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Despite questions about academic rigor, undergraduates use Wikipedia for opportunistic learning: self-regulated study to learn, relearn, or be introduced to concepts. STEM topics are potentially im...

This study provides an overview of the support provided for academic numeracy for first-year students across six Australian regional universities. Survey analysis of university academics provided an overview of the approaches used in academic numeracy in diverse cohorts. Further investigations via semi-structured interviews and secondary data were performed, providing details of the level of academic numeracy required in the subjects offered, identification of at-risk students and strategies for student support, and student responses to service provision. A case study at one university provided a more detailed view of the factors influencing attrition in first-year academic numeracy subjects. This case study highlighted issues related to a one-size-fits-all approach and findings argue for a more nuanced cohort-based approach that combines conventional statistical analysis with analysis that provides a more detailed view of complex scenarios. The study suggests that while support services are not responding well to the issue of attrition, better targeting individual student support may lead to improvements.

Mathematics teachers are often keen to find ways of connecting mathematics with the real world. One way to do so is to teach mathematical modelling using real data. Mathematical models have two components: a model structure and parameters within that structure. Real data can be used in one of two ways for each component: (a) to validate what theory or context suggests or (b) to estimate from the data. It is crucial to understand the following: the implications of using data in these different ways, the differences between them, the implications for teaching and how this can influence students’ perceptions of the real-world relevance of mathematics. Inappropriately validating or estimating with data may unintentionally promote poor practice and (paradoxically) reinforce in students the incorrect idea that mathematics has no relevance to the real world. We recommend that teachers approach mathematical modelling through mathematizing the context. We suggest a framework to support teachers’ choice of modelling activities and demonstrate these using examples.

Secondary mathematics prospective teachers can have conflicting experiences during their initial teacher education programme about the most appropriate pedagogies for their own learning and future classrooms. This chapter explores the beliefs of mathematics teacher educators (mathematics educators and mathematicians) to investigate how these inform their knowledge and practice and how prospective teachers describe differences in the beliefs communicated by those who teach them. In this mixed-methods study, Australian mathematicians and mathematics educators were surveyed about their beliefs about mathematics and mathematics teaching and learning. Follow-up interviews further explored their beliefs and decision-making about pedagogy used with prospective teachers. Prospective teachers completed the same survey, and interviews further explored the meanings of mathematics and mathematics teaching and learning that they take from their studies. Boundary dialogues between mathematicians and mathematics educators will allow them to collaborate to develop greater coherence for prospective teachers across their studies and promote school students’ outcomes.

This chapter presents a review of the re-emergence of spatial reasoning in Australasia as a potentially powerful but under-utilised bridging mechanism between real-world experiences and mathematics teaching and learning. This is the first time a chapter has been dedicated solely to spatial reasoning in the Mathematics Education Research Group of Australasia’s (MERGA’s) four yearly review and hence the chapter outlines preliminary studies that have formed the basis for the research profiled in the 2016–2019 period. The focus on primary years (Foundation to Year six) mathematics reflects a resurgence of insights from the 1980s amplified as a research focus on the interaction of spatial reasoning and mathematics development during childhood. Because mathematical concept formation is connected to interaction with the three-dimensional world in both a mathematical and non-mathematical way it will be important to spatialise the primary curriculum. The review includes coverage of the work of established Australasian research projects, along with smaller studies and literature emanating from intervention programs that are not nominally spatial, but have spatial underpinnings or spatial reasoning components. While further research is needed to explore teacher knowledge and practice, this chapter acknowledges the valuable contributions and global influence of re-emerging Australasian research.

The role of Wikipedia for learning has been debated because it does not conform to the usual standards. Despite this, people use it, due to the ubiquity of Wikipedia entries in the outcomes from po...

Middle year students often do not see the mathematics in the real world whereas the Australian Curriculum: Mathematics aims for students to be “confident and creative users and communicators of mathematics” (Australian Curriculum Assessment and Reporting Authority [ACARA] 2012). Using authentic and real mathematics tasks can address this situation. This paper is an account of how, working within a Knowledge Producing Schools’ framework, a group of middle year students addressed a real community issue, the problem of the lack of a teenage safe space using mathematics and technology. Data were collected for this case study via journal observations and reflections, semi-structured interviews, samples of the students’ work and videos of students working. The data were analysed by identifying the mathematics the students used determining the function and location of the space and focused on problem negotiation, formulation and solving through the statistical investigation cycle. The paper will identify the mathematics and statistics these students used as they addressed a real problem in their local community.

