Teacher change and professional development in mathematics education

It is generally agreed that if authentic teacher change is to occur then the tacit knowledge about how and why they act in certain ways in the classroom be accessed and reflected upon. While critical reflection can and often is an individual experience there is evidence to suggest that teachers are more likely to engage in the process when it is approached in a collegial manner; that is, when other teachers are involved in and engaged with the same process. Teachers do not enact their profession in isolation but rather exist within a wider community of teachers. An outside facilitator can also play an active and important role in achieving lasting teacher change. According to Stein and Brown (1997) “an important ingredient in socially based learning is that graduations of expertise and experience exist when teachers collaborate with each other or outside experts” (p. 155). To assist in the effective professional development of teachers, outside facilitators, when used, need to provide “a dynamic energy producing interactive experience in which participants examine and explore the complex components of teaching” (Bolster, 1995, p. 193). They also need to establish rapport with the participating teachers that is built on trust and competence (Hyde, Ormiston, & Hyde, 1994). For this to occur, professional development involving teachers and outside facilitators or researchers should not be a one-off event but an ongoing process of engagement that enables both the energy and trust required to develop. Successful professional development activities are therefore collaborative, relevant and provide individual, specialised attention to the teachers concerned. The project reported here aimed to provide professional development to two Year 3 teachers to enhance their teaching of a new mathematics content area, mental computation. This was achieved through the teachers collaborating with a researcher to design an instructional program for mental computation that drew on theory and research in the field.

The Global Youth Media Council : young people speaking and learning about media reform

The 5th World Summit on Media for Children and Youth held in Karlstad, Sweden in June 2010 provided a unique media literacy experience for approximately thirty young people from diverse backgrounds through participation in the Global Youth Media Council. This article focuses on the Summit’s aim to give young people a ‘voice’ through intercultural dialogue about media reform. The accounts of four young Australians are discussed in order to consider how successful the Summit was in achieving this goal. The article concludes by making recommendations for future international media literacy conferences involving young people. It also advocates for the expansion of the Global Youth Media Council concept as a grass roots movement to involve more young people in discussions about media reform.

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.

Understanding graphicacy : students’ making sense of graphics in mathematics assessment tasks

The ability to decode graphics is an increasingly important component of mathematics assessment and curricula. This study examined 50, 9- to 10-year-old students (23 male, 27 female), as they solved items from six distinct graphical languages (e.g., maps) that are commonly used to convey mathematical information. The results of the study revealed: 1) factors which contribute to success or hinder performance on tasks with various graphical representations; and 2) how the literacy and graphical demands of tasks influence the mathematical sense making of students. The outcomes of this study highlight the changing nature of assessment in school mathematics and identify the function and influence of graphics in the design of assessment tasks.

Mathematics funds of knowledge : sotmaute and sermaute fish in a Torres Strait Islander 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 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. This knowledge is then practised throughout their lives and passed onto the next generation of children. Through adopting a community research approach, funds of knowledge that can be used to validate the community’s identities as knowledgeable people, can also 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.

Negotiating the meaning of achievement standards in the Australian curriculum

Planning for assessment using the achievement standards in the implementation of the Australian Curriculum presents a challenge for teachers. The achievement standards differ in appearance and function from current assessment practices. This research inquiry used qualitative focus group discussions to investigate how Year 6 teachers from three Queensland schools negotiated the meaning of the English and Mathematics achievement standards for their assessment practice. A sociocultural theoretical perspective was used to analyse the data. Three significant influences on the teachers’ understanding of the achievement standards were their understanding of the achievement standard text, their beliefs about learning and assessment, and the assessment culture of the school. The opportunity to learn through supported professional conversations with peers, and the need for a shared assessment discourse were identified as necessities to support teachers as they seek to implement the new practices inherent in the achievement standards in the Australian Curriculum.

