[OCMA Annual Conference, Taras Gula* and Miroslav Lovric]

Have you struggled with creating good numeracy tasks, or are you looking for ways to reason about what makes a good numeracy task? We have adapted Conrad Wolfram’s computational thinking model (define-abstract-compute-interpret) to inform the development of a rubric which we are confident will survive scrutiny from OCMA attendee perspectives. We propose that this rubric will help college professors assess and improve the numeracy tasks they are currently using, and to develop new ones. With your help, we will stress test the rubric’s usefulness in practice by analysing numeracy tasks that we have selected, and invite you to bring along numeracy tasks of your own for us to examine.

Fern Resort Orillia

[Integrated Science Synthesis]

I will talk about my research in two areas: mathematics biology/medicine and mathematics education. Research in mathematics is easy (!) in the sense that ideas, objects and concepts are abstract, far from the complexities, chaos, and randomness of the real world in which we live. But what happens when we research humans? What mechanisms are triggered when a person, allergic to peanuts, bites into a Mars bar? How can we model their organism's reaction mathematically, and what are the benefits of doing so? Mathematics education is concerned about the processes of thinking and learning mathematics. What does it mean to learn something, to know something? I will discuss my attempts at trying to answer these questions in the context of the courses I've been teaching at Mac.

McMaster University

[Waterloo Teaching Seminar]

I will present my thinking and ideas about creating two mathematics courses at McMaster University which have different levels of integration of coding: mathematics for the life sciences students (light coding), and introduction to mathematical scientific computation for mathematics and statistics majors (all about coding). In both courses we use Python. Before a course starts, I’m happy and enthusiastic about it; I think (and make decisions) about its content, assessments, etc., and talk to my colleagues who have taught the course before me; I think about the best ways to make lectures active and involve students. However, when I come to my lecture, I see things quickly go sideways, sometimes far from the way I planned it. Often, I’m not happy about it. So, I can say that I’m quite good at not doing things right. So, I will discuss specific teaching strategies that I use in my classroom, and the ways student react (or not) to them. A part of it will be comparing teaching math to teaching coding, and my efforts to bring the two as close as possible. I will invite participants to comment, and will be happy to hear fresh ideas and suggestions.

University of Waterloo

[2022 Innovations in Education Conference]

In 1997, I published a paper textbook “Vector Calculus.” Twenty-five years later, my co-author and myself witnessed the e-birth of our virtual textbook “99 Numbers.” After two decades of publishing mathematics education research in peer-reviewed publications, I started writing for newspapers and online media, including CBC, Hamilton Spectator, and University Affairs. The two papers on the transition from high school to university mathematics, that I co-wrote with a colleague from New Zealand in 2007 and 2008, are quoted as often today as they were when they came out. Why do some things change, yet some others seem to successfully resist the forces of change? How is writing a paper textbook different from writing an e-book? How is learning from a paper textbook different from learning from an e-book? What do these differences tell us about the future? What prompted me to write a critical piece on teaching mathematics in the times of the pandemic for the CBC News? Students coming to university in 2022 are, in many ways, different from those who were with us in 2007. However, the two cohorts must have some things in common, as our analysis of the transitional issues seems to remain as relevant today at it was 15 years ago. Supported by research evidence, anecdotes and (hopefully) reactions from the audience to my provocations, I will attempt to sketch answers to my questions, which, I hope, will prove to be relevant beyond the boundaries of mathematics.

LRW, McMaster University

[National Numeracy Network 2022/23 Annual meeting; with Andie Burazin and Taras Gula, ML presenting]

The challenges that students face in applying their mathematical knowledge in contexts outside mathematics are well known and documented. In this talk we suggest a way of modifying teaching that might help reduce such challenges, in particular when students need to abstract situations in a numeracy task. Faced with a problem in context for which there is no formula or a known template or algorithm, students often do not know how to start; in part, this is due because they might not be aware of what is available to them. Hence the idea of teaching with a purpose to build an “abstraction toolbox.” For instance, such a toolbox would contain exponential reasoning. We will illustrate what this toolbox might offer for questions that ask a student to compare (two or more objects, events, graphs, phenomena, etc.).

