Future directions and perspectives for problem solving research and curriculum development

Since the 1960s, numerous studies on problem solving have revealed the complexity of the domain and the difficulty in translating research findings into practice. The literature suggests that the impact of problem solving research on the mathematics curriculum has been limited. Furthermore, our accumulation of knowledge on the teaching of problem solving is lagging. In this first discussion paper we initially present a sketch of 50 years of research on mathematical problem solving. We then consider some factors that have held back problem solving research over the past decades and offer some directions for how we might advance the field. We stress the urgent need to take into account the nature of problem solving in various arenas of today’s world and to accordingly modernize our perspectives on the teaching and learning of problem solving and of mathematical content through problem solving. Substantive theory development is also long overdue—we show how new perspectives on the development of problem solving expertise can contribute to theory development in guiding the design of worthwhile learning activities. In particular, we explore a models and modeling perspective as an alternative to existing views on problem solving.

Civics and citizenship education in the national history curriculum : conducting the same music or rehearsing an incomplete tune?

This paper raises some questions about teaching and teacher education in the social sciences in response to the decision to implement a national curriculum in Australia. In particular, it contends that the decision to focus on discipline-specific knowledge in the social sciences will not necessarily meet the hopes of the Melbourne Declaration and deliver a 21st century curriculum that prepares students for the future. In doing so, it suggests that social educators need to engage with the broader discourse and political context shaping the push for curriculum reform in Australia and makes reference to the marginalisation of civics and citizenship education in the latest draft of the Australian curriculum: History.

Mentors report on their own mentoring practices

There are only two ways to implement reform in an education system, namely through inservice education of existing teachers and preservice teacher education. Implementing the Australian Curriculum will require targeting both teachers and preservice teachers. Classroom teachers in their roles as mentors have a significant role to play for developing preservice teachers. What mentors do in their mentoring practices and what mentors think about mentoring will impact on the mentoring processes and ultimately reform outcomes. What are mentors’ reports on their mentoring of preservice teachers in science and mathematics? This mixed-method study presents mentors’ reports on their mentoring of primary preservice teachers (mentees) in mathematics (n=43) and science (n=29). Drawing upon a previously validated instrument (Hudson, 2007), this instrument was amended to allow mentors to report on their perceptions of their mentoring. A questionnaire elicited extended written responses that focused on: (1) the mentors’ rapport with their mentees, (2) successful mentoring strategies, (3) aspects that may lead the mentee to feel unsuccessful, and (4) ways to enhance their mentoring skills. Mentors claimed they mentored teaching mathematics more than science. However, 20% or more indicated they did not provide mentoring practices for 25 out of 34 survey items in the science and 9 out of 34 items in the mathematics. Educational reform will necessity mentors to be educated on effective mentoring practices so the mentoring process can be more purposeful. Indeed, mentors who have knowledge of such practices may address the potential issues of more than 20% of mentees not receiving these practices. These mentors also claimed that professional development on effective mentoring can enhance their skills. To ensure the greatest success for an Australian Curriculum will require targeting mentors for professional development in order to assist mentees’ development into the profession.

Comparing mentors’ reports on their own mentoring of primary preservice teachers

Implementing the Australian Curriculum will require targeting both teachers and preservice teachers as enactors of reform. Classroom teachers in their roles as mentors have a significant role to play for developing preservice teachers. What mentors do in their mentoring practices and what mentors think about mentoring will impact on the mentoring processes and ultimately reform outcomes. What are mentors’ reports on their mentoring of preservice teachers for teaching science and mathematics? This quantitative study presents mentors’ reports on their mentoring of primary preservice teachers (mentees) in mathematics (n=43) and science (n=29). Drawing upon a previously validated instrument (Hudson, 2007), this instrument was amended to allow mentors to report on their perceptions of their mentoring. Mentors claimed they mentored teaching mathematics more than science. However, 20% or more indicated they did not provide mentoring practices for 25 out of 34 survey items in the science and 9 out of 34 items in the mathematics. Educational reform will necessity mentors to be educated on effective mentoring practices for mathematics and science so the mentoring process can be more purposeful. Indeed, mentors who have knowledge of such practices may address the potential issues of more than 20% of mentees not receiving these practices. To ensure the greatest success for an Australian Curriculum mentors may need professional development in order to assist mentees’ development into the profession.

Students' perceptions of the relevance of mathematics in engineering

In this paper, we report on the findings of an exploratory study into the experience of students as they learn first year engineering mathematics. Here we define engineering as the application of mathematics and sciences to the building and design of projects for the use of society (Kirschenman and Brenner 2010)d. Qualitative and quantitative data on students' views of the relevance of their mathematics study to their engineering studies and future careers in engineering was collected. The students described using a range of mathematics techniques (mathematics skills developed, mathematics concepts applied to engineering and skills developed relevant for engineering) for various usages (as a subject of study, a tool for other subjects or a tool for real world problems). We found a number of themes relating to the design of mathematics engineering curriculum emerged from the data. These included the relevance of mathematics within different engineering majors, the relevance of mathematics to future studies, the relevance of learning mathematical rigour, and the effectiveness of problem solving tasks in conveying the relevance of mathematics more effectively than other forms of assessment. We make recommendations for the design of engineering mathematics curriculum based on our findings.

