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.