numeric

Mathscraft is a workshop for junior high school students that aims to give them the experience of doing maths the way research mathematicians do. It is coordinated and sponsored by the ARC Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS), and sessions are conducted by Anthony Harradine, (Prince Alfred College, Adelaide).

In a Mathscraft session there are up to 10 groups, each comprising three students (years 7-10), one teacher and one mathematician. The teams are given mathematical problems and are guided through a problem-solving process. The problems and the process are designed to mimic the mathematics that is done by research mathematicians - exploring, noticing patterns, making conjectures, proving them, figuring out why, and thinking of ways to extend the problem.

In this talk I'll describe the design of the problems and process (with examples), and explain the motivations behind them. I'll also talk about a Professional Development workshop that we ran for teachers in November last year, which had the aim of training them to run Mathscraft sessions in their own local areas. This workshop was sponsored by ACEMS and MATRIX.

A challenge with our large-enrolment courses is to manage assessment resources: questions, quizzes, assignments and exams. We want traditional in-class assessment to be easier, quicker and more reliable to produce, in particular where multiple versions of each assessment is required. Our approach is to

• Manage a library of past assessments
• Generate assessments from the library, with or without randomness
• Algorithmically generate new assessments

We have implemented this within standard software: LaTeX, Ruby, git, and our favourite mathematics software.

We will briefly show off our achievements in 2016, including new features of the software and how we've used them in our teaching. We then invite discussion on we we can do to help our colleagues use these tools.

We report upon insights gained into the BMath through: "Conversations: BMath Experiences". This is a project that was initiated by the BMath Convener in collaboration with NUMERIC. We invited first year BMath students to semi-structured conversations around their experiences in their degree. We will be sharing general insights that we have gained into the BMath through the project.

Speakers: Mike Meylan, Andrew Kepert, Liz Stojanovski and Judy-anne Osborn.

This forum is a follow-on from the seminar that Professor Willis gave three weeks prior, on maths that seems too good to be true; and his ideas for incorporating the surprisingly and enlivening into what and how we teach: he gave as exemplars the miracles of Pythagoreans triples and eigenvalues. A question raised in the discussion at that seminar was if/how might we use assessment to encourage the kinds of learning we would like. This forum will be an opportunity to further that conversation.

Jeff, Andrew and Massoud have each kindly agreed to give us 5 minute presentations relating to the latter year maths courses that they have recently been teaching, to get our forum started. Jeff may speak on his developments in his new course on Fourier methods, Andrew will talk about some of the innovations that were introduced into Topology in the last few offerings which he has been using and further developing, and Massoud has a range of OR courses he might speak about.

Everyone is encouraged to share examples of their own practice or ideas that they have that may be of interest to others.

Mathematics can often seen almost too good to be true. This sense that mathematics is marvellous enlivens learning and stimulates research but we tend to let remarkable things pass without remark after we become familiar with them. The miracles of Pythagorean triples and eigenvalues will be highlights of this talk.

The talk will include some ideas of what could be blending into our teaching program.

It is axiomatic in mathematics research that all steps of an argument or proof are open to scrutiny. However, a proof based even in part on commercial software is hard to assess, because the source code---and sometimes even the algorithm used---may not be made available. There is the further problem that a reader of the proof may not be able to verify the author's work unless the reader has access to the same software.

For this reason open-source software systems have always enjoyed some use by mathematicians, but only recently have systems of sufficient power and depth become available which can compete with---and in some cases even surpass---commercial systems.

Most mathematicians and mathematics educators seem to gravitate to commercial systems partly because such systems are better marketed, but also in the view that they may enjoy some level of support. But this comes at the cost of initial purchase, plus annual licensing fees. The current state of tertiary funding in Australia means that for all but the very top tier of universities, the expense of such systems is harder to justify.

For educators, a problem is making the system available to students: it is known that students get the most use from a system when they have unrestricted access to it: at home as well as at their institution. Again, the use of an open-source system makes it trivial to provide access.

