Mathematics curriculum reform : reproducing social inequalities

This book is essential reading for Australasian mathematics educators and other researchers with an interest in the history of mathematics curriculum, the culture of mathematics, gender, and social justice issues in mathematics. Drawing on the results of research conducted by the Educational Outcomes Research Unit at the University of Melbourne and historical documents, Richard Teese argues that the education system fails to diffuse the economic and cultural benefits assumed to flow from the completion of secondary schooling.

Identifying effective leadership practices for implementing a new mathematics curriculum in Taipei

This study explores successful junior high school principals’ leadership practices for implementing the reformed mathematics curriculum in Taipei. Avolio and Bass’s (2002) full range leadership theory was used to record data through interviews and observations of five Taipei “Grade A” junior high school principals. Findings revealed that specific leadership practices linked to management by exception-active and contingent reward (transaction leadership), and individualised consideration and idealised influence (transformational) were considered effective for implementing reform measures. Ensuring principals are aware of effective measures may further assist reform agendas.

Assessment and curriculum reform in China : the college English test and tertiary English as a foreign language education.

Educational assessment was a worldwide commonplace practice in the last century. With the theoretical underpinnings of education shifting from behaviourism and social efficiency to constructivism and cognitive theories in the past two decades, the assessment theories and practices show a widespread changing movement. The emergent assessment paradigm, with a futurist perspective, indicates a deviation away from the prevailing large scale high-stakes standardised testing and an inclination towards classroom-based formative assessment. Innovations and reforms initiated in attempts to achieve better education outcomes for a sustainable future via more developed learning and assessment theories have included the 2007 College English Reform Program (CERP) in Chinese higher education context. This paper focuses on the College English Test (CET) - the national English as a Foreign Language (EFL) testing system for non-English majors at tertiary level in China. It seeks to explore the roles that the CET played in the past two College English curriculum reforms, and the new role that testing and assessment assumed in the newly launched reform. The paper holds that the CET was operationalised to uplift the standards. However, the extended use of this standardised testing system brings constraints as well as negative washback effects on the tertiary EFL education. Therefore in the newly launched reform -CERP, a new assessment model which combines summative and formative assessment approaches is proposed. The testing and assessment, assumed a new role - to engender desirable education outcomes. The question asked is: will the mixed approach to formative and summative assessment provide the intended cure to the agony that tertiary EFL education in China has long been suffering - spending much time, yet achieving little effects? The paper reports the progresses and challenges as informed by the available research literature, yet asserts a lot needs to be explored on the potential of the assessment mix in this examination tradition deep-rooted and examination-obsessed society.

Integrating engineering education in the middle school mathematics curriculum

Many nations are experiencing a decline in the number of graduating engineers, an overall poor preparedness for engineering studies in tertiary institutions, and a lack of diversity in the field. Given the increasing importance of mathematics, science, engineering, and technology in our world, it is imperative that we foster an interest and drive to participate in engineering from an early age. This discuission paper argues for the intergration of engineering education within the elementary and middle school mathematics curricula. In doing so, we offer a definition of engineering education and address its core goals; consider some perceptions of engineering and engineering education held by teachers and students; and offer one approach to promoting engineering education within the elementary and middle school mathematics curriculum, namely through mathematical modeling.

Integrating Engineering Experiences within the Elementary Mathematics Curriculum

Engineering education for elementary school students is a new and increasingly important domain of research by mathematics, science, technology, and engineering educators. Recent research has raised questions about the context of engineering problems that are meaningful, engaging, and inspiring for young students. In the present study an environmental engineering activity was implemented in two classes of 11-year-old students in Cyprus. The problem required students to use the data to develop a procedure for selecting among alternative countries from which to buy water. Students created a range of models that adequately solved the problem although not all models took into account all of the data provided. The models varied in the number of problem factors taken into consideration and also in the different approaches adopted in dealing with the problem factors. At least two groups of students integrated into their models the environmental aspect of the problem (energy consumption, water pollution) and further refined their models. Results provide evidence that engineering model-eliciting activities can be successfully integrated in the elementary mathematics curriculum. These activities provide rich opportunities for students to deal with engineering contexts and to apply their learning in mathematics and science to solving real-world engineering problems.

