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.

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.

Language and literacy in mathematics: stepping stones or stumbling blocks in accelerating junior-secondary students

The authors have collaborated in the development and initial evaluation of a curriculum for mathematics acceleration. This paper reports upon the difficulties encountered with documenting student understanding using pen-and-paper assessment tasks. This leads to a discussion of the impact of students’ language and literacy on mathematical performance and the consequences for motivation and engagement as a result of simplifying the language in the tests, and extending student work to algebraic representations. In turn, implications are drawn for revisions to assessment used within the project and the language and literacy focus included within student learning experiences.

Aligning school reform and teacher education reform in the middle years : an Australian case study

This paper discusses the development of a new Bachelor of Education (Middle Years of Schooling) at The University of Queensland, Australia. The middle years of schooling have increasingly been the focus of education reform initiatives in Australia, but this has not been accompanied by significant increases in the number of teacher education institutions offering specialised middle schooling-level teacher preparation programmes. Considering the rapidly changing social and economic context and the emergent state of middle schooling in Australia, the programme represented a conceptual and practical opportunity and challenge for The University of Queensland team. Working collaboratively, the team sought to design a teacher education preservice programme that was both responsive and generative: that is, responsive to local school contexts and to current education research and reform at national and international levels; and generative of cutting-edge theories and practices associated with middle schooling, teachers' work, and teacher education. This paper focuses on one component of the Middle Years of Schooling Teacher Education programme at The University of Queensland; namely, the practicum. We first present the underlying principles of the practicum programme and then examine "dilemmas" that emerged early in the practicum. These issues and tensions were associated with the ideals of "middle years" philosophy and the pragmatics of school reform associated with that approach. Within this context, we explore what it means to be both responsive and generative, and describe how we as teacher educators negotiated the extremes these terms implied.

Thai students' engagement with cooperative learning in mathematics classrooms

Over the past decade, Thai schools have been encouraged by the Thai Ministry of Education to introduce more student-centred pedagogies such as cooperative learning into their classrooms (Carter, 2006). However, prior research has indicated that the implementation of cooperative learning into Thai schools has been confounded by cultural traditions endemic within Thai schools (Deveney, 2005). The purpose of the study was to investigate how 32 Grade 3 and 32 Grade 4 students enrolled in a Thai school engaged with cooperative learning in mathematics classrooms after they had been taught cooperative learning strategies and skills. These strategies and skills were derived from a conceptual framework that was the outcome of an analysis and synthesis of social learning, behaviourist and socio-cognitive theories found in the research literature. The intervention began with a two week program during which the students were introduced to and engaged in practicing a set of cooperative learning strategies and skills (3 times a week). Then during the next four weeks (3 times a week), these cooperative learning strategies and skills were applied in the contexts of two units of mathematics lessons. A survey of student attitudes with respect to their engagement in cooperative learning was conducted at the conclusion of the six-week intervention. The results from the analysis of the survey data were triangulated with the results derived from the analysis of data from classroom observations and teacher interviews. The analysis of data identified four complementary processes that need to be considered by Thai teachers attempting to implement cooperative learning into their mathematics classrooms. The paper concludes with a set of criteria derived from the results of the study to guide Thai teachers intending to implement cooperative learning strategies and skills in their classrooms.

Teaching English as an additional language in senior high school : critical discourses in critical times

This paper presents a Critical Discourse Analysis (CDA) of four policy documents currently offering ‘sets of possibilities’ for the teaching of English as an additional or second language (hereafter EAL/ESL) in senior classrooms in Queensland, Australia. The aim is to identify the ways in which each document re-presents the notion of critical literacy. Leximancer software, and Fairclough’s textually-oriented discourse analysis method (2001, 2003) are used to interrogate the relevant sections of the documents for the ways in which they re-present (sic) and construct the discourses around critical language study. This paper presents the description, interpretation and explanation of the discourses in these documents which constitute part of a larger project in which teacher interviews and classroom teaching are also investigated for the ways in which ‘the critical’ is constructed and contested in knowledge and practice.

Literacy models across nations : literacy and critical literacy in teacher training programs in India

The thrust towards constructivist learning and critical thinking in the National Curricular Framework (2005) of India implies shifts in pedagogical practices. In this context, drawing on grounded theory, focus group interviews were conducted with 40 preservice teachers to ascertain the contextual situation and the likely outcomes of applying critical literacy across the curriculum. Central themes that emerged in the discussion were: being teacher centred/ learner centred, and conformity/autonomy in teaching and learning. The paper argues that within the present Indian context, while there is scope for changes to pedagogy and learning styles, yet these must be adequately contextualised.

