Group composition : influences of optimism and lack thereof

Lesson video and video-stimulated post-lesson interviews were used to study the role of optimism in collaborative problem solving in a Grade 5/6 classroom for the purpose of informing group composition. This study focuses on the activity of two students who differed on the personal characteristic 'optimistic orientation'. It examines how the presence or absence of an optimistic orientation to failures (Seligman, 1995) contributed to these students' interactions with their groups and opportunities for collaborative creation of new knowledge. One group collaborated to develop mathematical knowledge that was new to each group member and the other group did not. These findings raise questions about how to group students who are not yet optimistic to enable collaborative activity, and how to build optimism.

Global education, travel and new imaginaries for teachers' work

This study investigated how teachers‘ knowledge and identities are influenced through their experience of travel. Understanding how teachers make meaning from and respond to travel revealed aspects of knowledge creation and identity formation. Set within contexts of globalisation, the study also investigated global education through analysis of changing definitions and meanings by taking an historical stance.
Through qualitative methodology semi-structured interviews were conducted with two teachers who had recently been on a study tour. The other form of data collection included a collection of four ‗travel‘ stories written by the researcher. The social imaginary was the concept employed to explain and analyse the impact of travel on teachers work and lives.

This small case study of three participants provided a depth of responses to the following three research questions.
1. What is global education?
2. How does the experience of travel shape teachers‘ work and identities?
3. How does teachers‘ work reconfigure global education?
The findings from this study revealed that global education has shifted from a position of marginality in curriculum and teaching practices to a more central location in education policies. The analysis of participants‘ responses to travel as a feature of globalisation, revealed new knowledge, additional teaching pedagogies and greater awareness of stereotypes both held and disclosed from students. The practices and thinking described by participants were consistent with calls for greater cosmopolitan teaching.

This study contributed understanding about how teachers embed global imaginaries in their teaching. This in turn builds understanding around how globalisation is reshaping local contexts and individuals‘ thinking and being. The findings challenge global education as a discrete framework and suggest teachers‘ experiences as influential on education now in a global world. The study confirms that globalisation is reshaping educators‘ work and lives towards a global education.

Numeracy test item readability during transition from pre-school to school

A key test used in Australia to assess the mathematical knowledge of young children uses illustrations of objects such as coins and three-dimensional shapes. This study explored the effects of giving 104 kindergarten children, aged 4-5 years, the questions with either moveable objects or illustrations. It
was found that children who were categorized by their teachers as having “higher levels of numeracy” scored well on test questions using either illustrations or objects, while children who were categorized as having “lower levels of numeracy” scored higher with objects than with illustrations. This result could have implications for consideration of test item readability in relation to graphicacy.

First of all, I split the 24 : strategies for mental computation

In this article, the author sets out some goals and classroom activities for the teaching of mental computation. The author also discusses the importance of allowing children to help each other and explains that there is benefit in children listening to mathematical strategies given by other children.

Leadership to improve mathematics outcomes in low SES schools and school networks

Instructional and transformational leadership is reportedly required to improve the mathematics outcomes of students in low socio-economic status school communities. This study of 43 schools in two networks of schools in rural Victoria explored leadership practices and found evidence to support both these leadership approaches along with distributed leadership practice. School leaders established network and school structures and relationships at various levels of the network and school organisation to enable and support ongoing improvement in teachers’ pedagogical content knowledge and teaching practice and to build the leadership capacity of teachers within their schools. The leaders’ knowledge of effective mathematics teaching practice enabled them to mentor teachers in their school or team and to support the practices of professional learning teams within their school.

Opportunities to promote mathematical content knowledge for primary teaching

Understanding the development of pre-service teachers’ mathematical content knowledge (MCK) is important for improving primary mathematics’ teacher education. This paper reports on a case study, Rose , and her opportunities to develop MCK during the four years of her program. Program opportunities to promote MCK when planning and practicing primary teaching included: coursework experiences and responding to assessment requirements. Discussion includes the Knowledge Quartet: foundation knowledge, transformation, connection and contingency. By fourth-year, Rose demonstrated development of different categories of MCK when practicing her teaching because of her program experiences.

Developing primary pre-service teachers' mathematical content knowledge during practicum teaching

While it is recognised that a teachers' mathematical content knowledge (MCK) is crucial for teaching, less is known about when different categories of MCK develop during teacher education. This paper reports on two primary pre-service teachers, whose MCK was investigated during their practicum experiences in first, second and fourth years of a four-year Bachelor of Education program. The results identify when and under what conditions pre-service teachers' developed different categories of their MCK during practicum. Factors that assisted pre-service teachers to develop their MCK included program structure providing breadth and depth of experiences; sustained engagement for learning MCK; and quality of pre-service teachers' learning experiences.

An aspect of mathematical understanding: the notion of 'connected knowing'

Much advice about teaching for understanding implies that teacher should help children to develop connections between aspects of their experience, knowledge, and skills. This paper outlines points from the literature about different types of connections and describes relevant points from four case study teachers said and did.

