Abstract: Espedido, Rosei; du Toit, Wilhelmina If, from a young age, students were taught that mathematics is not simply number-based content to be memorised but rather, in its purest form, is about acquiring and mastering a logical thought process, there would be less time dedicated to justifying why the learning of mathematics is important. In reality, students are unlikely to find themselves in a devastatingly life-changing situation should they not be able to demonstrate the congruent nature of two triangles. However the approach a student may choose to implement in dealing with the aforementioned situation is integral to the outcome. Learning experiences in mathematics foster the development of skills (including evaluation, reasoning and logical stepwise thinking) which all serve as invaluable tools for life beyond the classroom. So, why are mathematics teachers not more honest when addressing the questions posed by students? Why are they afraid of 'telling it like it is'? Why are we as teachers not making the relationship between mathematics and thinking processes clear enough that students also come to appreciate the content?

Abstract: Proffitt-White, Rob The Teachers First initiative is a grass-roots cluster-model approach for bringing together primary and secondary teachers and school principals: to analyse student performance data; design and practise activities and assessment tools; and promote teaching practices that address students' learning difficulties in mathematics. The balance of both top-down and bottom-up reform processes, seeded with the latest research evidence, allowed teachers to become both competent and confident in their effective teaching of mathematics. Its continued success is testament to our innovative school leaders and passionate teachers.

Abstract: de Mestre, Neville Consider N (> 1) people spaced regularly around the circumference of a circle. Now a circle has 360 degrees, and therefore there are many N for which the angle subtended at the centre of the circle by adjacent people is an integer. Ask your students to find them all. How can 19 19 = 361 help them?

Abstract: Kissane, Barry It seems that calculators continue to be misunderstood as devices solely for calculation, although the likely contributions to learning mathematics with modern calculators arise from other characteristics. A four-part model to understand the educational significance of calculators underpins this paper. Each of the four components (representation, calculation, exploration and affirmation) is highlighted and illustrated, mostly with relatively unsophisticated modern calculators such as those widely accessible to students in years 6-10, but also recognising some calculator features not available to younger Australian students. Intelligent use of calculators at these levels of schooling offers many opportunities for students to develop a solid understanding of key aspects of mathematics through their own actions, provided our apparentobsession with calculators as merely 'answering devices' is overcome.

Abstract: Dawe, Lloyd This paper addresses the continuing need for mathematics teachers to enrich their mathematical knowledge beyond the school curriculum, in order to effectively engage students in creative and imaginative thinking, particularly, but not exclusively, students who show exceptional promise. The author, a retired university professor, works staff and students in a girls' private school in Sydney for this purpose. The paper provides examples of imaginative problem solving gathered over a 5-year period, which has led to significant mathematical insight for both staff and students. It promotes the realisation of mathematical potential of students concurrently with the professional development of teachers. It is argued that this best happens in mathematics classrooms with experienced mathematics educators working alongside teachers.

Abstract: Espedido, Rosei Review(s) of: The smartest kids in the world and how they got that way, by Amanda Ripley, Publisher, Simon and Schuster Paperbacks, ISBN 978-1-4516-5442-4.

Abstract: de Mestre, Neville If you missed the recent great article in the Australian Mathematics Teacher (2015) by Pat Graham and Helen Chick, I strongly recommend that you obtain a copy and put it into practice in your classroom. As outlined in their paper, an incredibly useful set of information about the mathematical ability of your students will be revealed. You can look at the way your students try to solve the 20 matchsticks problem, their method of recording, their errors, and also the ramifications of the questions that they ask. When your students have completed and discussed the 20 matchsticks problem, they should be ready to tackle the following extensions.

Abstract: Perkins, Karen The topics of decimals and polygons were taught to two classes by using challenging tasks, rather than the more conventional textbook approach. Students were given a pre-test and a post-test. A comparison between the two classes on the pre- and post-test was made. Prior to teaching through challenging tasks, students were surveyed about their mindset in regards to mathematics and how they think they learn best. They were surveyed again at the completion of the project to see if there were any changes.

