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This is the report of an investigation in partnership with a team of junior secondary classroom teachers of the potential of posing more challenging tasks to their students. A range of data sources are used to represent the experience of teachers and students in a unit of work that incorporated a range of challenging tasks. Students learned the intended mathematics and they reacted positively to the challenges. The teachers identified both opportunities and constraints in such teaching, especially those related to changes to their pedagogies and assessment of student work.

The Encouraging Persistence Maintaining Challenge (EMPC) Project has been working with secondary teachers in Melbourne as they seek to build persistence in students, during work on challenging mathematics tasks. The authors have developed sequences of tasks in various topic areas for Years 7 and 8, which require students to connect different aspects of mathematics, to devise solution strategies for themselves and to explore more than one pathway to solutions. There is an expectation that students record the steps in their solutions, and justify their thinking to the teacher and other students. The authors have surveyed teachers on their strategies for encouraging student persistence, before and after the experience of teaching some challenging tasks which have been provided to them. This article provides examples of the kinds of challenging tasks teachers are using with students, and share teacher insights on helpful strategies.

Insights into teachers' planning of mathematics reported here were gathered as part of a broader project examining aspects of the implementation of the Australian curriculum in mathematics (and English). In particular, the responses of primary and secondary teachers to a survey of various aspects of decisions that inform their use of curriculum documents and assessment processes to plan their teaching are discussed. Teachers appear to have a clear idea of the overall topic as the focus of their planning, but they are less clear when asked to articulate the important ideas in that topic. While there is considerable diversity in the processes that teachers use for planning and in the ways that assessment information informs that planning, a consistent theme was that teachers make active decisions at all stages in the planning process. Teachers use a variety of assessment data in various ways, but these are not typically data extracted from external assessments. This research has important implications for those responsible for supporting teachers in the transition to the "Australian Curriculum: Mathematics."

Few educational studies have investigated how well information learned by medical students is retained over time. The primary aim of this study was to investigate how much of the paediatric core curriculum undergraduates remembered a year after originally passing their paediatrics examination. In addition, we looked at whether students' repeat performance is related to their approach to learning. Medical students were presented with 8 out of a possible 46 core curriculum short answer questions (Mark 1). A year later these same students were re-tested, without prior warning, on the same 8 questions (Mark 2) and a further 8 questions (Mark 3) from the bank of 46. The participants also completed the Revised two-factor Study Process Questionnaire to characterise their approach to learning. After a year, students scores had diminished by 51.2% (95% CI 48.2-54.2%, p < 0.0001) from a Mark 1 average of 89.1% (standard deviation, SD = 9.2%) to a Mark 2 average of 37.9% (SD 6.1%). Students who reported a superficial approach to learning achieved higher scores for mark 1 (4.1% increase (95 % CI 0.9-7.4%) per one standard deviation unit increase in Surface Approach score (p = 0.01). Neither deep nor surface approach to learning significantly predicted performance a year later (Marks 2 and 3). Students had forgotten more than half of the paediatric core curricular content that they had previously proven that they knew for their summative assessment. Adopting either a deep or superficial approach to learning did not predict ability to retain this information a year later.

Under the auspices of its 'Education Revolution', the Federal Labor Government is currently implementing a national curriculum for schools. Representing an important intervention into educational practice and governance, the Australian Curriculum offers a unique research opportunity, providing substantial scope for the examination of the changing systems and school-level practices entailed in large-scale curriculum reform. Research into the Australian Curriculum also presents a valuable opportunity to develop educational research methodologies that attend to the complex and multifaceted processes of curriculum reform, from systems to classrooms. Taking two of the disciplinary towers of modern curricula (English and mathematics) and Australia's two largest jurisdictions (New South Wales and Victoria) as the focus, this article draws on a three-year Australian Research Council Linkage Project to outline an approach to researching major curriculum reform.

