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.

Joint identification of infinite-frequency added mass and fluid-memory models of marine structures

This paper addresses the problem of joint identification of infinite-frequency added mass and fluid memory models of marine structures from finite frequency data. This problem is relevant for cases where the code used to compute the hydrodynamic coefficients of the marine structure does not give the infinite-frequency added mass. This case is typical of codes based on 2D-potential theory since most 3D-potential-theory codes solve the boundary value associated with the infinite frequency. The method proposed in this paper presents a simpler alternative approach to other methods previously presented in the literature. The advantage of the proposed method is that the same identification procedure can be used to identify the fluid-memory models with or without having access to the infinite-frequency added mass coefficient. Therefore, it provides an extension that puts the two identification problems into the same framework. The method also exploits the constraints related to relative degree and low-frequency asymptotic values of the hydrodynamic coefficients derived from the physics of the problem, which are used as prior information to refine the obtained models.

Theory and its role in mathematics education

The increased recognition of the theory in mathematics education is evident in numerous handbooks, journal articles, and other publications. For example, Silver and Herbst (2007) examined ―Theory in Mathematics Education Scholarship‖ in the Second Handbook of Research on Mathematics Teaching and Learning (Lester, 2007) while Cobb (2007) addressed ―Putting Philosophy to Work: Coping with Multiple Theoretical Perspectives‖ in the same handbook. And a central component of both the first and second editions of the Handbook of International Research in Mathematics Education (English, 2002; 2008) was ―advances in theory development.‖ Needless to say, the comprehensive second edition of the Handbook of Educational Psychology (Alexander & Winne, 2006) abounds with analyses of theoretical developments across a variety of disciplines and contexts. Numerous definitions of ―theory‖ appear in the literature (e.g., see Silver & Herbst, in Lester, 2007). It is not our intention to provide a ―one-size-fits-all‖ definition of theory per se as applied to our discipline; rather we consider multiple perspectives on theory and its many roles in improving the teaching and learning of mathematics in varied contexts.

Understanding speeding in school zones in Malaysia and Australia using an extended Theory of Planned Behaviour : the potential role of mindfulness

Speeding in school zones is a problem in both Malaysia and Australia. While there are differences between the countries in terms of school zone treatments and more generally, these differences do not explain why people choose to speed in school zones. Because speeding is usually an intentional behaviour, the Theory of Planned Behaviour (TPB) has been used to understand speeding and develop interventions, however it has limitations which can be addressed by extending the model to incorporate other constructs. One promising construct is mindfulness, which can improve the explanatory value of the TPB by taking into account unintentional speeding attributable to a lack of focus on important elements of the driving environment. We explain what mindfulness is (and is not), how it can assist in providing a better understanding of speeding in school zones, and how it can contribute to the development of interventions. We then outline a program of research which has been commenced, investigating the contribution of mindfulness to an understanding of speed choice in school zones in two different settings (Australia and Malaysia) using the TPB.

The potential of critical race theory in decolonizing university curricula

This paper critiques our experiences as non-Indigenous Australian educators of working with numerous embedding Indigenous perspectives curricular projects at an Australian university. Reporting on these project outcomes alone, while useful in identifying limitations, does not illustrate ways in which future embedding and decolonising projects can persist and evolve. Deeper analysis is required of the ways in which Indigenous knowledge and perspectives are perceived, and what ‘embedding’ IK in university curricula truly means to various educational stakeholders. To achieve a deeper analysis and propose ways to invigorate the continuing decolonisation of Australian university curricula, this paper critically interrogates the methodology and conceptualisation of Indigenous knowledge in embedding Indigenous perspectives (EIP) in the university curriculum using tenets of critical race theory. Accordingly, we conduct this analysis from the standpoint that EIP should not subscribe to the luxury of independence of scholarship from politics and activism. The learning objective is to create a space to legitimise politics in the intellectual / academic realm (Dei, 2008, p. 10). We conclude by arguing that critical race theory’s emancipatory, future and action-oriented goals for curricula (Dei, 2008) would enhance effective and sustainable embedding initiatives, and ultimately, preventing such initiatives from returning to the status quo (McLaughlin & Whatman, 2008).