Abstract: Espedido, Rosei Review(s) of: Maths handbook for teachers and parents; Explaining mathematical content and proficiencies, by Jack Bana, Linda Marshall and Paul Swan, Publisher RIC Publications Pty Ltd, ISBN 978-1-922116-79-6.

Abstract: Goos, Merrilyn At the special conference celebrating the 50th anniversary of the Australian Association of Mathematics Teachers (AAMT), I was asked to speak about challenges and opportunities in teaching mathematics as a stimulus for discussion of AAMT's "future directions". With an open invitation to be a little provocative I chose the five challenges depicted. I have framed these challenges as questions to draw you into a conversation with your colleagues and, vicariously, with me. I end my brief discussion of each challenge with another kind of question that I hope will point us towards opportunities and directions for the next 50 years.

Abstract: Prescott, Anne I stand in a stone-walled classroom in the middle of the hill country in Nepal, surrounded by the expectant faces of local school teachers. A space with no window glass, just shutters, a roof which leaks during the monsoon, and a floor which turns to mud during the same season.

Abstract: Chick, Helen The imagery from Google Maps can reveal some curiosities if you know where to look. Years ago someone discovered what looked like a jet plane sitting incongruously in an Adelaide park. Further analysis revealed the truth: the plane only appeared to be on the ground; it was, in fact, tracking into Adelaide airport and passing over the park when the photograph was taken.

Abstract: Beswick, Kim; Fraser, Sharon; Crowley, Suzanne According to McKenzie, Weldon, Rowley, Murphy and McMillan (2014, p. 67), in 2013, approximately 27% of Australian Year 7 - 10 mathematics teachers had received no teaching methodology education in mathematics and hence could be considered to be teaching out-of-field. The corresponding figure for science teachers was 20%. Furthermore, the likelihood of students being taught mathematics by an out-of-field teacher is greater in provincial or remote schools compared with metropolitan schools (Office of the Chief Scientist, 2012). Teachers in such rural or remote locations also tend to be less experienced and have limited access to professional learning and the support of expert colleagues compared with their metropolitan colleagues (Lyons, Cooksey, Panizzon, Parnell, and Pegg, 2006). Yet when an expert teacher is available, the task of mentoring out-of-field and less experienced colleagues is often undertaken with little acknowledgement or support. In this paper, we describe the initial stage of developing a framework designed to support out-of-field, less experienced 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. We begin with a brief description of teacher knowledge before describing the project and then presenting what we unearthed about expert teachers' thinking and knowledge.

Abstract: Collis, KF Contact with teachers, both formal and informal, over the last couple of years has revealed that, to the average teacher, the new mathematics curricula are causing mathematics to be regarded as more of a 'problem' subject than ever. This indictment of the subject is particularly prevalent among primary and lower secondary teachers, most of whom are not highly sophisticated in the subject matter area and find it difficult to re-orient their teaching and thinking to fit in with the new pattern demanded by what appears to be quite exotic subject matter. Let us examine briefly some of the basic problems involved.

Abstract: McQualter, JW Every mathematics teacher has differing views about how mathematics should be taught. These views overlap to form a body of accepted professional practice. Each mathematics teacher has his own way of selecting, organising and presenting mathematics to pupils. These have been called private theories about teaching mathematics (Bishop, 1971). The development of these private theories is the result of mathematics teachers feeling that public theories on mathematics teaching and learning cannot provide all the answers to the problems faced by individual teachers. Each teacher has developed his or her own set of beliefs about how to teach mathematics. Such beliefs can be grouped in four categories: beliefs about mathematics, beliefs about child development, beliefs about education psychology and beliefs about the relation between learning and teaching. (Rogers, 1979).

Abstract: White, Paul; Mitchelmore, Michael Some research into first year level tertiary students' understanding of calculus (White and Mitchelmore, 1992) revealed results as relevant to the junior years of high school as to the senior years. Basically, we found that many students were unable to use variables when they had to represent some actual, changing quantity and that their notions of functions were very hazy. As a result, even though they were all competent at factorizing,- expanding, solving and manipulating symbols in general, most could not cope with simple applied calculus problems.

