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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.

Since the 1990s, computer algebra systems (CAS) have been available in Australia as hand-held devices designed for students with the expectation that they will be used in the mathematics classroom. The data discussed in this paper was collected as part of a pilot study that investigated first year university mathematics and statistics students' understanding of functions and variables, as well as the use of technology in their last year of school (Year 12). Did their teachers discourage the use of CAS for algebra? Did the students actually learn how to use CAS to support their work in algebra or to support their learning of algebra? Did they find that, given the level of algebra, it was faster to work with pen-and-paper than to correctly enter algebraic expressions? The results reported in this paper are based on items included in a pilot survey. They raise questions rather than provide answers. The results do however tell us that, at least from these first year university students' recollection of their Year 12 experience, most or their VCE mathematics teachers made little use of CAS as a pedagogical tool in their classes, despite the institutional approval and encouragement indicated by both the State's curriculum and assessment for the past decade. A better understanding of the barriers to teachers using CAS technology to enhance their pedagogy is needed and then perhaps more effective professional learning programs can be provided for teachers.

This paper presents a study about using scientific simulations to enhance the process of mathematical modelling. The main component of the study is a lesson whose major objective is to have students mathematise a trajectory of a projected object and then apply the model to formulate other trajectories by using the properties of function transformations. It was hypothesised that situating the lesson in a modelling environment would enhance the meaning of transformations that are not often conceptualised in mathematics textbooks. The lesson is guided by inductive reasoning. As a medium of data gathering, a free simulation called "Projectile Motion" was used (available at http://phet. colorado.edu/sims/projectile-motion/projectile-motion_en.html). The inductively organised stages of the activity described in this paper were conducted with a group of (N = 22) mathematics students in a high school in Texas. The students' verbal reflections upon this type of novel learning environment supported the study hypothesis. Their perception of the process of studying function transformations has evolved into a meaningful and purposeful experience. Although, the unit was developed for high school math curriculum in the US, its objectives reflect the aims and scope of Australian math curriculum. The Victorian Certificate of Education Study Design (VCAA, 2010) states that students should model investigate and solve problems in unfamiliar situations. The proposed lesson supports this aim.

The importance of actively engaging in mathematics discourse in order to learn mathematics is well recognized. In this paper, I use Basil Bernstein's concepts of pedagogic discourse to document and analyse academic learning time of students in Years 8 and 9 at a suburban lower secondary school: in particular, for what proportion of class time students reported being academically engaged, their explanations for this engagement and how they felt about the discourse. It was found that many students had disengaged from mathematical endeavour as a result of the failure of the instructional discourse either to engage students or to serve the purpose of developing discipline-specific content knowledge. The reasons for this relate to the overemphasis on mundane mathematics resulting in some students lacking the cognitive tools to engage with the concepts and having neither the intrinsic nor instrumental motivation to persist with secondary school esoteric mathematics. The implications for mathematics curriculum development are discussed.

In this paper, the authors describe the initial stage of developing a framework designed to support out-of-field, less experiences or isolated mathematics and science teachers to make decisions about the use of resources in their teaching. The process highlighted the complexity and extent of the knowledge on which expert teachers draw in making such decisions and thus underscored the enormity of the task of teaching out-of-field. The eventual product, the Science, Technology, Engineering and Mathematics: Critical Appraisal for Teachers (STEMCrAfT) framework has proven useful not only for the target audience, but also as a tool for colleagues who take on a mentoring role. The authors begin with a brief description of teacher knowledge before describing the project and then presenting what they unearthed about expert teachers' thinking and knowledge.

This article aims to illustrate a process of making connections, not between mathematics and other activities, but within mathematics itself--between diverse parts of the subject. Novel connections are still possible in previously explored mathematics when the material happens to be unfamiliar, as may be the case for a learner at any career stage. The geometrical configuration explored in this paper, now known as "Ford circles" after Lester R. Ford, Sr. (1886-1967), is related to ideas about mutually tangent circles that were studied by, among others, Apollonius of Perga in the third century BC and by René Descartes in the 17th century. This exposition is intended to conjure the thoughts of a hypothetical mathematician attempting to find and explain some connections, in the process exploring some lines that turn out to be unproductive, and making observations that are really non sequiturs, before eventually achieving some success. The author suggests that seemingly innocent mathematical fragments can have connections to many related ideas. If a teacher is in possession of a broad subject knowledge, then the likelihood seems high that it is possible to draw out useful connections in the classroom or in well-designed projects and assignments. For this reason, the author claims that an ever-widening subject knowledge is of utmost importance in a teacher's program of professional development.