A focus on quality assurance of assessment processes in tertiary education within Australia and throughout the world has resulted in a changing landscape of assessment types and grading schemes over the last decade. The use of criteria and standards-based assessment systems are now very commonplace in tertiary education. There are a variety of models now used, but typically they include a criteria sheet and a levelled rubric. An alternative to the traditional matrix-style rubric is the Continua Model of a Guide to Making Judgments (GTMJ). In this paper, we analyse available assessment models and their capacity to guide the marking, grading and moderation of student assessment tasks. We specifically address standards descriptors used to identify the quality expected at each standard. The research was undertaken through a community of practice within the School of Education at a tertiary institution where the collective goal of enhancing assessment grading tools to improve student outcomes was appro...

LEARNING OBJECTIVES After studying this chapter, you should be able to: • improve lesson quality utilising collaborative enhancement based on current scientific knowledge and knowledge of how scientists solve problems, combined with personal and classroom students’ collective knowledge • reflect collaboratively on a teaching lesson using the affect-based critical moment protocol, or other reflection strategies • use an iterated structure to collaborate to improve teaching performance • utilise transferable teaching skills to deliver different types of content in science lessons. Introduction This chapter is the ‘mirror’ chapter to Chapter 1.5. It provides practical examples related to the theoretical outlines in Chapter 1.5, designed to improve competence and confidence in teaching and learning science. The first two examples in this chapter have been selected to illustrate processes of collaborative enhancement and reflection based around lesson delivery of a particular aspect of the Australian Curriculum. The second two examples illustrate how to use collaboration in iterative processes and in the development of transferable teaching skills. Questions Take 10 minutes to consider the following questions related to how this pre-service teacher is using scientific thinking, everyday thinking and problem solving in her classroom. Write in your own words how you might relate the following questions to your classroom teaching. 1 How is the pre-service teacher using problem solving in her introduction to this lesson? 2 It is the period after lunch on a hot Friday afternoon. How is she engaging her students? 3 How is she encouraging students to see science as part of everyday life? 4 What are some other ideas that you could use to engage this group of students? How would you try to find out what their interests are? 5 What benefit do you think this pre-service teacher obtained from collaborative enhancement and reflection? Collaborative enhancement in practice In Chapter 1.5 the term collaborative enhancement was used to refer to collaborations that can be organised and utilised to improve science teaching through enhancement of knowledge about science and how this can be used in the classroom. In this chapter, we show you how this can be done and illustrate some of the experiences that pre-service teachers have had in working with real-world scientists or people who have scientific expertise.

To improve the quality of education, the Kuwaiti Ministry of Education has encouraged schools to implement inquiry-based instruction. This study identifies psychosocial factors that predict teachers’ intention to use inquiry-based instruction in their science classrooms. An adapted model of Ajzen’s (1985) theory of planned behaviour—the Science Adoption Model—was used to study Kuwaiti science teachers’ beliefs. Four hundred and ninety-six teachers from all the government primary schools in Kuwait completed a questionnaire. The data were analysed using the Statistical Package for the Social Sciences (SPSS) to statistically examine the relationships among the constructs of the model. It was found that teachers’ attitudes towards using inquiry-based instruction significantly predicted their capacity to create and deliver inquiry-based lessons. Although Kuwaiti science teachers held positive beliefs about the implementation of inquiry-based instruction, many factors limited their use of this approach in their science classroom. One clear implication from this study is that educators need to overtly consider teachers’ beliefs as inquiry-based instruction reform is implemented.

Learning and teaching in higher education is framed by curriculum models. Over the past decade constructive alignment (Biggs and Tang, 2009, 2011) has become widely accepted as the curriculum planning model for Australian higher education. Constructive alignment privileges learning outcomes in curriculum design, learning and teaching and assessment. In this paper we reflect on the selection and adoption of particular curriculum frameworks in higher education in relation to the purposes and aims of the intended learning experience and the intended future professional. Our reflection is contextualised within the discipline area of mathematics. We argue that the journey towards becoming a member of a professional community is complex and that alternative curriculum models that facilitate a focus on that journey may be more appropriate under certain circumstances. We suggest that when designing a learning experience, it is necessary firstly to consider the type of learner or future professional you are trying to enable and secondly, to choose a curriculum design framework that best supports that goal.