This talk aims to introduce several very powerful and mature systems: the computer algebra systems Sage, Maxima and Axiom; the numerical systems Octave and Scilab; and the assessment system WeBWorK (or as many of those as time permits). We will briefly describe these systems: their history, current status, usage, and comparison with commercial systems. We will also indicate ways in which anybody can be involved in their development. The presenter will describe his own experiences in using these software systems, and his students' attitudes to them.

Depending on audience interests and expertise, the talk might include looking at a couple of applications: geometry and Gr\"obner bases, derivation of Runge-Kutta explicit formulas, cryptography involving elliptic curves and finite fields, or digital image processing.

The talk will not assume any particular mathematics beyond undergraduate material or material with which the audience is comfortable, and will be as polemical as the audience allows.

This talk is a practice talk for an invited talk I will soon give in Indonesia, in which I was asked to present on Education at a conference on Graph Theory.

In 1929 Alfred North Whitehead wrote: "The university imparts information, but it imparts it imaginatively. At least, this is the function it should perform for society. A university which fails in this respect has no reason for existence. This atmosphere of excitement, arising from imaginative consideration, transforms knowledge. A fact is no longer a bare fact: it is invested with all its possibilities."

In the light and inspiration of Whitehead's quote, I will discuss some aspects of the problem and challenge of mathematical education as we meet it in Universities today, with reference to some of the ways that combinatorics may be an ideal vehicle for sharing authentic mathematical experiences with diverse students.

Liz will talk about how the UoN could make more use of the flipped classroom. The flipped classroom is an approach where content is provided in advance to students and instead of the traditional lecture the time is spent interacting with students through worked examples etc.

Liz will examine impacts on student learning, but also consider how to make this approach manageable to staff workloads and how lecture theatres design can be altered to facilitate this new way of learning.

The previous assessment method for MCHA2000 - Mechatronic Systems (which is common to many other courses) allowed students collect marks from assessments and quizzes during the semester and pass the course without reaching a satisfactory level of competency in some topics. In 2013, we obtained permission from the President of Academic Senate to test a different assessment scheme that aimed at preventing students from passing without attaining a minimum level of competency in all topics of the course. This presentation discusses the assessment scheme tested and the results we obtained, which suggest that the proposed scheme makes a difference.

MCHA2000 is a course about modelling, simulation, and analysis of physical system dynamics. It is believed that the proposed model is applicable to other courses.

Bio: A/Prof Tristan Perez, Lecturer of MCHA2000. http://www.newcastle.edu.au/profile/tristan-perez

Yes! Finally there is some discrete maths in the high school curriculum! Well, perhaps.

In this talk I will go over the inclusion of discrete mathematics content in the new national curriculum, the existing plans for its implementation, what this will mean for high school teachers, and brainstorm ideas for helping out, if they need our help. I will also talk about "This is Megamathematics" and perhaps, if we have time, we can play a little bit with "Electracity".

Presenters: Judy-anne Osborn, Ben Brawn, Mick Gladys.

Eric Mazur is a Harvard physicist who has become known for the strategies that he introduced for teaching large first year service (physics) classes, in such a way that seems to improve the students' conceptual understanding of the material whilst not hurting their exam performance. The implementation of the ideas include the use of clicker-like technology (Mick Gladys will talk about his own implementation using mobile phones) as well as lower tech card-based analogues. We will screen a Youtube video showing Professor Mazur explain his ideas, and then describe how we have adapted some of them in maths and physics.

In response to a recent report from Australia's Chief Scientist (Prof Ian Chubb), the Australian government recently sought applications from consortia of universities (and other interested parties) interested in developing pre-service programs that will improve the quality of mathematics and science school teachers. In particular, the programs should:

• be multi-institutional and cross-faculty and
• produce teachers who view mathematics and science as contemporary, dynamic, forward-looking and collaborative human endeavours.

At UoN, a group of us from Education and MAPS produced the outline of a vision for our own BTeach/BMath program which builds on local strengths. In the context of very tight timelines, this became a part of an application together with five other universities. In this seminar we will outline the vision that we produced, and invite further contributions and participation, with a view to improving the BMath/BTeach program regardless of the outcome of the application of which we are a part.