Integrating engineering education within the elementary and middle school mathematics curriculum

Many nations are experiencing a decline in the number of graduating engineers, an overall poor preparedness for engineering studies in tertiary institutions, and a lack of diversity in the field. Given the increasing importance of mathematics, science, engineering, and technology in our world, it is imperative that we foster an interest and drive to participate in engineering from an early age. This discussion paper argues for the integration of engineering education within the elementary and middle school mathematics curricula. In doing so, we offer a definition of engineering education and address its core goals; consider some perceptions of engineering and engineering education held by teachers and students; and offer one approach to promoting engineering education within the elementary and middle school mathematics curriculum, namely through mathematical modeling.

The impact of outcomes-driven curriculum reform on teacher perspectives of professional practice

This thesis is the result of an investigation of a Queensland example of curriculum reform based on outcomes, a type of reform common to many parts of the world during the last decade. The purpose of the investigation was to determine the impact of outcomes on teacher perspectives of professional practice. The focus was chosen to permit investigation not only of changes in behaviour resulting from the reform but also of teachers' attitudes and beliefs developed during implementation. The study is based on qualitative methodology, chosen because of its suitability for the investigation of attitudes and perspectives. The study exploits the researcher's opportunities for prolonged, direct contact with groups of teachers through the selection of an over-arching ethnography approach, an approach designed to capture the holistic nature of the reform and to contextualise the data within a broad perspective. The selection of grounded theory as a basis for data analysis reflects the open nature of this inquiry and demonstrates the study's constructivist assumptions about the production of knowledge. The study also constitutes a multi-site case study by virtue of the choice of three individual school sites as objects to be studied and to form the basis of the report. Three primary school sites administered by Brisbane Catholic Education were chosen as the focus of data collection. Data were collected from three school sites as teachers engaged in the first year of implementation of Student Performance Standards, the Queensland version of English outcomes based on the current English syllabus. Teachers' experience of outcomes-driven curriculum reform was studied by means of group interviews conducted at individual school sites over a period of fourteen months, researcher observations and the collection of artefacts such as report cards. Analysis of data followed grounded theory guidelines based on a system of coding. Though classification systems were not generated prior to data analysis, the labelling of categories called on standard, non-idiosyncratic terminology and analytic frames and concepts from existing literature wherever practicable in order to permit possible comparisons with other related research. Data from school sites were examined individually and then combined to determine teacher understandings of the reform, changes that have been made to practice and teacher responses to these changes in terms of their perspectives of professionalism. Teachers in the study understood the reform as primarily an accountability mechanism. Though teachers demonstrated some acceptance of the intentions of the reform, their responses to its conceptualisation, supporting documentation and implications for changing work practices were generally characterised by reduced confidence, anger and frustration. Though the impact of outcomes-based curriculum reform must be interpreted through the inter-relationships of a broad range of elements which comprise teachers' work and their attitudes towards their work, it is proposed that the substantive findings of the study can be understood in terms of four broad themes. First, when the conceptual design of outcomes did not serve teachers' accountability requirements and outcomes were perceived to be expressed in unfamiliar technical language, most teachers in the study lost faith in the value of the reform and lost confidence in their own abilities to understand or implement it. Second, this reduction of confidence was intensified when the scope of outcomes was outside the scope of the teachers' existing curriculum and assessment planning and teachers were confronted with the necessity to include aspects of syllabuses or school programs which they had previously omitted because of a lack of understanding or appreciation. The corollary was that outcomes promoted greater syllabus fidelity when frameworks were closely aligned. Third, other benefits the teachers associated with outcomes included the development of whole school curriculum resources and greater opportunity for teacher collaboration, particularly among schools. The teachers, however, considered a wide range of factors when determining the overall impact of the reform, and perceived a number of them in terms of the costs of implementation. These included the emergence of ethical dilemmas concerning relationships with students, colleagues and parents, reduced individual autonomy, particularly with regard to the selection of valued curriculum content and intensification of workload with the capacity to erode the relationships with students which teachers strongly associated with the rewards of their profession. Finally, in banding together at the school level to resist aspects of implementation, some teachers showed growing awareness of a collective authority capable of being exercised in response to top-down reform. These findings imply that Student Performance Standards require review and, additional implementation resourcing to support teachers through times of reduced confidence in their own abilities. Outcomes prove an effective means of high-fidelity syllabus implementation, and, provided they are expressed in an accessible way and aligned with syllabus frameworks and terminology, should be considered for inclusion in future syllabuses across a range of learning areas. The study also identifies a range of unintended consequences of outcomes-based curriculum and acknowledges the complexity of relationships among all the aspects of teachers' work. It also notes that the impact of reform on teacher perspectives of professional practice may alter teacher-teacher and school-system relationships in ways that have the potential to influence the effectiveness of future curriculum reform.

