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More mathematical graduates than ever: behind the figures from UOA
by
Bill Barton
Department of Mathematics, University of Auckland
Coauthors: Louise Sherryn
The Pipeline Project is an international project looking at mathematics graduates from secondary and tertiary systems. The New Zealand data, like other countries, has been hard to mine--but we now have a comprehensive time-series for The University of Auckland.
This talk will examine this data and ask questions about some of the trends. We will also relate it to known data from other universities and data overseas.
Date received: October 29, 2008
Annotations and digital ink in teaching electronically and via the access grid ... in Australia and the UK ... and NZ?
by
Bill Blyth
Australian Mathematical Sciences Institute
In recent years it has become common for mathematics lecturers to use computer projection in their lectures and seminar presentations. Often some handwriting on a whiteboard is used for asides: for clarification, for worked examples and sketches. If the handwriting is done electronically, as is necessary over the Access Grid, it is referred to as Digital Ink.
We will give a brief overview of e-teaching approaches. This will include using the beamer class in LaTeX to produce pdf slides (with stepped uncovering of a slide) and annotation of any pdf file using PDF Annotator (and jarnal). We will demonstrate using a TabletPC to produce highlighting (note that a laser pointer is not effective in an AGR) and annotations of pdf "notes" or slides. When using a TabletPC, WindowsXP provides a very good (and fully integrated) Digital Ink with Word, PowerPoint and Excel. Digital Ink within Maple and also with an interactive whiteboard will be demonstrated. We discuss an example of marking remote student work (as a pdf file and using PDF Annotator).
We'll make a few preliminary comments about the Australian national program of collaborative teaching of Honours mathematics and statistics via the Access Grid (AG); and also comment about the taught courses for PhD students in the mathematical sciences in the UK using Access Grid. A comprehensive seminar series has been given in Canada and has begun in Australia. Since NZ has KAREN, a network of AG Rooms, opportunities for Australia & New Zealand collaborations abound.
Date received: October 30, 2008
eLearning and automated assessment using Maple
by
Bill Blyth
Australian Mathematical Sciences Institute & RMIT University
Coauthors: Alexandra Labovic (RMIT University)
In the first semester of a traditional calculus course, the weekly Maple lab sessions are not used to directly support the lectures ... nearly half of the work is at school level! A major aim is for the students to enjoy the experience of using Maple.
Students work in groups of size 2 to 4. After Maple introductions, they complete an Introduction to Animation session and then choose an extended animation project from a list of five problems. They have to demonstrate their animations in the lab for assessment. Students enjoy the animation project.
Following the animation projects, Spot the Curve uses plots and animations to understand horizontal and vertical translation of curves: students identify the randomly generated translations used and appreciate automatic marking within Maple. Student feedback has been very positive.
Our trapezoidal rule assignment is now more fun: it's disguised as a Fish Pond (a trout farm). Trapezoidal rule is used to approximate the cross-sectional area (and hence the number of trout) ... the students download a template for individualized fish ponds, with automatic marking. These projects are enjoyable deep learning activities.
The Fish Pond assignment could be set and automatically marked with standard Computer Aided Assessment, CAA, systems such as MapleTA. However in second semester, we have introduced a pendulum assignment for which students obtain immediate automatic marking of numeric and symbolic (exact) answers and save their comments and plots in their Maple file. A tutor marks these elements and generates a full marking report (all in Maple) for students. This can’t be implemented with CAA systems currently available, such as MapleTA.
Developing innovative eLearning and eAssessment materials is resource intensive and so collaboration, using collaborative environments such as the Access Grid, is particularly appealing.
Date received: October 30, 2008
Digitally assisted discovery and proof in mathematics
by
Jonathan Borwein
Newcastle and Dalhousie
I will argue that the mathematical community (appropriately defined) is facing a great challenge to re-evaluate the role of proof in light of the power of current computer systems, of modern mathematical computing packages and of the growing capacity to data-mine on the internet. With great challenges come great opportunities.
I intend to illustrate the current challenges and opportunities for the learning and doing of mathematics. For example, the knowledgeable user of Maple and Google if presented with the unremarkable number
a=1.4331274267223117583?
can "discover" within seconds-via various pathways-that it has the more remarkable continued fraction
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 , ?]