Sustaining teacher professionalism in the context of standards referenced assessment reform

Standards referenced reform, tied to reporting, engages directly with assessment issues related to accountability. Assessment is the key to good education and is inseparable from curriculum. In an accountability context, standards are used as a lever to improve the reliability and consistency of teacher judgement; and classroom evidence is used by education systems for reporting and tracking achievement over time. Assessment is thus a powerful driver for change and is at the heart of the teaching-learning dynamic. The relationship between the learner, learning and assessment needs to be kept central and the idea of teacher empowerment is fundamental. This chapter is a call to honour and sustain teacher professionalism through educative forms of school-based and teacher-led evaluation, assessment and communities of judgement practice. It supports the argument for a central place for classroom assessment in the role of assessment in educational accountability...

…Where did I lose you? Accessing the literacy demands of assessment

In this study we sought to find out how teachers could make assessment fairer for Indigenous students in learning mathematics, given the context of the high stakes of the National Assessment Program Literacy and Numeracy (NAPLAN). Today, teachers are experiencing the full range of demands from their own students who require individual attention, through to system level expectations of improved performances for all students. Many staff experience reform fatigue with limited time for critical reflection and a reduction in support for the use and the analysis of the overwhelming amount of data that has become available in recent years. Over the past three years we worked with teachers in seven schools to gradually refine our research focus to centre on how we might best support teachers in this demanding context with the important outcome of improved teaching and learning of mathematics with particular consideration of how to respond to the cultural needs of Indigenous (Aboriginal and Torres Strait Islander) students.

Greek or not : the use of symbols and abbreviations in mathematics

The use of symbols and abbreviations adds uniqueness and complexity to the mathematical language register. In this article, the reader’s attention is drawn to the multitude of symbols and abbreviations which are used in mathematics. The conventions which underpin the use of the symbols and abbreviations and the linguistic difficulties which learners of mathematics may encounter due to the inclusion of the symbolic language are discussed. 2010 NAPLAN numeracy tests are used to illustrate examples of the complexities of the symbolic language of mathematics.

A framework for mathematics graphical tasks : The influence of the graphic element on student sense making

Graphical tasks have become a prominent aspect of mathematics assessment. From a conceptual stance, the purpose of this study was to better understand the composition of graphical tasks commonly used to assess students’ mathematics understandings. Through an iterative design, the investigation described the sense making of 11–12-year-olds as they decoded mathematics tasks which contained a graphic. An ongoing analysis of two phases of data collection was undertaken as we analysed the extent to which various elements of text, graphics, and symbols influenced student sense making. Specifically, the study outlined the changed behaviour (and performance) of the participants as they solved graphical tasks that had been modified with respect to these elements. We propose a theoretical framework for understanding the composition of a graphical task and identify three specific elements which are dependently and independently related to each other, namely: the graphic; the text; and the symbols. Results indicated that although changes to the graphical tasks were minimal, a change in student success and understanding was most evident when the graphic element was modified. Implications include the need for test designers to carefully consider the graphics embedded within mathematics tasks since the elements within graphical tasks greatly influence student understanding.

Contextualizing a university-school STEM education collaboration : distributed and self-activated leadership for project outcomes

Implementing educational reform requires partnerships, and university-school collaborations in the form of investigative and experimental projects can aim to determine the practicalities of reform. However, there are funded projects that do not achieve intended outcomes. In the context of a new reform initiative in education, namely, science, technology, engineering and mathematics (STEM) education, this article explores the management of a government-funded project. In a university school partnership for STEM education, how can leadership be distributed for achieving project outcomes? Participants included university personnel from different STEM areas, school teachers and school executives. Data collected included observations, interviews, resource materials, and video and photographic images. Findings indicated that leadership roles were distributed and selfactivated by project partners according to their areas of expertise and proximal activeness to the project phases, that is: (1) establishing partnerships; (2) planning and collaboration; (3) project implementation; and (4) project evaluation and further initiatives. Leadership can be intentional and unintentional within project phases, and understanding how leadership can be distributed and selfactivated more purposefully may aid in generating more expedient project outcomes.