Abstract: Moloney, Kevin; Stacey, Kaye Although students first learn about decimal notation in primary schools, it is well known that secondary students in many countries, including Australia, do not have an adequate knowledge of the concepts involved. Even some students who can calculate with decimals do not understand the comparative sizes of the numbers involved. Understanding decimal notation is an important part of basic numeracy. Our society makes widespread use of metric measurement for scientific and everyday purposes. Computers and calculators use decimal digital displays, so making sense of input and output decimal numbers is essential. In this article, we will demonstrate some of the ways in which students think about decimal notation and how this changes as students get older. Our testing at one school, which seems to us to be quite a typical Australian high school, showed that about a quarter of students still had important misconceptions in Year 10. We present a simple test that teachers can use to help them diagnose the mistakes that their students are making and we discuss some of the help that is appropriate. In this article 'decimals' will refer to 'decimal fractions' and 'fractions' will refer to 'common fractions'.

Abstract: Dossel, Steve Introduction teachers of mathematics have been faced for many years with the problems caused by the negative attitudes students have developed towards the subject. Such negative attitudes lead to avoidance strategies, disruptive behaviours, and maths anxiety. In this article, maths anxiety will be defined and its relationship to achievement in mathematics will be explored, before the factors leading to the creation of maths anxiety are discussed in some detail. Finally, methods of prevention or reduction of maths anxiety will be examined.

Abstract: Dawe, Lloyd In recent years there has been a growing body of research which is highly informative about the impact of language in the mathematics classroom. Thus studies on the reading of mathematical text, teacher speech, small group discourse and pupil's understanding of mathematical terms and symbolism appear in the literature. Studies of bilingual children learning mathematics in English as a second language have thrown a good deal of light on cultural forces which shape expectations about the way mathematics should be learned. A whole new perspective of pupils' use of language switching, the active role played by parents and the importance of first language competence has emerged. This paper is an attempt to draw together these different findings and 10 discuss their implications for classroom teachers.

Abstract: Perso, Thelma In discussing the widespread misunderstandings of Australian Aboriginal number systems, John Harris (1990, p.137) recently suggested that "Aboriginal people [want their children]...to learn the three R's [sic] and to grow up Aboriginal". In essence this means that most Aboriginal people recognise that for their children to be 'successful' in a Western society, they need to understand and be fluent or have facility with Western mathematics and standard Australian English, while at the same time embracing the Aboriginal culture and world view.

Abstract: Brinkworth, Peter The term 'numeracy' was coined by the writers of the Crowther Report (1959) in reference to the need for sixth formers in Britain to have an adequate background in scientific and quantitative thinking before proceeding to university or college. In effect, it was an elitist concept of numeracy aimed at providing the nation with numerate scientists, technologists, businessmen and industrialists, who could take advantage of new ways of solving problems using mathematical and statistical techniques.

Abstract: Watson, Jane Readers of E. T. Bell's Men of Mathematics might conclude that the only woman mathematician of any note in history was the Russian Sonya Kovalevsky. This is not so, and as the number of women in all fields of mathematics is on the increase, it is appropriate to fill in some of the gaps in our knowledge of the contributions made to mathematics by women. The first two discussions are followed by examples which are suitable for secondary schools and illustrate the opportunity for combining mathematical history and lore with the curriculum. The third portrait leads into a delightful story with a moral for teachers.

Abstract: Goos, Merrilyn Wondering whether we are really making a difference to young people's mathematics learning is a question that most teachers have probably wrestled with at some stage of their careers. However, evidence from a multitude of research studies shows that students' mathematics learning and their dispositions towards mathematics are indeed influenced - for better or for worse - by the teaching that they experience at school (see Mewborn, 2003, for a review of this research). In other words, teachers do matter. It is difficult for researchers to specify exactly how different types of teaching and teacher qualities affect student achievement because this would require untangling the complicated relationships that exist between teacher characteristics, teaching practices, and student learning. Nevertheless, the general trends in these relationships are clear. In this article I want to illustrate some of these trends by drawing on my experiences in working with pre-service and practising mathematics teachers and their students, and in doing so to propose three reasons why teachers matter. I will then give some examples of how teachers can matter to their students in a more practical sense.