Bounded and unbounded knowledge : teaching and learning in a web 2 world

beginning of serious problems for the business models of publishers. The ease with which content can be accessed, copied and distributed disrupts the control of those whose role has been to manage and profit from the intellectual property rights of content producers. In effect, the number of “publishers” increased many fold as the Web and other Internet-based technologies became the dominant mode of content distribution. In education, and in other fields, matters of intellectual property, copyright and quality control came to the fore. More recently, with the advent of web based software that makes publishing online available to anyone with access to the Internet the number of “publishers” and modes of publication have increased massively. The shift from a Web which was, for many a read only environment to a read/write Web poses not only ongoing problems for the traditional distributors of content but also now, for the traditional producers of content and knowledge. In this respect, the role of universities as designers and producers of learning materials for credentialed learning is also under challenge. Just as publishers explore alternative business models to adapt to the new digital environment, now universities have begun to explore new ways of working with so-called Web2 software to support teaching and learning online. In particular, some Web2 software affords new opportunities for and different modes of collaboration, which in the view of some points to student participation in knowledge production. While these developments represent important and significant shifts for universities, this paper draws attention to the lack of empirical data and situated contextual knowledge concerning intellectual property rights for knowledge constructed in a collaborative context. In addition, we explore issues in relation to the maintenance of academic integrity and quality where knowledge building takes place in a collaborative, online environment.

Using everyday experiences in teaching secondary mathematics in Malawi : possibilities and constraints for change

Proponents of socially and culturally oriented mathematics education have argued that teaching approaches which value and connect with the learner's prior knowledge and everyday experience are more likely to promote active, meaningful, relevant and liberatory learning than approaches which rely on transmission and abstract presentation of mathematical content. In Malawi, proposals to reform the outdated secondary mathematics curriculum have been made with the aim of aligning mathematics instruction with the social and political changes in the current Malawian society. Using a case study approach, this study investigated the extent to which everyday experiences could be used as a vehicle for changing the learning and teaching of secondary mathematics in Malawi. The study was collaborative, taking place over a period of five months in severely overcrowded and poorly resourced classes in two schools. It involved three mathematics teachers in a cycle of planning and teaching mathematics lessons based on the use of everyday experiences, and observation of and reflection on these lessons, in order to document the effects of using everyday experiences on student learning and teachers' teaching practices. The data was collected through student questionnaires; classroom observations and fieldnotes; interviews and reflective meetings with teachers; and informal meetings with key education officials in Malawi. Mathematics examination results from students involved in this study and a corresponding group from the previous year were collected. A reflective and critical approach was adopted in the interpretation and discussion of the data. Teachers' participation in this study resulted in heightened awareness of their teaching roles and the value of linking school mathematics with everyday experience. The study also shows that students found mathematics interesting and important to learn despite their lack of success in it. In addition, the study documented a number of constraints to change in mathematics instruction such as teachers' focus on mathematics content and examination requirements, and students' resistance to inquiry learning. It also recorded possibilities and barriers to collaboration both between teachers and researchers, and teachers themselves. The findings of this study are timely since they could serve to inform the reform of the Malawian secondary mathematics curriculum currently being undertaken, which began without a critical examination of the classroom conditions necessary to accommodate a socio-politically relevant mathematics education.

Teacher's professional knowledge and the teaching of reading in the early years

What are the sources of teachers’ professional knowledge for the teaching of reading? This paper reports findings from a study that investigated the role of teachers in the current Research-Policy-Praxis Nexus (RPPN). This was achieved by a specific focus upon constructions of reading in the early years in Victoria, Australia. All of the teacher participants either implemented or coordinated the Victorian Early Years Literacy Program (EYLP) in the primary school setting. These teachers were interviewed in order to hear their views on reading development and reading pedagogy and to identify the sources of this professional knowledge. The findings from this study are important for all teachers and teacher educators as they have implications for teaching practise, teacher education and teacher professional development programs.

First year pre-service teachers' mathematical content knowledge : methods of solution to a ratio question

In this article, pre-service teachers' mathematics content knowledge is explored through the analysis of two items about ratio from a Mathematical Competency, Skills and Knowledge Test. Pre-service teachers' thinking strategies, common errors and misconceptions in their responses are presented and discussed. Of particular interest was the range and nature of common incorrect responses for one whole-whole ratio question. Results suggested pre-service teachers had difficulty interpreting a worded multi-step, ratio (scale) question, with errors relating to ratio and/or conversion of measurement knowledge. These difficulties reveal underdeveloped knowledge of mathematical structure and mathematical connections as well as an inability to deconstruct key components of a mathematical problem. Most pre-service teachers also lacked knowledge of standard procedures and methods of solutions.

Teaching secondary school mathematics : research and practice for the 21st century

For the last decade or so, educational policy makers and researchers in many countries have been calling for significant changes to the way mathematics is taught in secondary schools. Australian mathematics curriculum documents now promote learning goals that go beyond mastery of a pre-determined body of knowledge and procedures - the traditional emphasis on facts, skills, formulae - to include mathematical reasoning and problem solving, communication, and real world applications. There is also pressure to move away from over-reliance on teacher-centred practices such as exposition and individual seatwork, towards activities that promote learners' involvement in constructing, applying, and evaluating mathematical ideas. Further impetus for reform comes from research recommending that if learners are to develop mathematically powerful forms of thinking and habits of mind, then classrooms should immerse them in the authentic practices of the discipline by supporting a culture of collaboration and sense-making. Teaching Secondary School Mathematics - incorporates recent developments in research and practice and applications to teaching mathematics in Australian secondary schools. Covering such areas as curriculum, pedagogy and assessment; teaching mathematical content; equity and diversity in the classroom; and professional and community engagement, it is an invaluable resource for all practising and pre-service mathematics teachers.