Assessment of oral proficiency in EAP programs : a case for pair interaction

Reliability and validity in the testing of spoken language are essential in order to assess learners' English language proficiency as evidence of their readiness to begin courses in tertiary institutions. Research has indicated that the task chosen to elicit language samples can have a marked effect on both the nature of the interaction, including the power differential, and assessment, raising the issue of ethics. This exploratory studey, with a group of 32 students from the Peoples's Republic of China preparing for tertiary study in Singapore, compares test-takers' reactions to the use of an oral proficiency interview and a pair interaction.

Constituting the teacher of reading in contemporary Australian literacy debates

This chapter documents the history of the National Inquiry into the Teaching of Literacy and the subsequent fate of the figure of the teacher, in terms of how the inquiry has acted to background the teacher and bring new figures into prominence. The classroom teacher is being moved out of a central role of authority in literacy education, in spite of claims about the importance of the teacher in parts of the report. Authority is now being placed in the figure of the scientific researcher who decides what the best techniques are, and develops diagnostic tools that the teacher must use in order to decide which of the techniques to apply. Specialist literacy teachers, well “trained”by these experts, are needed to ensure that teachers do what the experts recommend (evidence-based practice). Thus, the classroom literacy teacher becomes a cipher for applying expertly designed techniques and tests.

Direct instruction in mathematics : issues for schools with high Indigenous enrolments : a literature review

Direct instruction, an approach that is becoming familiar to Queensland schools that have high Aboriginal and Torres Strait Islander populations, has been gaining substantial political and popular support in the United States of America [USA], England and Australia. Recent examples include the No Child Left Behind policy in the USA, the British National Numeracy Strategy and in Australia, Effective Third Wave Intervention Strategies. Direct instruction, stems directly from the model created in the 1960s under a Project Follow Through grant. It has been defined as a comprehensive system of education involving all aspects of instruction. Now in its third decade of influencing curriculum, instruction and research, direct instruction is also into its third decade of controversy because of its focus on explicit and highly directed instruction for learning. Characteristics of direct instruction are critiqued and discussed to identify implications for teaching and learning for Indigenous students.

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.

Playing with Grammar in the Early Years : Learning about Language in the Australian Curriculum : English