Abstract: White, Paul; Sullivan, Peter; Warren, Elizabeth; Quinlan, Cyril Some teachers are concerned that a problem solving approach to teaching may reduce attention to the key concepts and procedures of mathematics. The polarisation of positions concerning problem solving and investigations versus the notion of a secondary mathematics teacher 'as an expositor and director of learning' (Allen, 1998, p.3) is illustrated by the debate raging in the US tagged the 'Math Wars'. A similar situation has arisen in New South Wales. The Stage 5 mathematics syllabus introduced in 1997 contained a whole strand on mathematical investigations. However, due to some strong opposition claiming such investigations take students away from content focused mathematics, this section was temporarily made optional and is currently under review.

Abstract: Truran, John Chance and data is becoming a more important part of the mathematics curriculum in both primary and secondary schools. It is natural to assume that a question like "What is the probability of ...?" is a good question. After all, it is often asked in school textbooks. But using this question can lead to very serious difficulties.

Abstract: Bouckley, Winifred Reference in the notes on the N.S.W. Higher School Certificate Third' Levell Mathematics Syllabus (1065) to Envelopes has focussed attention on the little-known, activity of Curve Stitching.

Abstract: Koop, Anthony J Hand-held calculators are rapidly becoming a part of the everyday environment of both adults and children. Hand-held calculators, hereafter called calculators, are inexpensive, readily available and can be used, even by young children, with relative ease. The 'Report of the Conference on Needed Research and Development on Handheld Calculators in School Mathematics' (National Institute of Education National Science Foundation, 1977) indicates that calculators "...have the potential for replacing the paper and pencil calculations that have been a major component of elementary school arithmetic."

Abstract: Coad, Lance The acronym STEM doubtless will conjure many meanings, and it will not serve my purpose to discuss or debate them all. I wish, rather, to reflect for a moment only on the function, role or place of mathematics when included as part of an integrated STEM activity, and this from the perspective of a teacher of mathematics. I will not attempt to expound upon what it is that constitutes an integrated STEM activity, save to suggest that it would be an educational activity designed to incorporate elements of some or all of science, technology, engineering and mathematics - and even the arts, in which case we would have a STEAM activity.

Abstract: Gough, John When we hear the words "strategy board game" we tend to think of classic counter-moving games such as chess, draughts (checkers), Reversi (Othello), Chinese checkers, or Stratego. Other board games, such as 'Ludo', and Backgammon use dice to direct the moves of counters.

Abstract: de Mestre, Neville Nichomachus was a Greek who lived around 100 AD near Jerusalem. He was the first to publish the link between number and geometry.

Abstract: Nivens, Ryan Andrew As many students can attest, cars are interesting. They come in various colours, they have interesting accessories, and they move us to where we want to go. Many years ago, the students of Pythagoras thought that numbers were interesting and had a saying that "All is number." As children are taught to embrace mathematics as a dynamic and useful subject, we can show them an interesting context of mathematics where cars and numbers intersect in licence plates.

Abstract: Espedido, Rosei Review(s) of: Learning to love math: Teaching strategies that change student attitudes and get results, by Judy Willis, M.D., Publisher ASCD Publications, ISBN 978-1-4166-1036-6.

Abstract: Moss, Diana L; Lamberg, Teruni This discussion-based lesson is designed to support Year 6 students in their initial understanding of using letters to represent numbers, expressions, and equations in algebra through making thinking explicit, exploring each other's solutions, and developing new mathematical insights.

Abstract: Prodromou, Theodosia New technologies have completely altered the ways that citizens can access data. Indeed, emerging online data sources give citizens access to an enormous amount of numerical information that provides new sorts of evidence used to influence public opinion. In this new environment, two trends have had a significant impact on our increasingly data-driven society: 1) the increasing use of large-scale databases within the open data movement, and 2) the growing use of big data.

Abstract: Ward, Lauren; Lyden, Sarah; Fitzallen, Noleine Context based learning (CBL) is a powerful tool that utilises areas of student interest framed in meaningful contexts to foster development of new skills and understanding. A rich context that students are familiar with can excite their desire to learn and motivate them to develop their knowledge in a wide range of disciplines simultaneously (Broman, Bernholt, and Parchmann, 2015).For middle school students, engineering activities that relate to real-world problems provide suitable CBL contexts for acquiring conceptual scientific and mathematical understanding.