This paper explores how a secondary school in western Sydney used educational research as an impetus to change its mathematical education culture over a three year period. Key changes occurred in four areas: leadership; pedagogy; structures for teaching and learning; and mathematical environments. These included increased professional conversations, adoption of a numeracy lesson structure, regular use of manipulatives and open ended tasks and a structured intervention program for mathematically vulnerable students. Critical to the development of these changes were partnerships with a university academic and the CEDP system leadership team as well as school leadership participation in professional learning.

Logarithms continue to play an important role in mathematics (most significantly in calculus), science, and engineering. It is therefore important for students to understand logarithms as real numbers as well as the characteristics of logarithmic functions. Exploration of challenges in understanding logarithms as real numbers and logarithmic functions as well as their graphs provides insight that can be used as the basis for instruction. This paper discusses and shares evidence of students' difficulties collected from various courses over time. The authors share concepts related to logarithms that can help students build an understanding of these functions, and present some ways that misconceptions related to these concepts are manifested to suggest what teachers can listen for as they explore logarithms with students.

When questioned, secondary mathematics teachers in rural and regional schools in Australia refer to their limited opportunities to engage and share experiences with peers in other schools as an under-utilised and cost-effective mechanism to support their professional learning and enhance their students' learning. The paper reports on the creation and evaluation of a network of learning communities of rural secondary mathematics teachers around a common purpose--enhancement and increased engagement of student learning in mathematics. To achieve this goal, teams of teachers from six rural schools identified an issue hindering improved student learning of mathematics in their school. Working collaboratively with support from university personnel with expertise in curriculum, assessment and quality pedagogy, teachers developed and implemented strategies to address an identified issue in ways that were relevant to their teaching contexts. The research study identifies issues in mathematics of major concern to rural teachers of mathematics, the successes and challenges the teachers faced in working in learning communities on the issue they identified, and the efficacy of the professional learning model.

This paper examines the relationships between interests and subject choice in senior secondary schooling, and between interests and occupational choices. Career interest results (N = 7477) were obtained from the "Career Interest Test" ("Version 3.1") administered on the Federal Government's "My Future" website (http://www.myfuture.edu.au) and were then compared with the nature of high school course enrolments and structure of employment. Work-related interests were fairly evenly spread across Outdoor, Practical, Scientific, Creative, Business, Office and People Contact activities. In contrast, employment in Australia was skewed towards Business and Practical activities (48.6%). On the other hand, Mathematics courses (20.1%) and Science (17.1%) dominated senior secondary school enrolments. It is possible that the interests and preferences of Australians are not satisfied either by the curriculum offered to them or by the work opportunities available. (Contains 4 tables and 5 figures.)

In the teaching of calculus, the algebraic derivation of the derivative (gradient function) enables the student to obtain an analytic "global" gradient function. However, to the best of this author's knowledge, all current technology-based approaches require the student to obtain the derivative (gradient) at a single point by implementing differentiation using first principles. This paper shows that the ability of spreadsheets to fit a polynomial to a set of discrete (x,y) points enables students to not just evaluate a gradient at a single point, but at a whole family of points, thus generating the analytic global gradient function of secants without doing any algebraic manipulations. Students can then perform "numerical experiments" to see the effect of taking the limit as the secants tend to tangents of the original function. Finally, students can derive the rules for differentiation through exploration and experimentation, again, without doing any algebraic manipulations. This approach enables the class to focus on the concepts being taught, rather than being hindered by the mechanics of (for example) trying to factorize a cubic polynomial. (Contains 4 figures and 1 table.)

While mathematics education research has become increasingly concerned with issues of equity, including girls' participation in the subject, the field remains troubled with conceptualising and operationalising gender. To date, few studies of gender and school mathematics participation have moved beyond conflating gender with sex or categorising masculinities and femininities through the body. This failure to engage with gender conceptualisation has persisted despite the apparent intractability of girls' underrepresentation in senior secondary mathematics in many contexts, including Australia. In this article, I provide fresh insights into girls' mathematics participation by employing a conceptualisation of gender as heteroglossic to explore the post-compulsory mathematics participation choices of two school students, one girl and one boy. Using these theoretical tools to decentre the students' bodies, I demonstrate that the reasons why these students chose to participate in Mathematics Advanced do not distinguish them by their sex/gender, as would be expected in the monoglossic gender system. While femininity was performed, both students' subject choices were primarily characterised as masculine performances, including establishing themselves as having mathematics brains and seeking to use their mathematics participation to attain prestige. I argue that recognising and normalising girls' masculinity and boys' femininity, rather than simply categorising gender differences, will be essential to increasing girls' belonging and participation in mathematics. This will require greater attention to the differences within, and similarities between, the categories of boy and girl. [ABSTRACT FROM AUTHOR]