This article draws on the outcomes of a 4-year project where complex instruction was used as the basis for a reform in mathematics teaching in remote Aboriginal communities in Australia. The article describes the overall project in terms of the goals and aspirations for learning mathematics among remote Indigenous Australians. Knowing that the approach had been successful in a diverse setting in California, the project team sought to implement and evaluate the possibilities of such reform in a context in which the need for a culturally responsive pedagogy was critical. Elements of complex instruction offered considerable possibilities in aligning with the cultures of the remote communities, but with recognition of the possibility that some elements may not be workable in these contexts. Complex instruction also valued deep knowledge of mathematics rather than a tokenistic, impoverished mathematics. The strategies within complex instruction allowed for mathematical and cultural scaffolding to promote deep learning in mathematics. Such an approach was in line with current reforms in Indigenous education in Australia where there are high expectations of learners in order to break away from the deficit thinking that has permeated much education in remote Australia. The overall intent is to demonstrate what pedagogies are possible within the constraints of the remote context.

It is widely accepted that mathematical learning builds upon students' prior knowledge and understandings, and their identities. In this study, this phenomenon is explored with indigenous students in remote community schools in outback Australia. Through one-on-one task-based interviews, it was found that these students had some clear understandings of the measurement concepts involved, although these understandings were often idiosyncratic to these students in this context. The task-based one-on-one interview gave better insights into students' knowledge than the written form of the National Assessment Program-Literacy and Numeracy assessment. Nevertheless, the students' conceptions provide a useful basis upon which to build subsequent knowledge, understanding and skills in the forms required by the formal mathematics curriculum.

This article promotes the use of mathematically appropriate, engaging and challenging tasks to support learning that is worthwhile. The authors share insights from a three-lesson design experiment and the three tasks along with the results from their implementation are explored.

The Australian Curriculum: Mathematics encourages teachers to consider seriously the four proficiencies: Understanding, Fluency, Problem Solving and Reasoning. In responding to the reasoning proficiency, many teachers may find that the language of the classroom may well change. In this article, we discuss the meaning given to the term reasoning within the AC:M and elsewhere, share an example of a classroom task with the potential to develop mathematical reasoning, consider the language involved in describing reasoning, and present some survey responses on teachers' current understanding and use of the relevant terms. (Contains 3 tables, 2 figures and 1 footnote.)

At some stage in the planning process, teachers develop or select tasks which prompt the type of activity that can offer students experiences that can help them learn the intended content. This article presents results from an item on a survey that invited teachers to match particular content descriptions with selected tasks. While many teachers matched the tasks with the content descriptions that we anticipated they would, there were also many teachers who chose descriptions that we consider do not match the tasks. It is suggested that teachers should discuss within their planning teams the purpose and potential of particular tasks, and that such discussions also form part of teacher professional learning. It is recommended that the notion of matching tasks to the curriculum is incorporated into teacher learning sessions. (Contains 1 table.)

We are interested in exploring the processes teachers use when planning. We sought responses from teachers on aspects of their planning from a survey of various aspects of their decisions. We found that, while there is diversity in processes teachers use for planning, a consistent theme was that teachers make deliberative decisions at all stages in the planning process. Likewise teachers make active use of assessment information, especially to address the needs of their students. There are important implications from our findings for those who support teachers in the transition to the Australian Curriculum: Mathematics. (Contains 2 tables.)

In recent years, there has been greater attention in research and professional development work to discussion of the kinds of knowledge teachers need to teach effectively in the mathematics classroom. It seems reasonable that in planning at the school level, teaching team level and then specifically for a given lesson, teachers might have a sense of the most important mathematical ideas on which they wish to focus. In this article, we discuss written statements by teachers in surveys regarding the most important ideas on which they intended to focus in their next teaching topic. There was considerable variation in teachers' capacity to articulate these important ideas. We discuss the implications of this for teacher professional learning and planning. (Contains 1 footnote.)

The Australian Curriculum: Mathematics (AC:M) prompts consideration of planning processes teachers typically use (as a whole school, in grade levels, and at the classroom level). In order to gain insights into the nature of the planning decisions teachers make, Australian teachers drawn from every state and territory were invited to respond to a survey on planning processes, during professional learning programs or voluntarily online through the Australian Association of Mathematics Teachers' website. In this article, we provide background to the overall project in which this survey was situated, and describe the process through which the survey was developed. Subsequent articles in this journal detail some important findings from the survey data. (Contains 1 table and 1 footnote.)