Modelling as a vehicle for philosophical inquiry in the mathematics curriculum

Philosophical inquiry in the teaching and learning of mathematics has received continued, albeit limited, attention over many years (e.g., Daniel, 2000; English, 1994; Lafortune, Daniel, Fallascio, & Schleider, 2000; Kennedy, 2012a). The rich contributions these communities can offer school mathematics, however, have not received the deserved recognition, especially from the mathematics education community. This is a perplexing situation given the close relationship between the two disciplines and their shared values for empowering students to solve a range of challenging problems, often unanticipated, and often requiring broadened reasoning. In this article, I first present my understanding of philosophical inquiry as it pertains to the mathematics classroom, taking into consideration the significant work that has been undertaken on socio-political contexts in mathematics education (e.g., Skovsmose & Greer, 2012). I then consider one approach to advancing philosophical inquiry in the mathematics classroom, namely, through modelling activities that require interpretation, questioning, and multiple approaches to solution. The design of these problem activities, set within life-based contexts, provides an ideal vehicle for stimulating philosophical inquiry.

National curriculum reform and equipping pre-service teachers to teach about Australia in the Asian Century

Currently a range of national policy settings are reshaping schooling and teacher education in Australia. This paper presents some of the findings from a small qualitative pilot study conducted with a group of final year pre-service teachers studying a secondary social science curriculum method unit in an Australian university. One of the study’s research objectives aimed at identifying how students reflected on their capacity to navigate curriculum change and, more specifically, on teaching about Australia and Asia in the forthcoming implementation of the first national history curriculum. The unit was designed and taught by the researcher on the assumption that beginning social science teachers need to be empowered to deal with the curriculum change they’ll encounter throughout their careers. The pilot study’s methodology was informed by a constructivist approach to grounded theory and its scope was limited to one semester with volunteer students. Of the pre-service teacher reflections on their preparedness to teach, this paper reports on the content, pedagogy and learning they experienced in one segment of the unit with specific reference to the new history curriculum’s ‘Australia in a world history’ approach and the development of Asia literacy. The findings indicate that whilst pre-service teachers valued the opportunity to engage with learning experiences which enhanced their intercultural understanding and extended their pedagogical and content knowledge on campus, the nature of the final practicum in schools was also influential in shaping their preparedness to enter the profession.

Globalisation and national curriculum reform in Australia : the push for Asia literacy

This chapter explores the policy context for the push for a national curriculum and the inclusion of Asia literacy for schooling in Australia in the light of current links between globalisation, education and policy analysis and the notion of the learning/knowledge society of the twenty-first century. It is anticipated that discussion of the Australian context will be insightful for those other nations concerned with positioning Asia in school curricula, including for example, New Zealand, Canada, USA and UK. In doing so, the chapter considers the challenges to the implementation of Asia literacy in Australia with specific reference to current and future teachers for, as with many nations, the teaching profession in Australia is on the cusp of generational change as large numbers of teachers aged in their mid to late fifties embark on retirement (Teaching Australia, 2007). A major challenge in addressing these demographic shifts in Australia, lies with meeting the demand for replacement teachers and preparing future teachers (Skilbeck, & Connell, 2004; McKenzie, 2012) with Asia-related knowledge.