External management of curriculum change

At a time of rapid curriculum reform, some schools are turning to external change agents for assistance, but what's the best way to initiate such an approach?

Principals’ and teacher leaders’ perceptions of their role and interaction under current Chinese reform : a case study in Shandong province

This study aims to explore the perceptions of principals and teacher leaders regarding their roles and the interaction between these roles in Chinese urban primary schools at the time of unprecedented curriculum reform. This involves a complexity of factors such as the influence of globalisation, the impact of traditional Chinese cultural attitudes towards education through Confucianism, and the implementation requirements of the current education reforms. All of these wider contextual factors help to shape the leadership practices that are described in the study. A qualitative exploratory case study approach has been utilised to undertake this investigation. The conceptual framework for this study draws upon scholars‘ work from Western countries but has been adapted in order to address three research questions for the study‘s focus on the context in Shandong province, Mainland China. Three research questions were addressed: First, what are principals‘ perceptions of their leadership roles in Mainland China under current educational reform? Second, what are teacher leaders‘ perceptions of their leadership roles in Mainland China under current educational reform? And finally, what are principals‘ and teacher leaders‘ perceptions of how their roles interact? With reference to the principals in the study, the findings confirm Gurr‘s (2008) comprehensive leadership model relating to four roles, specifically, learning and teaching, symbolic and cultural awareness, future orientation, and accountability. Significantly, some sub-roles that emerge from the data are uniquely Chinese. For example, school culture construction is a very deliberate process in which principals and their staff talked openly about and were involved in creating a positive school climate comprising spiritual, material, and system dimensions. Another finding relates to school feature construction. This refers to the process that principals and staff used to make their schools distinctive and different from other schools and included such features as the school‘s philosophy and the school-based curriculum. In seeking to understand the nature of teacher leadership in Chinese primary schools, this research confirms some findings identified in Western literature. For instance, teacher leaders in Shandong province were involved in decision-making, working with parents and community members, undertaking and planning professional development for staff, and mediating between colleagues (Day & Harris, 2002; Harrison & Killion, 2007; Leithwood, Jantzi, & Steinbach, 1999; Muijs & Harris, 2006; Smylie, 1992). However, some new aspects, such as a heightened awareness of the importance of accountability, emerge from this study. The study‘s conceptual framework also draws upon some significant insights from micropolitics and, in particular, two core constructs, namely cooperation and conflict (Blase, 1991), to explore the interactions between principals and teacher leaders. In this study, principals and teacher leaders employed exchange and facilitation as two strategies in cooperative processes; and they adopted enforcement and compromise in conflictive processes. Finally, the study‘s findings indicate that principals and teacher leaders were developing new ways of interacting in response to the requirements of significant education reform. Most principals were exercising their power through (Blase, 1991) their teacher leaders who in turn, were working in alignment with their principals to achieve the desired outcomes in schools. It was significant that this form of 'parallel leadership' (Crowther, Ferguson, & Ham, 2009) characterised the teacher leadership roles at this period of change to the curriculum in Mainland China.

The science curriculum : the decline of expertise and the rise of bureaucratise

The content for the school science curriculum has always been an interplay or contest between the interests of a number of stakeholders, who have an interest in establishing it at a new level of schooling or in changing its current form. For most of its history, the interplay was dominated by the interests of academic scientists, but in the 1980s the needs of both future scientists and future citizens began to be more evenly balanced as science educators promoted a wider sense of science. The contest changed again in the 1990s with a super-ordinate control being exerted by government bureaucrats at the expense of the subject experts. This change coincides with the rise in a number of countries of a market view of education, and of science education in particular, accompanied by demands for public accountability via simplistic auditing measures. This shift from expertise to bureaucratise and its consequences for the quality of science education is illustrated with five case studies of science curriculum reform in Australia.

Assessing the potential of mathematics textbooks to promote deep learning

Curriculum documents for mathematics emphasise the importance of promoting depth of knowledge rather than shallow coverage of the curriculum. In this paper, we report on a study that explored the analysis of junior secondary mathematics textbooks to assess their potential to assist in teaching and learning aimed at building and applying deep mathematical knowledge. The method of analysis involved the establishment of a set of specific curriculum goals and associated indicators, based on research into the teaching and learning of a particular field within the mathematics curriculum, namely proportion and proportional reasoning. Topic selection was due to its pervasive nature throughout the school mathematics curriculum at this level. As a result of this study, it was found that the five textbook series examined provided limited support for the development of multiplicative structures required for proportional reasoning, and hence would not serve well the development of deep learning of mathematics. The study demonstrated a method that could be applied to the analysis of junior secondary mathematics in many parts of the world.