The potential of combining phenomenography, variation theory and threshold concepts to inform curriculum design in higher education

This chapter describes an innovative method of curriculum design that is based on combining phenomenographic research, and the associated variation theory of learning, with the notion of disciplinary threshold concepts to focus specialised design attention on the most significant and difficult parts of the curriculum. The method involves three primary stages: (i) identification of disciplinary concepts worthy of intensive curriculum design attention, using the criteria for threshold concepts; (ii) action research into variation in students’ understandings/misunderstandings of those concepts, using phenomenography as the research approach; (iii) design of learning activities to address the poorer understandings identified in the second stage, using variation theory as a guiding framework. The curriculum design method is inherently theory and evidence based. It was developed and trialed during a two-year project funded by the Australian Learning and Teaching Council, using physics and law disciplines as case studies. Disciplinary teachers’ perceptions of the impact of the method on their teaching and understanding of student learning were profound. Attempts to measure the impact on student learning were less conclusive; teachers often unintentionally deviated from the design when putting it into practice for the first time. Suggestions for improved implementation of the method are discussed.

Unlocking the learning potential of incarcerated Indigenous and low SES young people; Mathematics outcomes for future success: a discussion paper

This presentation provides a beginning discussion about what the literature reports about incarcerated young people. Incarcerated Indigenous and low SES young people typically have very low literacy and mathematics skills which precludes them from future education and or employment opportunities, thus continuing the cycle of disadvantage, exclusion and despair(Payne, 2007). Being locked out of learning, they are stuck in a cycle of underachievement, a scenario which contributes to unacceptably high levels of recidivism(ACER, 2014). Success at education is considered an important protective factor against delinquent behaviours such as offending, substance abuse and truancy. Youth education and training centres provide educational opportunities for the incarcerated Indigenous youth but achievement continues to be lower than expected, particularly in mathematics. This presentation provides an introductory literature review focusing on incarcerated young people and education. It is also the preliminary writing for a small pilot project currently being conducted in one Youth Education and Training Centre in Australia.

The potential benefits of divergent thinking and metacognitive skills in STEAM learning: A discussion paper

In the wake of an almost decade long economic downturn and increasing competition from developing economies, a new agenda in the Australian Government for science, technology, engineering, and mathematics (STEM) education and research has emerged as a national priority. However, to art and design educators, the pervasiveness and apparent exclusivity of STEM can be viewed as another instance of art and design education being relegated to the margins of curriculum (Greene, 1995). In the spirit of interdisciplinarity, there have been some recent calls to expand STEM education to include the arts and design, transforming STEM into STEAM in education (Maeda, 2013). As with STEM, STEAM education emphasises the connections between previously disparate disciplines, meaning that education has been conceptualised in different ways, such as focusing on the creative design thinking process that is fundamental to engineering and art (Bequette & Bequette, 2012). In this article, we discuss divergent creative design thinking process and metacognitive skills, how, and why they may enhance learning in STEM and STEAM.

An activity theory framework for industrial design

Ethnography has gained wide acceptance in the industrial design profession and curriculum as a means of understanding the user. However, there is considerable confusion about the particularities of its practice accompanied by the absence of an interoperable vocabulary. The consequent interdisciplinary effort is a power play between disciplines whereby the methodological view of ethnography marginalises its theoretical and analytical components. In doing so, it restricts the potential of ethnography suggesting the need for alternative methods of informing the design process. This article suggests that activity theory, with an emphasis on human activity as the fundamental unit of study, is an appropriate methodology for the generation of user requirements. The process is illustrated through the adaptation of an ethnographic case study, for the design of classroom furniture in India.