The same user may then quickly discover (from, say, JSTOR, MathWorld, Wikipedia or elsewhere) that such arithmetic continued fractions only arise as ratios of Bessel functions (of which they may never have heard, but in the new order, so what?). Indeed, a = I0(2)/I1(2) where I0 and I1 are the Bessel functions of the first kind of order zero and one respectively. Armed with this knowledge a proof is easy.
The continued fraction-a concept which a lamentably small number of university mathematics students meet, perhaps because hand-computation is difficult-itself affords a fine illustration of the power of computers to make concepts more accessible. It provides one of many fine illustrations of the value of seeking different representations for the same object and so to provide for better motivated learning of new concepts. Above all the growing richness of this matrix of tools places an extra onus on us to understand and explicate the appropriate role of proof. As Jacques Hadamard put it "The object of mathematical rigor is to sanction and legitimize the conquests of intuition, and there was never any other object for it".
I shall also explore some of the impediments to the assimilation of these new techniques into our parole. These include inertia, organizational and technical bottlenecks, under-prepared or mis-prepared teachers of mathematics, and the lack of material from which to train them.
Reference: Jonathan Borwein and Keith Devlin, The Computer as Crucible: an Introduction to Experimental Mathematics, AK Peters, 2008.
Date received: September 29, 2008
Distance education with discrete mathematics
by
Graham Clarke
RMIT University
Discrete Mathematics provides opportunities and challenges as a subject for distance education. The nature of the challenges has changed with new developments in technology, but many problems remain. We review some difficulties and successes in the provision of Discrete Mathematics to students in remote and distant locations.
Date received: October 30, 2008
An urgent mathematical mustering: calling all king Terry's horses & all king Tao's men
by
Patricia Cretchley
USQ and QUT
Financial imperatives and managerial ambitions are dictating funding foci in Australian Universities and elsewhere. Some managers use a numbers cut-off to justify withdrawing of majors with relatively small numbers, typically mathematics. The damaging effects to mathematics programs and staffing are certainly but not only being felt in regional universities in Australia, as the Flinders and USQ stories tell.
To promote discussion on what more we can be do to protect mathematics programs from destructive education policies and management, I outline the Flinders/USQ stories and the people inexorably linked by the damage done in these two universities.
The Cast reads like that of a Fairy Tale: The Villian Dean, the Hero Fields Medalist, and the delightful Talented Child whose urgent plea to Terry Tao sets the scene for a mathematics support campaign second to none, internationally. And a Cast of Thousands of aspiring mathematics students, not all of them Regional Peasants!
But the synopsis is not a Fairy Tale. What unfolds is a large-scale Tragedy of damage to mathematics students and academics, and the destruction of decades of careful mathematics program-building. As one of those closely affected, I report the agonies of academics and students sadly... but determinedly.
This talk is designed to help set the scene for a Round Table that focuses on issues of the educational funding and management of mathematics in Australian and New Zealand. What we can learn from these events, each other's experiences, and practices elsewhere? How do we best steer our mathematical futures?
Date received: November 20, 2008
Fermat's Last Theorem in romantic mathematics
by
Miroslav Haviar
M Bel University, Slovakia
Coauthors: Pavel Klenovcan
Several years ago we established a course of Romantic Mathematics offered for all students at M Bel University in Slovakia with a particular target group being the future teachers of Mathematics. The course has been based on S. Singh's book Fermat's Last Theorem and its aim has been to achieve that students would become: (i) better aware of the history and current developments of Mathematics and (ii) more enthusiastic about the beauty and the challenges of Mathematics via the thrilling stories like the one of Andrew Wiles.
We share our experience about teaching (or rather performing) this course and illustrate the work of students.
Date received: October 30, 2008
Challenging pre-service primary teachers
by
Carolyn Kennett
Macquarie University
Coauthors: Dilshara Hill
Pre-service primary teachers bring to their studies a wide range of mathematical backgrounds, beliefs and experiences. It is in the interests of mathematics as well as the improved education of our children that these students come out of university with positive attitudes and experiences in mathematics.