As teacher/researchers interested in the pursuit of socially-just outcomes in early childhood education, the form and function of language occupies a special position in our work. We believe that mastering a range of literacy competences includes not only the technical skills for learning, but also the resources for viewing and constructing the world (Freire and Macdeo, 1987). Rather than seeing knowledge about language as the accumulation of technical skills alone, the viewpoint to which we subscribe treats knowledge about language as a dialectic that evolves from, is situated in, and contributes to a social arena (Halliday, 1978). We do not shy away from this position just because children are in the early years of schooling. In ‘Playing with Grammar’, we focus on the Foundation to Year 2 grouping, in line with the Australian Curriculum, Assessment and Reporting Authority’s (hereafter ACARA) advice on the ‘nature of learners’ (ACARA, 2013). With our focus on the early years of schooling comes our acknowledgement of the importance and complexity of play. At a time where accountability in education has moved many teachers to a sense of urgency to prove language and literacy achievement (Genishi and Dyson, 2009), we encourage space to revisit what we know about literature choices and learning experiences and bring these together to facilitate language learning. We can neither ignore, nor overemphasise, the importance of play for the development of language through: the opportunities presented for creative use and practice; social interactions for real purposes; and, identifying and solving problems in the lives of young children (Marsh and Hallet, 2008). We argue that by engaging young children in opportunities to play with language we are ultimately empowering them to be active in their language learning and in the process fostering a love of language and the intricacies it holds. Our goal in this publication is to provide a range of highly practical strategies for scaffolding young children through some of the Content Descriptions from the Australian Curriculum English Version 5.0, hereafter AC:E V5.0 (ACARA, 2013). This recently released curriculum offers a new theoretical approach to building children’s knowledge about language. The AC:E V5.0 uses selected traditional terms through an approach developed in systemic functional linguistics (see Halliday and Matthiessen, 2004) to highlight the dynamic forms and functions of multimodal language in texts. For example, the following statement, taken from the ‘Language: Knowing about the English language’ strand states: English uses standard grammatical terminology within a contextual framework, in which language choices are seen to vary according to the topics at hand, the nature and proximity of the relationships between the language users, and the modalities or channels of communication available (ACARA, 2013). Put simply, traditional grammar terms are used within a functional framework made up of field, tenor, and mode. An understanding of genre is noted with the reference to a ‘contextual framework’. The ‘topics at hand’ concern the field or subject matter of the text. The ‘relationships between the language users’ is a description of tenor. There is reference to ‘modalities’, such as spoken, written or visual text. We posit that this innovative approach is necessary for working with contemporary multimodal and cross-cultural texts (see Exley and Mills, 2012). We believe there is enormous power in using literature to expose children to the richness of language and in turn develop language and literacy skills. Taking time to look at language patterns within actual literature is a pathway to ‘…capture interest, stir the imagination and absorb the [child]’ into the world of language and literacy (Saxby, 1993, p. 55). In the following three sections, we have tried to remain faithful to our interpretation of the AC:E V5.0 Content Descriptions without giving an exhaustive explanation of the grammatical terms. Other excellent tomes, such as Derewianka (2011), Humphrey, Droga and Feez (2012), and Rossbridge and Rushton (2011) provide these more comprehensive explanations as does the AC:E V5.0 Glossary. We’ve reproduced some of the AC:E V5.0 glossary at the end of this publication. Our focus is on the structure and unfolding of the learning experiences. We outline strategies for working with children in Foundation, Year 1 and Year 2 by providing some demonstration learning experiences based on texts we’ve selected, but maintain that the affordances of these strategies will only be realised when teaching and learning is purposively tied to authentic projects in local contexts. We strongly encourage you not to use only the resource texts we’ve selected, but to capitalise upon your skill for identifying the language features in the texts you and the children are studying and adapt some of the strategies we have outlined. Each learning experience is connected to one of the Content Descriptions from the AC:E V5.0 and contains an experience specific purpose, a suggested resource text and a sequence for the experience that always commences with an orientation to text followed by an examination of a particular grammatical resource. We expect that each of these learning experiences will take a couple if not a few teaching episodes to work through, especially if children are meeting a concept for the first time. We hope you use as much, or as little, of each experience as is needed. Our plans allow for focused discussion, shared exploration and opportunities to revisit the same text for the purpose of enhancing meaning making. We do not want the teaching of grammar to slip into a crisis of irrelevance or to be seen as a series of worksheet drills with finite answers. Strategies for effective practice, however, have much portability. We are both very keen to hear from teachers who are adopting and adapting these learning experiences in their classrooms. Please email us on b.exley@qut.edu.au or lkervin@uow.edu.au. We’d love to continue the conversation with you over time.

Exploring with Grammar in the Primary Years: Learning about Language in the Australian Curriculum: English

