# Jonathan M. Borwein

# Commemorative Conference

## 25—29 September, 2017

# ◄Education►

Theme chaired by Judy-anne Osborn and Naomi Borwein

**Keynote talk:**Breaking the Symbol Barrier — a New Approach to Learning Mathematics

We have known since the publication of the book

I'll finish by drawing a parallel between this work and the Experimental Mathematics for which Jon Borwein was a leading developer.

*Street Mathematics and School Mathematics*by Nunes et al in 1993 that children (and adults) learn and perform mathematics far more effectively when they engage with it in a real-life context as opposed to the formal symbols of abstract mathematics. The problems so many have with mathematics are rooted not in the mathematical thinking (at the conceptual level) but the "interface" issues of handling an abstract linguistic structure. I have spent the last ten years developing and testing alternative representations of various mathematical concepts in an attempt to "break the symbol barrier (to effective math learning)" that*Street Mathematics*highlighted. I will demonstrate three of those alternative representations (one already available in app form, the other two in the final stages of development) and discuss some of the research that has been carried out on those three learning apps and others designed in a similar way. I will also say something about the possibilities for transfer, both from one mathematical concept to another when carried out in a "symbol free" way, and from "symbol free" learning to mastery of the same concept using traditional symbolic representations.I'll finish by drawing a parallel between this work and the Experimental Mathematics for which Jon Borwein was a leading developer.

Deciphering the Schism in Math/Education

This talk analyses the ideological, cultural, and heuristic roots that often invisibly dictate disciplinary boundaries between math and education. Part of my
doctoral research involves the investigation of disciplinary rifts, or turf wars, in academia; after decades of observing the international mathematics community,
such an analytic lens will be applied to math education. Indeed, it is important to not just consider the microlevel of curriculum and pedagogy, but underlying trends
that foster and govern the latent schism between math educators and mathematicians. In this talk, I will use real life examples and anecdotes to explore how this
academic conflict follows standard patterns of interdisciplinary schisms. Recognising these patterns is integral to bridging the gulf.

Why Students Hate Statistics and Why it Matters to the Reproducibility of Medical Research

Among his numerous achievements, Jon Borwein promulgated the need to institute a culture of reproducibility. From

*Statistics Done Wrong*(Reinhart, 2015) to findings from a recent National Academies of Sciences, Engineering, and Medicine workshop convened to address questions about the reproducibility of scientific research, lack of statistics education has been identified as a major culprit in the generation of poor science. In this talk, we give an overview of the statistical fields required to conduct medical research, explore barriers to learning statistics, and share successful teaching strategies developed at the University of Florida to engage clinicians in medical research.
Crossing Boundaries:
Fostering Collaboration between Mathematics Educators
and Mathematicians in Initial Teacher Education Programs

Prospective teachers of mathematics need both subject matter knowledge and pedagogical content knowledge — in other words, they
need to know not only the content but also how to teach it. In most initial teacher education programs these two kinds of knowledge are
usually taught in separate courses, designed and delivered separately by mathematicians (content) and mathematics educators (how to teach
the content). Consequently, few opportunities exist to interweave content and pedagogy in ways that develop professional knowledge for
teaching. This talk will describe a national project —

*Inspiring Mathematics and Science in Teacher Education*— that developed strategies for combining knowledge of mathematics content and pedagogy by fostering genuine, lasting collaboration between communities of mathematicians and mathematics educators. It will focus on the boundary practices that led to new ways of working between the two communities, as well as new approaches to mathematics teacher education.
Mathematics Education in the Computational Age: Challenges and Opportunities

In the spirit of Jonathan Borwein's opportunistic and inventive use of computers in the development of the field of Experimental
Mathematics, this paper recommends a computational "turn" in school mathematics. At a time when students are increasingly moving away
from mathematics in the senior years of schooling we need to reconsider the relevance of current mathematics curricula and traditional
approaches to mathematics pedagogy. Computational applications are transforming the world that we live in and just as Experimental
Mathematics challenged the foundations of the discipline of mathematics, computational approaches are also changing almost all
traditional fields of study. By persisting with the teaching of manual computation in school mathematics, we are denying the current and
future worlds of our students. By doing so, we risk increasing our students' lack of interest in mathematics as it will progressively be
seen as an historical curiosity of little relevance. This paper proposes some key questions for mathematics educators to consider in
order to make mathematics more relevant and of interest to today's students.