University of New Mexico, Albuquerque, NM

[National Numeracy Network 2022/23 Annual meeting; with Taras Gula, TG presenting]

Making distinctions between mathematical and numeracy tasks in theory leads to challenges for the practicing teacher who would like to provide their students with quality numeracy tasks.
Mathematical tasks: about mathematical ideas and objects and their relations (live in abstract world). Numeracy tasks: about concrete objects and their relations; context-centred phenomena (use abstract to make sense of concrete). We have adapted Conrad Wolfram’s computational thinking model (define-abstract-compute-interpret) to inform the development of a rubric which we are confident will survive scrutiny from both the theoretical and practical perspectives. We propose that this rubric will help the adult education teacher assess and improve the numeracy tasks they are currently using, and to develop new ones.
With your help, we will stress test the rubric’s usefulness in practice by analysing numeracy tasks that we have selected, and invite you to bring along numeracy tasks of your own for us to examine.

University of New Mexico, Albuquerque, NM

[Fields Math Education Forum Andie Burazin,Taras Gula, and ML presenting]

For many generations, schools and universities taught mathematics. But only since the latter half of the 20th century, this ‘classical’ education started to re-focus somewhat towards the competencies afforded by numeracy. Numeracy (or rather innumeracy) became a concern when multiple international surveys revealed numerous weaknesses and inadequacies in people’s ability to reason with quantitative information in contexts that are directly related to their lives. There have been numerous attempts to conceptualize numeracy (aka quantitative reasoning, quantitative literacy). In this introductory session, we will suggest an alternative approach to thinking about numeracy, which - among other benefits - suggests an approach to teaching of numeracy through the focus on the numeracy tasks. After challenging the audience to reflect on, and criticize, our suggestions for numeracy tasks, we will suggest a rubric that can be used to determine whether or not a given task is a good numeracy task.

Fields Institute, Toronto

[FYMSiC meetup (with Andie Burazin)]

Scaffolding.

Online

[CMS Summer Meeting, Plenary]

In this lecture I will connect what we have learned in the past to what we're presently learning, in order to discuss things that might affect, or be part of, mathematics teaching and mathematics education in 10 years or so. I will include some of the activities that I've been working on with my colleagues: teaching numeracy, creating authentic applications, and using coding to experiment and learn math. Needless to say, I will also share some fun math problems that I've recently encountered.

Memorial University, St John's NL (in person)

[OER Grant Lightning Round; MacPherson Institute]

TBA

McMaster University, virtual

TBA

HEQCO, virtual

Numeracy is not remedial mathematics, it is not mathematics, and it's not liberal arts mathematics. Numeracy is numeracy.

University of Toronto Mississauga, virtual

[Math and Stats Outreach presentation]

How does mathematics help us understand the properties of the space we live in? Do we really live in three-dimensional space? Is our universe finite or infinite?

Virtual lecture

[Pi Day lecture in Math and Stats and Integrated Science]

Using math to explore properties of our space.

Virtual lecture

[Session for high school students and teachers]

Thinking about transition to university (and university mathematics) - what makes someone succeed, or to say the least, what can you do to reduce your transition pains?

Virtual, St. Joan of Arc HS in Mississauga

[McMaster Science Society Academic Roundtable]

TBA

Virtual

[Fields Math Education Forum; co-organizer]

Abstract. This session focuses on current research initiatives in undergraduate mathematics education. We highlight research in key areas including: instructional methods, student learning and reasoning, teacher knowledge and education, as well as student transitions from secondary to post-secondary. Our speakers include international scholars and leaders in the field, and they will join us to provide a glimpse of the current research landscape and a view toward future directions as they share stories of their work.

