About the book

Tools and Mathematics book cover
"Tools and Mathematics" is an exploration of tools and mathematics and issues in mathematics education related to tool use. It comprises five parts: the first part reflects on doing a mathematical task with different tools, followed by a mathematician's account of tool use in his work. The second considers prehistory and history: tools in the development from ape to human; tools and mathematics in the ancient world; tools for calculating; and tools in mathematics instruction. The third part opens with a broad review of technology and intellectual trends, circa 1970, and continues with three case studies of approaches in mathematics education and the place of tools in these approaches. The fourth part considers issues related to mathematics instructions: curriculum, assessment and policy; the calculator debate; mathematics in the real world; and teachers' use of technology. The final part looks to the future: task and tool design and new forms of activity via connectivity and computer games. Because the tools created and used in mathematics (from ruler and compass to computer-enabled visualisation) have such a large impact on both mathematical thinking both in research and education, we hope the workshop’s theme will be a common point of interest that will enable many further such creative collaborations.


Tools and Mathematics:

Instruments for learning

29 November—1 December, 2016


Incorporating the Mathematical Educational
Software Interest Group
's second annual meeting


Workshop booklet available

The workshop booklet is available as a PDF.

Programme and presentations

The programme is now available below. Links to presentations will be added to it as they become available.

The workshop incorporates a discussion panel on "Changing the way people think, move and feel mathematically: the contribution of digital technologies", with Paul Drijvers, Celia Hoyles, Ulrich Kortenkamp, Richard Noss and Judy-anne Osborn (details below), and plenary talks by Michael Assis, Michael Barnsley, Naomi Borwein, John Monaghan, Luc Trouche and Uri Wilensky.

Discussion panel — November 30th, 4:30pm-6pm

Topic: Changing the way people think, move and feel mathematically: the contribution of digital technologies

Chaired by Elena Prieto (CARMA, Australia) & Celia Hoyles (Institute of Education, London)

Panel members:

Many decades ago, Seymour Papert rose to the challenge of developing a theory and an appropriate language—such as objects-to-think-with, body syntonicity and aesthetic engagement—that could describe the way in which the use of digital technology changes the way people think, move and feel mathematically. Since then, the emergence of new digital technologies and new theories have helped researchers recognise the breadth and depth of that change and simultaneously provide a framework for the design and implementation of computational tools for learning mathematics.

The possibility of putting mathematical objects into motion, for example, fundamentally changes the nature of these objects, how they are perceived and reasoned about; moving these objects changes the bodily actions and gestures of both learners and teachers; making the objects transform, collide and overlap changes the stories that can be told about them. Research on the use of digital technology has also provided an extraordinary "window" on mathematical meaning making, to use the metaphor provided by Celia Hoyles and Richard Noss, in part because of the visibility of thought, motion and feeling enabled in expressive digital technology environments. Like Papert, Jonathan Borwein recognised that the task is essentially epistemological not only psychological – nothing less than the construction of a new, computationally based mathematics. He often argued that computational mathematics is a "more honest" form of mathematics in that it "does not hide or obscure the experimental process by which a mathematical hypothesis is discovered".

In the light of the above views, this panel will address the new ways people think, move and feel mathematically, thanks to the opportunities offered by digital technologies.

Invited Speakers


The workshop is free but please make sure that you register at Eventbrite.


Abstract submission is now open. Please sign up on the abstracts page, where you can edit, save and submit your abstract. Note that this is a separate sign-up to the workshop registration.


The workshop, hosted by CARMA, will be held at the University of Newcastle's Sydney campus (55 Elizabeth Street, Sydney). The room is ELI 122.

Draft Programme

29 Nov
30 Nov
1 Dec
10:00 amPlenary speaker:
Naomi Borwein
"From Lipschitz to Homo Habilis Mathematicus: a case study of Jon Borwein"
Plenary speaker:
John Monaghan
"Tool and mathematics - tools matter"
Plenary speaker:
Luc Trouche
"From Scribal to Digital Schools, an Inspiring Journey in Mathematics (Education)"
11:00 amMorning tea
11:30 amAnthony Morphett
"Using visual blocks to support mathematical syntax"
Jana Visnovska
"Designing for tool use in mathematics classrooms"
Matt Skerritt
"Tools for Teaching Computational Mathematics"
12:00 noonScott Lindstrom
"Phase Plotting in Differential Geometry"
David Sherwood
"Round Table on Calculators"
Paul Abbott
"Sums, Products, and the Zeta Function: Visualizing a $1,000,000 Problem"
12:30 pmLunch
2:00 pmPlenary speaker:
Michael Assis
"Origami Mathematics in Education"
Plenary speaker:
Michael Barnsley
"The tools of fractal geometry, 1978-2016"
Plenary speaker:
Uri Wilensky
"Phenomena-based and Generative modeling - integration of computational math and science"
3:00 pmBill Blyth
"Applied optimization problems solved using algebra and approximation in the small (algebraic – no calculus) with visualisation enabled by CAS (Maple)"
Bill Blyth
"eTeaching and eAssessment of Vector Calculus"
3:30 pmAfternoon teaAfternoon tea
4:00 pmTristram Alexander
"The computer as a tool to develop mathematical thinking"
Sitti Patahuddin
"Understanding Mathematics Teachers' TPACK through the Examination of Critical Instructional Events"
4:30 pmLjiljana Brankovic
"Gamification of STEM courses: What Works and How to Do it"
Discussion panel
(4:30 - 6:00)
5:00 pm
5:30 pm
6:00 pm
6:30 pm
for 7:00 pm
Venue: Vapiano
(Corner of King and York streets, Sydney)

Organising Committee

Accommodation Suggestions

Contact Information

If you have any questions, please contact

Juliane Turner


Telephone: (02) 492 15483