Essential to teachers' planning are decisions regarding what should be taught. Curriculum documents are the most obvious authority. But what is a "curriculum document" for a mathematics teacher in Australia? Are there other credible sources of information that Australian teachers draw on when deciding what to teach? This article examines the responses of a national sample of Australian teachers to a survey examining their planning practices. (Contains 2 figures.)

Much research on early measurement learning is small-scale and dependent on the items used. While such research is helpful for indicating the key aspects of learning length, it does not give teachers a clear indication of the expectations for student learning of them. This paper presents substantial data from a large project that used individual interviews to assess student learning against "growth points" or key stages in children's learning, over a range of domains including length. Data from interviews conducted twice a year with more than 1000 children in each of the first three years of school are used to indicate appropriate targets for student achievement. Basically it is suggested that the key targets for the learning of length in the first three years of school are, respectively, learning to compare, learning to use a unit iteratively, and measuring using formal units. (Contains 4 tables.)

Various explanations and solutions have been proposed over the last decade in relation to the implications of students' apparent lack of engagement with middle years schooling in Australia. This article reports on responses to a questionnaire by 333 Year 8 students (aged about 13, in the second year of high school) on perceptions of factors relating to their engagement with the academic curriculum. While the majority of students reported a strong sense of the importance of, and opportunities in, schooling, and saw English, mathematics and science connected to those opportunities, this orientation was not matched by corresponding positive engagement with these same subjects. There was diversity in the responses of students, and it is recommended that schools take steps to identify individual students' perceptions of factors influencing their engagement, and where appropriate, deal with those perceptions. (Contains 7 tables.)

The Task Types and Mathematics Learning project is investigating the opportunities and constraints that teachers experience when using particular types of mathematics tasks. Some assumptions underlying this aspect of the project are: (1) that teachers seeking a balanced curriculum choose to use a mix of types of tasks; (2) open-ended questions offer students and teachers opportunities for both creativity and different ways of thinking about mathematics; and (3) trialling exemplars of particular types of tasks, reflecting on the experience by writing a report, and reporting back to colleagues involves substantial teacher learning, and can form the basis of sustainable professional development. This article explains what is meant by content specific open-ended tasks, illustrates the ways that teachers wrote up trials of such tasks in their classrooms, and uses excerpts from teachers' reporting on their trials at meetings of project teachers from a cluster of nearby schools, to illustrate the type of teacher learning that resulted from this process. (Contains 1 figure.)

This article illustrates a teaching exploration at an Indigenous Community School in the Kimberley region of Western Australia that sought to use a specific way of thinking about particular content domain, subtraction, to develop focused, mathematically-rich learning experiences. First, the authors explain the importance of having clear mathematical goals (knowing where you are going), and then they describe some illustrative activities (how to get there) that were used over the four 90-minute lessons. They also present data that indicate that there was positive student achievement as a result of the experience. (Contains 2 figures.)

Children with neurodevelopmental disabilities such as cerebral palsy (CP), spina bifida, or inborn errors of metabolism frequently have associated gastrointestinal problems. These include oral motor dysfunction leading to feeding difficulties, risk of aspiration, prolonged feeding times, and malnutrition with its attendant physical compromise. Gastrostomy tube feeding is increasingly being used in these children to circumvent oral motor dysfunction and prevent malnutrition. Foregut dysmotility causes several problems such as dysphagia from oesophageal dysmotility, gastro-oesophageal reflux disease, and delayed gastric emptying. Gastro-oesophageal reflux disease is common in these children but often fails to respond to medical management and may require surgical treatment. Finally, constipation is often a problem that may be overlooked in this population. This article focuses on these associated gastrointestinal manifestations and discusses the current diagnostic and therapeutic options available.

