).