Abstract: Haggar, Fred; Krcic, Senida Selecting the 'better' solution to a problem between the first one that comes to mind and the alternative that may follow is not a 'fait-accompli'. After all, is it better if it is more economical? Or is it better if it is more elegant? Moreover, taking shortcuts does not always lead to a shorter solution. Consider the simple example of a rectangle modified so as to preserve its area.

Abstract: Gough, John Turner's opinion piece Relevance (2015) got me thinking. Do we really need to make the mathematics we teach relevant to our students? Can we do this? Or are there alternatives that circumvent this recurring nightmare catch-cry?

Abstract: Coupland, Mary Recently I attended a symposium for researchers in science education and those interested in such research. The topic was 'Imagining Futures', and as an exercise we were asked to consider two continuums/spectrums of aspects of education that were independent, and placed as intersecting axes. This created four quadrants as a frame for imagining possible futures for science education. For example, one axis could be 'purposes of education', varying from individual empowerment at one end to social good at the other. Another axis might be 'the nature of knowledge', varying from (say) a view that knowledge is fixed, to a view that knowledge is always contestable and changing. It was a very interesting day and I found myself thinking later on about the way that our opinions on educational issues are often framed by the use of continuums.

Abstract: Wilkie, Karina J Senior secondary mathematics students who develop conceptual understanding that moves them beyond "rules without reasons" to connections between related concepts (Skemp,1976, 2002, p. 2) are in a strong place to tackle the more difficult mathematics application problems. Current research is examining how the use of challenging tasks at different levels of schooling might help students develop conceptual knowledge and proficiencies in mathematics as promoted in the Australian curriculum - understanding, fluency, problem solving, and reasoning (ACARA, 2009). Challenging tasks require students to devise solutions to more complex problems that they have not been previously shown how to solve, and for which they might develop their own solution methods (Sullivan et al., 2014). Another key area of research is on formative assessment which has been found to be effective for increasing student motivation and achievement under certain conditions (for example, Brookhart, 2007; Karpinski and D'Agostino, 2013).

Abstract: Galligan, Linda A National Numeracy Report (COAG, 2008) and the Australian Curriculum (2014) have recognised the importance of language in mathematics. The general capabilities contained within the Australian Curriculum: Mathematics (2014) highlight literacy as an important tool in the teaching and learning of mathematics, from the interpretation of word problems to the discussion of mathematics in the classroom. The nationally commissioned National Numeracy Report (COAG, 2008), recommended that the language and literacies of mathematics be explicitly taught since language can be a significant barrier to understanding mathematics. As teachers routinely assess students' understanding of mathematics through literacy (often through reading and writing), students may struggle to understand the mathematics because they have specific language difficulties associated with assessment tasks set. Chapter 2 of the National Numeracy Review Report highlights the role of language in mathematics learning, and identifies a number of features of language that can have an impact on understanding mathematics.

Abstract: Lewis, Robert We have all heard the rhyme, and perhaps taught it ourselves to our students. When dividing one fraction by a second fraction, invert, that is, flip the second fraction, then multiply it by the first fraction. To multiply fractions, simply multiply across the denominators, and multiply across the numerators to get the resultant fraction. So by inverting the division of fractions we turn it into an easy multiplication of fractions problem.

Abstract: Cox, Teodora Mathematics teachers are frequently looking for real-life applications and meaningful integration of mathematics and other content areas. Many genuinely seek to reach out to students and help them make connections between the often abstract topics taught in school. In this article I share several ideas to help teachers foster student curiosity about mathematical ideas, by exploring children's literature and other fiction.

Abstract: Bentley, Brendan Have you ever looked at an object and found yourself thinking how visually attractive that object appears to the eye? Interpersonal considerations to one side, we might be referring to the intrinsic properties which appear visibly in physical objects or images. For instance, your mind might implicitly declare, "That painting is just fabulous", "What an amazing looking building", or "What an interesting shape". It may have been a piece of furniture, an item of clothing or even a flower in your garden that virtually demanded your attention.