Successful outcomes in vocational education and training courses and mathematics: how pedagogy and expectations influence achievement

This paper reports on a four year Australian Research Council funded Linkage Project titled Skilling Indigenous Queensland, conducted in regional areas of Queensland, Australia from 2009 to 2013. The project sought to investigate Vocational Education and Training (VET) and teaching, Indigenous learners’ needs, employer culture and expectations and community culture and expectations to identify best practice in numeracy teaching for Indigenous VET learners. Specifically it focused on ways to enhance the teaching and learning of courses and the associated mathematics in such courses to benefit learners and increase their future opportunities of employment. To date thirty - nine teachers/trainers/teacher aides and two hundred and thirty - one students consented to participate in the project. Nine VET courses offered in schools and Technical and Further Education Institutes (TAFE) were nominated to be the focus on the study. This paper focuses on student questionnaire responses and interview responses from teachers/trainers one high school principal and five students as a result of these processes, the findings indicated that VET course teachers work hard to adopt contextualising strategies to their teaching; however this process is not always straight forward because of the perceptions of how mathematics has been taught and learned by trainers and teachers. Further teachers, trainers and students have high expectations of one another with the view to successful outcomes from the courses.

Changing agendas in international research in mathematics education

Handbooks serve an important function for our research community in providing state-of-the-art summations, critiques, and extensions of existing trends in research. In the intervening years between the second and third editions of the Handbook of International Research in Mathematics Education, there have been stimulating developments in research, as well as new challenges in translating outcomes into practice. This third edition incorporates a number of new chapters representing areas of growth and challenge, in addition to substantially updated chapters from the second edition. As such, the Handbook addresses five core themes, namely, Priorities in International Mathematics Education Research, Democratic Access to Mathematics Learning, Transformations in Learning Contexts, Advances in Research Methodologies, and Influences of Advanced Technologies...

A continuum to characterise and support teacher interpretation of an innovative curriculum

A continuum for describing the degree to which teachers interpret the various features of a curriculum is presented. The continuum has been developed based upon the observation of classroom practices and discussions with a group of teachers who are using an innovative junior secondary mathematics curriculum. It is anticipated that the ongoing use of the continuum will lead to its improvement as well as the refinement of the curriculum, more focussed support for the teachers,improved student learning, and the building of explanatory theory regarding mathematics teaching and learning.

The place of writing in first grade Kuwaiti english education : a sociological case study

A hybridized society, Kuwait meshes Islamic ideologies with western culture. Linguistically, English exists across both foreign language and second language nomenclatures in the country due to globalization and internationalization which has seen increasing use of English in Kuwait. Originally consisting of listening, speaking, reading and writing, the first grade English curriculum in Kuwait was narrowed in 2002 to focus only on the development of oral English skills, and to exclude writing. Since that time, both Kuwaiti teachers and parents have expressed dissatisfaction with this curriculum on the basis that this model disadvantages their children. In first grade however, the teaching of pre-writing has remained as part of the curriculum. This research analyses the parameters of English pre-writing and writing instruction in first grade in Kuwaiti classrooms, investigates first grade English pre-writing and writing teaching, and gathers insights from parents, teachers and students regarding the appropriateness of the current curriculum. Through interviews and classroom observations, and an analysis of curriculum documents, this case study found that the relationship between oral and written language is more complex than suggested by either the Kuwaiti curriculum reform, or international literature concerning the delayed teaching of writing. Intended curriculum integration across Kuwait subjects is also far more complex than first believed, due to a developmental mismatch between English pre-writing skills and Arabic language capabilities. Findings suggest an alternative approach to teaching writing may be more appropriate and more effective for first Grade students in the current Kuwait curriculum context. They contribute also to an emerging interest in the second and foreign language fields in the teaching of writing to young learners.

Promoting interdisciplinarity through mathematical modelling

This article presents one approach to addressing the important issue of interdisciplinarity in the primary school mathematics curriculum, namely, through realistic mathematical modelling problems. Such problems draw upon other disciplines for their contexts and data. The article initially considers the nature of modelling with complex systems and discusses how such experiences differ from existing problem-solving activities in the primary mathematics curriculum. Principles for designing interdisciplinary modelling problems are then addressed, with reference to two mathematical modelling problems— one based in the scientific domain and the other in the literary domain. Examples of the models children have created in solving these problems follow. A reflection on the differences in the diversity and sophistication of these models raises issues regarding the design of interdisciplinary modelling problems. The article concludes with suggested opportunities for generating multidisciplinary projects within the regular mathematics curriculum.

Graduate Attribute Mapping With the Extended CDIO Framework

The CDIO (Conceive-Design-Implement-Operate) Initiative has been globally recognised as an enabler for engineering education reform. With the CDIO process, the CDIO Standards and the CDIO Syllabus, many scholarly contributions have been made around cultural change, curriculum reform and learning environments. In the Australasian region, reform is gaining significant momentum within the engineering education community, the profession, and higher education institutions. This paper presents the CDIO Syllabus cast into the Australian context by mapping it to the Engineers Australia Graduate Attributes, the Washington Accord Graduate Attributes and the Queensland University of Technology Graduate Capabilities. Furthermore, in recognition that many secondary schools and technical training institutions offer introductory engineering technology subjects, this paper presents an extended self-rating framework suited for recognising developing levels of proficiency at a preparatory level. A demonstrator mapping tool has been created to demonstrate the application of this extended graduate attribute mapping framework as a precursor to an integrated curriculum information model.