This new volume, Exploring with Grammar in the Primary Years (Exley, Kevin & Mantei, 2014), follows on from Playing with Grammar in the Early Years (Exley & Kervin, 2013). We extend our thanks to the ALEA membership for their take up of the first volume and the vibrant conversations around our first attempt at developing a pedagogy for the teaching of grammar in the early years. Your engagement at locally held ALEA events has motivated us to complete this second volume and reassert our interest in the pursuit of socially-just outcomes in the primary years. As noted in Exley and Kervin (2013), we believe that mastering a range of literacy competences includes not only the technical skills for learning, but also the resources for viewing and constructing the world (Freire and Macdeo, 1987). Rather than seeing knowledge about language as the accumulation of technical skills alone, the viewpoint to which we subscribe treats knowledge about language as a dialectic that evolves from, is situated in, and contributes to active participation within a social arena (Halliday, 1978). We acknowledge that to explore is to engage in processes of discovery as we look closely and examine the opportunities before us. As such, we draw on Janks’ (2000; 2014) critical literacy theory to underpin many of the learning experiences in this text. Janks (2000) argues that effective participation in society requires knowledge about how the power of language promotes views, beliefs and values of certain groups to the exclusion of others. Powerful language users can identify not only how readers are positioned by these views, but also the ways these views are conveyed through the design of the text, that is, the combination of vocabulary, syntax, image, movement and sound. Similarly, powerful designers of texts can make careful modal choices in written and visual design to promote certain perspectives that position readers and viewers in new ways to consider more diverse points of view. As the title of our text suggests, our activities are designed to support learners in exploring the design of texts to achieve certain purposes and to consider the potential for the sharing of their own views through text production. In Exploring with Grammar in the Primary Years, we focus on the Year 3 to Year 6 grouping in line with the Australian Curriculum, Assessment and Reporting Authority’s (hereafter ACARA) advice on the ‘nature of learners’ (ACARA, 2014). Our goal in this publication is to provide a range of highly practical strategies for scaffolding students’ learning through some of the Content Descriptions from the Australian Curriculum: English Version 7.2, hereafter AC:E (ACARA, 2014). We continue to express our belief in the power of using whole texts from a range of authentic sources including high quality children’s literature, the internet, and examples of community-based texts to expose students to the richness of language. Taking time to look at language patterns within actual texts is a pathway to ‘…capture interest, stir the imagination and absorb the [child]’ into the world of language and literacy (Saxby, 1993, p. 55). It is our intention to be more overt this time and send a stronger message that our learning experiences are simply ‘sample’ activities rather than a teachers’ workbook or a program of study to be followed. We’re hoping that teachers and students will continue to explore their bookshelves, the internet and their community for texts that provide powerful opportunities to engage with language-based learning experiences. In the following three sections, we have tried to remain faithful to our interpretation of the AC:E Content Descriptions without giving an exhaustive explanation of the grammatical terms. This recently released curriculum offers a new theoretical approach to building students’ knowledge about language. The AC:E uses selected traditional terms through an approach developed in systemic functional linguistics (see Halliday and Matthiessen, 2004) to highlight the dynamic forms and functions of multimodal language in texts. For example, the following statement, taken from the ‘Language: Knowing about the English language’ strand states: English uses standard grammatical terminology within a contextual framework, in which language choices are seen to vary according to the topics at hand, the nature and proximity of the relationships between the language users, and the modalities or channels of communication available (ACARA, 2014). Put simply, traditional grammar terms are used within a functional framework made up of field, tenor, and mode. An understanding of genre is noted with the reference to a ‘contextual framework’. The ‘topics at hand’ concern the field or subject matter of the text. The ‘relationships between the language users’ is a description of tenor. There is reference to ‘modalities’, such as spoken, written or visual text. We posit that this innovative approach is necessary for working with contemporary multimodal and cross-cultural texts (see Exley & Mills, 2012). Other excellent tomes, such as Derewianka (2011), Humphrey, Droga and Feez (2012), and Rossbridge and Rushton (2011) provide more comprehensive explanations of this unique metalanguage, as does the AC:E Glossary. We’ve reproduced some of the AC:E Glossary at the end of this publication. We’ve also kept the same layout for our learning experiences, ensuring that our teacher notes are not only succinct but also prudent in their placement. Each learning experience is connected to a Content Description from the AC:E and contains an experience with an identified purpose, suggested resource text and a possible sequence for the experience that always commences with an orientation to text followed by an examination of a particular grammatical resource. Our plans allow for focused discussion, shared exploration and opportunities to revisit the same text for the purpose of enhancing meaning making. Some learning experiences finish with deconstruction of a stimulus text while others invite students to engage in the design of new texts. We encourage you to look for opportunities in your own classrooms to move from text deconstruction to text design. In this way, students can express not only their emerging grammatical understandings, but also the ways they might position readers or viewers through the creation of their own texts. We expect that each of these learning experiences will vary in the time taken. Some may indeed take a couple if not a few teaching episodes to work through, especially if students are meeting a concept or a pedagogical strategy for the first time. We hope you use as much, or as little, of each experience as is needed for your students. We do not want the teaching of grammar to slip into a crisis of irrelevance or to be seen as a series of worksheet drills with finite answers. We firmly believe that strategies for effective deconstruction and design practice, however, have much portability. We three are very keen to hear from teachers who are adopting and adapting these learning experiences in their classrooms. Please email us on b.exley@qut.edu.au, lkervin@uow.edu.au or jessicam@ouw.edu.au. We’d love to continue the conversation with you over time. Beryl Exley, Lisa Kervin & Jessica Mantei

Negotiating Chineseness through learning Chinese as a Heritage Language in Australia: The role of habitus

While education researchers have drawn on the work of a wide diversity of theorists over the years, much contemporary theory building in these areas has revolved around the work of Pierre Bourdieu. Theory as Method in Research develops the capacity of students, researchers and teachers to successfully put Bourdieu’s ideas to work in their own research and prepare them effectively for conducting Masters and Doctoral scholarships. Structured around four core themes, this book provides a range of research case studies exploring educational identities, educational inequalities, school leadership and management, and research in teacher education. Issues as diverse as Chinese language learning and identity, school leadership in Australia and the school experience of Afro-Trinidadian boys, are covered, intertwined with a set of innovative approaches to theory application in education research. This collection brings together, in one comprehensive volume, a set of education researchers who place Pierre Bourdieu’s key concepts such as habitus, capital and field at the centre of their research methodologies. Full of insight and innovation, the book is an essential read for practitioners, student teachers, researchers and academics who want to harness the potential of Bourdieu’s core concepts in their own work, thereby helping to bridge the gap between theory and method in education research.