It is widely acknowledged that students come to dislike mathematics, and see it as more irrelevant and distasteful, the further they progress through their schooling. In this chapter we examine this issue through empirical data and relevant literature to identify possible stages in students’ schooling where their affective views of mathematics appear to change. We also discuss key features of their mathematics education and schooling at these critical times and identify pedagogical practices that may be appropriate to ameliorate any apparent declines. The quantitative data showed that: in general the students did see mathematics as useful, but there was a decrease in students’ attitude to, and confidence with, mathematics at the transition to secondary school but this was not inclusive of all students. The qualitative data showed that students want challenging material, opportunities to collaborate and teacher support in their mathematics classes. This has implications for researchers and mathematics educators, policy makers and curriculum developers, and teachers and school leaders engaged in the teaching of mathematics.

The affective domain has been of interest to mathematics educators and researchers for many years. However, there has been a lack of clarity about the nature and make-up of the affective domain, and so in this chapter we begin by first discussing a conceptual background and framework of affect in relation to mathematics education. This is a contested space, and so we outline an understanding of mathematical affect as including beliefs, values, attitudes and emotions, and this will underpin the empirical and theoretical work reported in this book. The relationship between affect and mathematics and mathematics education is specifically discussed, to this end the concept of mathematical identity is posited as a way to include affective, cognitive and conative aspects of learning. Finally, all these aspects of learning mathematics are considered in the light of middle schooling and adolescent students.

Through their middle school years (Years 5–9) students develop beliefs about mathematics and mathematics education which are substantially influenced by their experiences in mathematics classrooms. In this chapter we report and discuss the findings from our empirical studies related to the mathematical beliefs and attitudes of middle year’s students towards mathematics. In general, these students held utilitarian beliefs about mathematics, and they thought that mathematics was important and useful, and this was in-line with the curriculum emphasis on numeracy. However, they also saw mathematics as a gatekeeper to good jobs and future education. Overall, the middle school students had a positive attitude towards mathematics but they did not want to be a mathematician. The data did not indicate that these students had either strong traditional beliefs or high maths anxiety.

There is a general understanding that mathematics is not popular or well-liked among students and people in general. In this chapter we report on findings of t-tests and ANOVAs from a large quantitative New Zealand study (n = 1784) which investigated the affective responses of students vis-a-vis gender, cultural identity, socio-economic status (SES) and type of school. The analysis revealed that: while males liked mathematics more than females, females liked school more; Maori and Pasifika students were more positive towards mathematics, but more likely to have a traditional belief and more anxiety; and, students from lower SES backgrounds were less positive in their affective responses to mathematics and mathematics education. These findings reflect many of the results of previous studies, indicating that some long-standing concerns still remain and these views are deeply ingrained in society, and therefore, demand attention.

There has been a long and consistent history of poor affective outcomes in mathematics education however the findings reported in this book give hope that issues of the past can be overcome. Following a selective review of literature related to mathematics teaching and learning, the concept of mathematical identity is discussed as a way of addressing students’ knowledge, skill and affective development in mathematics. Then mathematics education is considered as a critical practice. Here it is suggested that teaching practices and the practice architectures of mathematics teaching and learning could be more conscious and considerate of the affective dimension if: teachers develop their own mathematical identities; there is understanding of the particular arrangements that enable and constrain mathematics teaching and learning; and, overt attention is paid to students’ emotions and their beliefs about themselves as mathematical learners as the engage in their classroom mathematical experiences. It is concluded that it would be rational, sustainable and just to develop mathematics education that is inclusive of matters related to mathematical affect.

Although much has been written about tertiary students’ and pre-service teachers’ ideas about mathematics very little has included the voices of school students. In this chapter we report on findings from a large quantitative New Zealand study (n = 1784) and four smaller qualitative studies (from Australia and New Zealand) of middle years students to identify their ideas about mathematics and mathematics education. The key findings across the studies were that: mathematics is primarily about numbers and times-tables in particular; students’ feelings about mathematics were related to their success in assessment; students’ affective response diminished with year of schooling; and girls still believe that boys are better at mathematics. It is important that the voice of students is heard, particularly while they are at school, because they are the ones learning, and having their learning effected by, their affective views of mathematics.