A perceived lack of engagement of many students in middle years mathematics classes provides a challenge for educators. In this article we report a project that investigated students' perceptions of the extent to which their own efforts influence their achievement at mathematics and their life opportunities. We conducted 2 hour interviews with over 50 students, as well as collecting other data. The results suggest that a student's orientation to learning mathematics is not predicted by their achievement. Even students who were confident, successful and persistent exhibited short-term goals. It seems that classroom culture may be an important determinant of under-participation in schooling.

The basic unit of school based mathematics teaching is the lesson. This article is a contribution to understanding teacher actions that facilitate successful lessons, defined as those that engage all students, especially those who may sometimes feel alienated from mathematics and schooling, in productive and successful mathematical thinking and learning. An underlying assumption is that lessons can seek to build a sense in the students that their experience has elements in common with the rest of the class and that this can be done through attention to particular aspects of the mathematical and socio-mathematical goals. We examine three teacher actions that address the mathematical goals: using open-ended tasks, preparing prompts to support students experiencing difficulty, and posing extension tasks to students who finish the set tasks quickly; as well as actions that address the socio-mathematical goals by making classroom processes explicit. To illustrate and elaborate these actions, we describe a particular lesson taught to a heterogeneous upper primary (age 11-12) class.

Many students are unsuccessful in the study of school mathematics, not because of some innate ability, but because of pedagogical practices. Bernstein (1996) has argued that pedagogy serves as a mechanism for cultural reproduction, so that for those students whose cultures are different from that represented in and through pedagogy, the task of constructing school mathematics is made more difficult. The paper explores the ways in which a teacher changes the pedagogic relay in order to be more inclusive of her students. Her practice is informed by understanding the ways in which pedagogy is a subtle tool for marginalization in mathematics.

Reviews studies featured in this issue of "Journal of Mathematics Teacher Education" and examines the way that the study of practice can contribute to mathematics teacher education. Studying teaching in simulated or real situations offers considerable potential for both stimulating thinking about the application of theory to practice and creating personal theories for the study of practice. (KHR)

Presents perspectives and issues associated with developments in teacher education in Australia, considering factors that affect teacher education nationally and discussing specific state-based influences on preservice and inservice teacher education. The paper suggests that teacher educators can initiate debate in the education community about the goals and purpose of teacher education. (SM)

Discusses the advantages of teaching with open-ended tasks and compares students' responses to open-ended, closed-area, and perimeter tasks. (ASK)

Reports results from one component of a larger project that explored the classroom potential of content-specific, open-ended tasks. Examines responses from 1200 students to comparable closed and open-ended tasks and explores the effect of using specific contexts for such tasks. Concludes that both open-ended and closed tasks can contribute to effective classroom programs. (Contains 14 references.) (Author/ASK)

A survey of 125 teacher educators' and experienced teachers' views of quality mathematics teaching identified 6 major components: communicating, problem solving, building understanding, engaging, nurturing, and organizing for learning. Presents a model that suggests a way to link the categories. (24 references) (Author/MKR)

Examined the quality of responses of six classes of grade six students to four questions requiring multiple and generalized solutions posed under varying conditions. Results indicated that this type of question can be useful in classrooms because students can respond at a variety of levels. (13 references) (MDH)

A study of beginning elementary teachers' mathematics instruction practices sought to identify the main factors influencing those practices. For all seven teachers studied, the perceived needs and expectations of students affected planning, interactive thinking, and lesson evaluation. (GLR)

Presents three features of "Good" questions: requires students to do more than simply remember a strategy to answer; promotes student learning while answering the question; and have several acceptable answers. Considers how questions can be used to cater to the range of student abilities. (MDH)

Reported is a study of a teaching practice experience which sought to increase the self-awareness of a group of student teachers and to ascertain the extent to which students are able to reflect on their teaching. Discussed are change in schools, and the self-evaluations of student teachers. (CW)

Discussed is the case for problem solving in mathematics classrooms. The characteristics of "good" questions are identified. The assessment of questions and questioning techniques is considered. (CW)