EFL teachers' professional dilemmas with moral curriculum reform in Indonesia

This project explored how EFL teachers working in different sectors in Indonesia experienced moral education reform. Teachers working in either state schools or Islamic private schools were interviewed and their classes were observed. The thesis indicated that systemic investment in teachers' professionalism contributed to teachers' emerging dilemmas and their resolutions. Teachers in the better resourced state sector reported more dilemmas related to the implementation of the reform and resolved these dilemmas by using professional judgement, while teachers in the less resourced sector reported dilemmas related to their context and failed to implement the curriculum.

Bhutanese eighth grade students' and teachers' perceptions of their classroom learning environment in relation to the new mathematics curriculum

This thesis examined how Bhutanese eighth grade students and teachers perceived their classroom learning environment in relation to a new standards-based mathematics curriculum. Data were gathered from administering surveys to a sample of 608 students and 98 teachers, followed by semi-structured interviews with selected participants. The findings of the study indicated that participants generally perceived their learning environments favorably. However, there were differences in terms of gender, school level, and school location. The study provides teachers, educational leaders, and policy-makers in Bhutan new insights into students' and teachers' perceptions of their mathematics classroom environments.

Problem solving in a 21st century mathematics curriculum

Research on problem solving in the mathematics curriculum has spanned many decades, yielding pendulum-like swings in recommendations on various issues. Ongoing debates concern the effectiveness of teaching general strategies and heuristics, the role of mathematical content (as the means versus the learning goal of problem solving), the role of context, and the proper emphasis on the social and affective dimensions of problem solving (e.g., Lesh & Zawojewski, 2007; Lester, 2013; Lester & Kehle, 2003; Schoenfeld, 1985, 2008; Silver, 1985). Various scholarly perspectives—including cognitive and behavioral science, neuroscience, the discipline of mathematics, educational philosophy, and sociocultural stances—have informed these debates, often generating divergent resolutions. Perhaps due to this uncertainty, educators’ efforts over the years to improve students’ mathematical problem-solving skills have had disappointing results. Qualitative and quantitative studies consistently reveal mathematics students’ struggles to solve problems more significant than routine exercises (OECD, 2014; Boaler, 2009)...

Curriculum reform in testing and accountability contexts

Recent international educational developments have important implications for the skills and understandings in curriculum and assessment that teachers develop, both in pre-service and in practice. Global developments in curriculum and assessment reform require teachers to utilise a network of knowledges and develop a repertoire of assessment skills and understandings. In a context of testing, accountability and auditing, data analysis skills are increasingly required to examine pedagogic practices for the development of intervention teaching and learning strategies to improve learning outcomes for all students (Marsh, 2009). However, too often the data are used predominantly for accountability purposes that serve at national levels as a catalyst for measurement, comparison and allocation of funding (Lingard and Sellar, 2013). With increased accountability demands brought about by global competitiveness and programs for international measurement of educational attainment, there has also emerged an increase in the use of testing, which in some countries has become the dominant form of assessment. For example in Australia, national testing of students in Years 3, 5, 7 and 9 began in 2008 under the National Australia Program – Literacy and Numeracy (NAPLAN). The results from this program for each school are published on the My School website (www.myschool.edu.au), increasing the competitive nature of the testing and intensifying the demands on teachers and schools. In particular, there has been a shift in the enacted curriculum in Australia to a focus on literacy and numeracy because the curriculum is tested.

Does flexibility in secondary level mathematics curriculum affect degree performance?

The authors have much experience in developing mathematics skills of first-year engineering students and attempting to ensure a smooth transition from secondary school to university. Concerns exist due to there being flexibility in the choice of modules needed to obtain a secondary level (A-level) mathematics qualification. This qualification is based on some core (pure maths) modules and a selection from mechanics and statistics modules. A survey of aerospace and mechanical engineering students in Queen’s University Belfast revealed that a combination of both mechanics and statistics (the basic module in both) was by far the most popular choice and therefore only about one quarter of this cohort had studied mechanics beyond the basic module within school maths. Those students who studied the extra mechanics and who achieved top grades at school subsequently did better in two core, first-year engineering courses. However, students with a lower grade from school did not seem to gain any significant advantage in the first-year engineering courses despite having the extra mechanics background. This investigation ties in with ongoing and wider concerns with secondary level mathematics provision in the UK.