Students continue to reject mathematics when they have a choice, particularly in the senior school years and at tertiary levels (Australian Academy of Science, Mathematics and statistics: critical skills for Australia’s future. The national strategic review of mathematical sciences research in Australia, Australian Academy of Science, Canberra, 2006; Grootenboer P, Zevenbergen R, Identity and mathematics: towards a theory of agency in coming to learn mathematics. In: Watson J, Beswick K (eds) Mathematics: essential research, essential practice. Proceedings of the 30th annual conference of the Mathematics Education Research Group of Australasia, Tasmania, vol. 1. MERGA, Adelaide, pp 335–344, 2007). Furthermore, students continue to see mathematics as irrelevant, dull and of little practical value and so many complete their formal mathematics education with poor mathematical identities and feeling mathematically disenfranchised. Despite the hope that modern technologies would result in improved and more effective mathematics pedagogy and improve student interest in this field, student disengagement is a continuing problem. Taking a more open approach to the definition of technology than is often the case in mathematics classrooms, this chapter explores the potential mathematical investigations that make use of what might be thought of as old-fashioned technologies. We demonstrate the role these forgotten technologies play within an investigative approach designed to support the development of particular mathematical concepts for a group of at risk and disenfranchised learners and show how we can develop new relationships between kids and mathematics.

A new self-refocusing slice selection 90 degrees pulse is presented and its incorporation in the SPACE localization sequence described. Experimental comparisons are made with the self-refocusing pulse reported by Geen (H. Geen, S. Wimperis and R. Freeman, J. Magn. Reson. 85, 620 (1990)). The main source of localization error in the SPACE sequence is traced to the hard pi/2 pulse and the development of a shaped-pulse version of the sequence is described. This required the calculation of a slice-selective pulse capable of rotating coherent transverse magnetization to the z-axis. The RF power requirements for these experiments are also discussed.

Water-suppression techniques can be divided into two types, those that result in zero net excitation of the water resonance and those in which the water magnetization is randomized prior to observation of the spectrum of interest. The randomization mechanism may involve selective irradiation, use of natural spin relaxation, or application of a homospoil gradient pulse to dephase selectively excited transverse spin coherence. Destruction techniques considered in this paper will involve the latter of these processes. Nonexcitation methods usually involve a binomial-type pulse cluster which results in off-resonance excitation but zero net rotation on resonance ( 1). Although the water-suppression factor of these methods is usually high ( > 1000)) they suffer from the major limitation that the spectral response is either not flat and/ or there is a large linear phase distortion of the spectrum. Destruction techniques are attractive because the final read pulse can be a hard 90” pulse which ensures uniform excitation of the spectrum with minimal phase distortion. The aim of these methods is the establishment of (S,) = (3,) = (&) = 0 over some selective band in frequency space. For those that utilize a pulsed field gradient, selectivity is achieved by the application of a shaped RF pulse which generates transverse spin coherence over a narrow band and the coherence is dephased by the field gradient. In a previous paper (2) we discussed the difficulties of maintaining high-resolution conditions (Au < 1 Hz) during data acquisition following a field gradient pulse. The major problems can be overcome by preemphasis of the gradient pulse and by applying a correction current through the Z0 coil during data acquisition to ensure that the static magnetic field is stable. Decoupling of the gradient coils from the magnet, shim set, and bore tubes by shielding and isolation may also alleviate these induced eddy current problems. In this paper we consider the nature of the shaped pulse to achieve the optimum water suppression. As well, we introduce a new mechanism to achieve water suppression using a pulsed field gradient and a selective noise pulse. All spectra were obtained on a Bruker MSL-200 spectrometer interfaced to an Oxford Instruments 4.7 T, 13 cm vertical bore magnet. Gradient pulses and Z0 correction were controlled by a Bruker MSL preemphasis unit and were applied to the

A novel method for reducing the rf power requirements of selective pulses employed for z magnetization slice inversion in localized NMR spectroscopy is presented. Following slice preparation by the use of frequency‐incremented sine pulses, the slice gradient is reduced, which narrows the frequency width of the slice. This allows the use of relatively low‐power selective inversion pulses, an important consideration for in vivo applications. © Academic Press, Inc.

The new Australian Senior Secondary Curriculum: Mathematics contains more statistics than the existing Australian Curricula. This case study examines how a group of Queensland mathematics teachers ...