Margaret Marshman

Teachers and Textbooks: On Statistical Definitions in Senior Secondary Mathematics.

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 define the word “statistics” and five statistical terms from the new curricula. These definitions are compared to those used in some commonly-used Queensland mathematics textbooks and in the glossaries of new Australian Senior Secondary Curriculum: Mathematics. The findings of this study suggest that many teachers do not have a good understanding of statistical concepts and that they rely on procedural definitions (instrumental understanding). This is reflected in the presentation of statistics in Queensland senior secondary mathematics textbooks. Definitions in the glossaries of the new curricula are generally better but perhaps other simpler concepts could be introduced first to develop relational understanding.

Improving the quality of assessment by using a community of practice to explore the optimal construction of assessment rubrics

Abstract 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 approached through a process of peer review. In our results section, we analyse the efficacy of an internal peer-review model as part of a community of practice and the professional learning about grading tools that occurs.

The Affective Domain, Mathematics, and Mathematics Education

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.

Evaluating Wikipedia as a Self-Learning Resource for Statistics: You Know They'll Use It

ABSTRACT 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 popular search engines. It is important for academic disciplines, including statistics, to ensure they are correctly represented in a medium where anyone can assume the role of discipline expert. In this context, we first develop a tool for evaluating Wikipedia articles for topics with a procedural component. Then, using this tool, five Wikipedia articles on basic statistical concepts are critiqued from the point of view of a self-learner: “arithmetic mean,” “standard deviation,” “standard error,” “confidence interval,” and “histogram.” We find that the articles, in general, are poor, and some articles contain inaccuracies. We propose that Wikipedia be actively discouraged for self-learning (using, for example, a classroom activity) except to give a brief overview; that in more formal learning environments, teachers be explicit about not using Wikipedia as a learning resource for course content; and, because Wikipedia is used regardless of considered advice or the organizational protocols in place, teachers move away from minimal contact with Wikipedia towards more constructive engagement.

Students’ Beliefs and Attitudes About Mathematics and Learning Mathematics

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.

Differences in the Affective Responses of Various Groups

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.

Building Positive Affect in Mathematics

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.

Changes in Affective Responses to Mathematics Through the Middle School Years

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.

Investigating Students’ Ideas About Mathematics and Mathematics Education

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.

Scissors, Papers Rock: Old-World Technologies for Future-Proofing Pedagogy. Re-engaging Students in Mathematics Classrooms

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.