As teachers of mathematics we should be aware of the need to challenge some traditional erroneous beliefs about mathematics as well as facilitating successful experiences in mathematics. We look at some of the things that work and some that don’t in a first year course specifically designed for pre-service primary and early childhood teachers.
Date received: November 3, 2008
American Indian participation in mathematics in the U.S. - obstacles and opportunities
by
Bob Megginson
University of Michigan
This talk will focus on some of the barriers that have prevented the greater participation of U.S. American Indians in the mathematical sciences. A bit about American Indian educational history in the U.S. will be presented, where it is relevant to participation in mathematics, along with a discussion of some perceptions about American Indian ability to do mathematics that have been damaging. Though the audience will likely not need convincing, the talk will end with some evidence that the ability of American Indians to do mathematics should certainly not be in question.
Date received: November 20, 2008
Advanced features in mathematics typesetting and presentation
by
Ross Moore
Macquarie University
As methods of electronic communication have been developed, so also has the (La)TeX software been evolving to take advantage of newly emerging technologies. The typesetting of mathematics has always presented challenges that are much greater than for normal prose, whatever the language. With the adoption of Unicode on all modern computing platforms, the trend will be toward electronic documents in which all manner of content, including mathematics and/or exotic scripts, can coexist and remain easily searchable and copyable (if not editable) with standard software tools. In this talk I will present some techniques which should be of particular interest for handling mathematical content, whether by a publisher, researcher, teacher or student. Examples will be shown that are readily available on the AustMS website and course unit sites at Macquarie University, and elsewhere.
Date received: October 24, 2008
Demise of the "back of envelope" sketch?
by
Ross Moore
Macquarie University
We teachers, and our students, see sophisticated technical graphics all the time in movies and on TV shows, whether for entertainment or enlightenment. General purpose mathematical software tools, such as Mathematica, Maple and others, provide the capability to produce detailed graphics which can better present some mathematical ideas than the "back of envelope" or "chalk-board" sketches that we all grew up with. It cannot be leaving a good impression or creating adequate comprehension, when we try to present complex geometrical ideas using just roughly drawn sketches.
In this talk I'll show some of the graphics that I have been using in a course on Vector Calculus, to illustrate functions and vector fields in 2 and 3 dimensions, and their integrals over curves and surfaces. That is, "div, curl, and all that...", visualised with accurately-drawn 2D and 3D graphics, employing colours and transparency (i.e., opacity), and animations, to help develop a better understanding of what the integrals mean. Furthermore, at least with Mathematica, the presentations used in lectures can be saved as well-presented PDFs for the lecture "notes". These PDFs can retain the full quality of the graphics and include the animations.
It is not my contention that all lecturers need to become graphic artists; but that some of us should be gaining good experience with these software tools, and sharing the fruits with our colleagues and students.
Date received: October 24, 2008
The use of reflective journals in a first year mathematics unit
by
Leanne Rylands
University of Western Sydney
Coauthors: Carmel Coady
``I hate maths'', ``I can't do maths''. Anecdotal evidence suggests that more and more students are entering university with very negative feelings towards maths. Most such students avoid maths if at all possible.
In 2008 our we introduced a new subject specifically designed to help students develop strategies to lessen the effects of maths anxiety and test phobia, as well as to revise basic maths and build their confidence. A reflective journal was part of the assessment in this mathematics subject.
I will talk about our experiences with this so far.
Date received: October 30, 2008
The decline of Australian mathematical sciences capability
by
Jan Thomas
Australian Mathematical Sciences Institute
In 1995 a review of Australian mathematical sciences found them to be facing challenges but to be in reasonably good health. In 2006 another review found a very different situation with difficulties at every level from inadequate primary teacher education to a narrowing research base. In short, the mathematical sciences in Australia are in crisis. This is having a profound effect on opportunities for students in schools to access a quality mathematics education. Australia does not have enough graduates in mathematics and statistics and this affects teacher supply. Increasingly access to a quality mathematics education equates with being able to pay private school fees. In the late 1980s, Australia came close to recognising, and was beginning to cater for, all students’ mathematics education needs. In 2008 we have managed to turn this around so there is now an impossible gateway for many. Data behind this situation will be presented and discussed
Date received: October 29, 2008