Sometimes it is easier to see than to say

The aim of this presentation is to support Jon's claim that "sometimes it is easier to see than to say." We will demonstrate dynamic
visual models of several mathematical facts that were established by ancient mathematicians. We will contrast the clarity of the models by
outlining "strict" mathematical proofs based on those timeless ideas.

Education-led Workshop: Maths, Education, Research and Culture

This panel discussion is inspired by the connectedness of Jon's thinking on all things mathematical and educational. I will begin with a description of some of what I have learnt from Jon, and then provide some questions about which our Panel discussion will be focused.

Conversations never end with Jon, a bit like his talks! His presentations were always grand panoplies of which he would draw upon samples according to mood and need, picking up threads again at a later time, re-envisaged for a new purpose, but with ever the same underlying themes of discovery, joy, surprise, and human narrative. The slides of his many talks are still available on the Founding Director's link on the CARMA website. Whenever Jon was speaking, he was teaching. Why? I think it was because he was himself an insatiable learner; and that learning about mathematics and people was a great joy in his life which he wanted to share, and still does through his prolific legacy.

Q1. Can research practices be fruitfully incorporated in school mathematics?

Q2. Can mathematics be taught in such a way that the general population do not fear it?

Q3. How can we change mathematics research training to be more inclusive of a diversity of people and cultures?

Q4. How do the specific characters and needs of the research areas effect the above questions?

__About Jon: Learner and Teacher__I first met Jon Borwein at an AustMS dinner, where we happened to be seated next to each other. Although we hadn't known each other before, we were soon in vigorous talk about Education, and what really matters in what we as Educators bring and do. Like every conversation with Jon, it was about ideas and people, with Jon making his points in assured rapid-fire, solidly backed-up if queried on any particular, interwoven with vignettes of stories drawn from all over the world. By good fortune I was at the launch of Jon's CARMA centre at the University of Newcastle, and later joined the group first as a postdoc and later as Faculty, and Education representative on the CARMA Executive. From that vantage, I've had the privilege of continuing that first conversation, for roughly seven years.Conversations never end with Jon, a bit like his talks! His presentations were always grand panoplies of which he would draw upon samples according to mood and need, picking up threads again at a later time, re-envisaged for a new purpose, but with ever the same underlying themes of discovery, joy, surprise, and human narrative. The slides of his many talks are still available on the Founding Director's link on the CARMA website. Whenever Jon was speaking, he was teaching. Why? I think it was because he was himself an insatiable learner; and that learning about mathematics and people was a great joy in his life which he wanted to share, and still does through his prolific legacy.

__Focus questions for the panel discussion:__Q1. Can research practices be fruitfully incorporated in school mathematics?

Q2. Can mathematics be taught in such a way that the general population do not fear it?

Q3. How can we change mathematics research training to be more inclusive of a diversity of people and cultures?

Q4. How do the specific characters and needs of the research areas effect the above questions?

Active Learning in Pure Mathematics

Active learning encompasses a range of student-centred strategies where students learn through structured experience. It is often distinguished from passive learning by the activities that happen within the classroom.
This presentation will share my experiences in adopting active learning practices within a third-year undergraduate pure mathematics course, including my influences, observations, challenges and successes.
By embracing a philosophy that education is a means to develop and transform individuals, I will demonstrate how I have developed and transformed.

AMSI’s Advanced Collaborative Environment (ACE)

Back in 2004 Jon convinced Garth Gaudry to include a national network of Access Grid Rooms in AMSI's bid for the International Centre of Education in
Mathematics. Jon became a mentor for what is now known as the ACE network which delivers honours subjects, seminars, forums and short courses. I will
talk about what has been achieved, and importantly the exciting developments taking place from next year.