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: 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: Thomson, Ian Using 'live editing' it is possible to write code that can be run a section at a time. This makes it easier to spot and correct errors. It can also be used to create an interactive mathematical story.

Abstract: Zembat, Ismail O Most students can follow this simple procedure for division of fractions: 'Ours is not to reason why, just invert and multiply.' But how many really understand what division of fractions means - especially fraction division with respect to the meaning of the remainder. Think about the 'bags problem' and its solution, using only diagrams.

Abstract: Miller, Geoffrey; Obara, Samuel A mathematical mnemonic is a visual cue or verbal strategy that is used to aid initial memorisation and recall of a mathematical concept or procedure. Used wisely, mathematical mnemonics can benefit students' performance and understanding. Explorations into how mathematical mnemonics work can also offer students opportunities to engage in proof and reasoning. This article will firstly illustrate how dissecting the so-called "butterfly method" for adding and subtracting fractions can deepen a student's comprehension of fraction arithmetic. Secondly, the article will exemplify how the same dissection process can be applied to other mathematical mnemonics.

Abstract: Quinnell, Lorna Compared to the use of the word "average" in the media and in everyday conversations, an average is used very precisely in mathematics. This is complicated by the fact that there are three different types of averages: means, medians, and modes. As with other concepts, scaffolding understanding of mathematical averages is important. Such understanding is one of the proficiency strands or key ideas in the 'Australian Curriculum: Mathematics' (ACARA, 2015a). The aim of a focus on understanding avoids superficial statements about averages, and of descriptions referring to methods of calculating averages with no connections to conceptual understanding and to real-life applications. Developing understanding of averages can be achieved through multiple scaffolding activities, including activities that focus on real data, and activities that extend to critical thinking about the use of the words average and median in the media.

Abstract: Roddy, Mark "Why do I need to learn this'" Every teacher has heard this question at one time or another. It is a particularly common refrain in mathematics, especially at higher grade-levels. Students struggle to learn concepts and to demonstrate their mastery of the skills we prescribe, and they want assurances that there is some point. We can, and should, provide students with examples of applications that come from both their everyday lives, and from the lives we see them coming to lead in the future. So, for example, it's not incorrect to say that you must know how to determine the area of a rectangle because then you will be able to estimate how much paint will be needed to cover a wall in your house. That's a good start but it's not enough.

Abstract: Wetherell, Chris This is an edited extract from the keynote address given by Dr Chris Wetherell at the 26th Biennial Conference of the Australian Association of Mathematics Teachers Inc. The author investigates the surprisingly rich structure that exists within a simple arrangement of numbers: the times tables.

Abstract: de Mestre, Neville Around 430 BCE it is reported that a typhoid epidemic carried off about a quarter of the population of Athens in ancient Greece. As usual the gods were blamed for this disaster, but could be approached for help through the high priests in the Temple of Apollo in Delos. When the gods were asked what could be done to halt this raging epidemic, they apparently replied that the altar in the temple would have to be doubled in size.

Abstract: Gough, John Div 'Blokus' is an abstract strategy board game for 2 to 4 players. It uses polyominoes which are plane geometric figures formed by joining one or more equal squares edge to edge (refer Figure 1). Polyominoes have been described as being "a polyform whose cells are squares", and they are classified according to how many cells they have. ie. number of cells. (Wikipedia, 2017 March 19). Polyominoes and other mathematically patterned families of shapes were invented by Solomon Golomb, and popularised by Martin Gardner.

Abstract: Gough, John We are familiar with metric units of measurement, such as metres for length; hectares for area (Figure 1); litres for volume; and grams, kilograms and tonnes for mass.

Abstract: Thomson, Ian When I was a child in a land far away, I scooped up snowflakes and stared at them in wonderment and awe. So meltingly ephemeral. Gone in an instant. And yet there, in the palm of my hand, I held all eternity. But how can that be'

Abstract: King, Alessandra During their middle and early high school years, students generally finalise their attitude towards mathematics and their perception of themselves as students of mathematics, in terms of aptitude, motivation, interest, and competence (NCTM, 2000). Therefore, giving them varied opportunities to foster a positive and successful approach to the study of mathematics is critical, and can help them appreciate the relevance, usefulness, and creativity of the subject. Most teachers are looking for innovative ways to capture, foster, and encourage their students' interest in mathematics, whilst at the same time conveying the required content. Furthermore, various educational organisations extol the power and usefulness of technological tools in the mathematics classroom. For example, the Common Core Standards (CCSSI, 2010) state that mathematically proficient students "are able to use technology to explore and deepen their understanding of concepts" (p. 7). NCTM's Principles to Actions states that "an excellent mathematics program integrates the use of mathematical tools and technology as essential resources to help students learn and make sense of mathematical ideas, reason mathematically, and communicate their mathematical thinking" (2014, p. 78). The Australian Curriculum: Mathematics (ACARA, 2014) includes the use of graphing software to foster the critical and creative thinking processes, and the ability to generate solutions.

Abstract: de Mestre, Neville Suppose that there is an inexhaustible supply of $3 and $5 vouchers from the local supermarket. They may only be exchanged for items that cost an exact number of dollars made up from any combination of the vouchers. What is the highest amount not able to be obtained'

Abstract: Robichaux-Davis, Rebecca R Progressing from additive to multiplicative thinking is critical for the development of middle school students' proportional reasoning abilities. Yet, many middle school mathematics teachers lack a thorough understanding of additive versus multiplicative situations. This article describes a sequence of instructional activities used to develop the proportional reasoning skills of middle school pre-service teachers. The activities could also be implemented in middle school classrooms.

Abstract: Neumann, Hanna Dr Peter Neumann, son of the late Professor Hanna Neumann, will be the keynote speaker at AAMT's biennial conference 'Capital Maths', which will be held in Canberra from 11-13 July 2017. Prof. Hanna Neumann gave the Presidential Address at AAMT's inaugural conference in 1966. The conference was held at Monash University and had the theme of 'mathematical unity'. Below is a transcript of Professor Hanna Neumann's address.

Abstract: Attard, Catherine Mathematics education features regularly in the media. The most recent international testing results highlight a decline in Australia's mathematics achievement when compared to other countries. So, who's responsible' Is it teachers, or should parents and the broader community share some of the blame' Typically, teachers are the first to be blamed because they work at the coal face, spending significant amounts of time with students, making them an easy target. But shouldn't the wider community, as a society that considers it acceptable to proudly claim "I'm not good at maths" take some portion of the blame'

Abstract: Gough, John A response to the opinion piece, The M in STEM: what is it really' John Gough provides a response to the opinion piece, written by Lance Coad (AMT, 72 (2)).

Abstract: Stohlmann, Micah Battleship is a game of guessing, strategy, and logical thought that has been around since the 1930s. In the game, players position ships of various sizes on a grid that their opponent cannot see. Players take turns guessing the location of the ships and the game continues until all of one player's ships are sunk. This game can be adapted to incorporate mathematics by using Desmos, a free online graphing calculator that runs in the window of any modern web browser.

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.