Virtual, Fields Institute, Toronto

[CMS CMS COVID-19 Research and Education Meeting (CCREM)]

Invited talk: My path to (virtual) happiness.

Virtual

TBA

BIRS, Banff, Alberta

[Fields Math Education Forum day]

Fields Institute, Toronto

[Presentation for visiting high school students from Bishop Tonnos Catholic Secondary School]

McMaster University

[Fields Institute]

The Higher Education Quality Council of Ontario (HEQCO) recently conducted research that suggests that one-quarter of graduating students score below adequate on measures of numeracy. This is concerning and raises an important question: How during the course of their postsecondary education can we best and most effectively upgrade the numeracy skills of postsecondary students in ways that serve them well in their personal and professional lives? The purpose of this one-day conference is to gather individuals (numeracy experts from HEQCO and from Ontario universities, department chairs, representatives of colleges and universities, and other numeracy experts) in order to better understand numeracy and teaching numeracy, to identify obstacles to improving numeracy skills and to brainstorm solutions.

This inaugural conference is by invitation only.

Fields Institute, Toronto

[Fields Institute]

Although the conference venue is a mathematics institute, this is not a mathematics conference. We plan to mobilize mathematics education researchers and health care professionals to work together, on practical issues related to improving health numeracy education among health care professionals, patients, and their families. Our discussions will be guided by the existing literature on numeracy and adult numeracy, pedagogical experiences of mathematics educators and experts working on health education, as well as the experiences of health care professionals, and those directly involved - the patients. Health numeracy is defined as “the degree to which individuals have the capacity to access, process, interpret, communicate, and act on numerical, quantitative, graphical, biostatistical, and probabilistic health information needed to make effective health decisions.” Although there is clear evidence that health numeracy, and numeracy in general, need to be improved, it is less clear exactly which aspects of health numeracy should be targeted for improvement. In an extensive, though informal, search we have come across many online tools that purport to help children, teenagers and adults improve general numeracy and mathematics skills; however, they all focused on computational skills, which are but one aspect of mathematics and of numeracy, and were not targeted to specifically improve health numeracy.

Fields Institute, Toronto

[Health Numeracy Project]

Lecture and workshop for practicing medical professionals and researchers in medicine.

Princess Margaret Cancer Research Tower 4th floor, room 204

[Fall Preview 2019 presentations]

McMaster University, PGCLL 104 and 127

[Science 1A03 lecture]

MDCL 1305

[Math and Stats Seminar]

I will discuss two recent projects that I have been involved with at my university. A couple of years ago, McMaster University formed a Literacy and Numeracy Committee, with a mandate to look into initiatives that could improve our students’ literacy and quantitative reasoning skills. Related to it, I crated a course, called “Numbers for Life” (Math 2UU3), in which we discuss authentic contexts that require quantitative reasoning (numeracy). I will talk about the course design and its content. Related to it – as part of my SSHRC-funded work, we (collaboration with a colleague from George Brown College) have developed conceptualization of health numeracy and are building a teaching and learning instrument for health care professionals, patients and general public. My other SSHRC-funded collaborative project (Queens, SFU, Western, McMaster) involves studying affordances of computational thinking (CT) and implementation of CT in school and university curriculum. In particular, I will talk about how we introduced Python programming labs into our first-year course “Mathematics for Life Sciences” (Math 1LS3).

University of Waterloo, MC 5501

[Faculty Threads Colloquium]

I plan to outline two SSHRC funded projects that I have been working on: computational thinking and introduction of computer labs into our Math for Life Sciences course (Math 1LS3); and conceptualization of numeracy, resulting in the course design for Numbers of Life (Math 2UU3), and in the creation of an online teaching tool for health numeracy.

McMaster University, Hamilton Hall 305

[Adults Learning Mathematics conference; with Andrijana Burazin (UTM) and Taras Gula (GBC) (ML presenting)]

After a brief introduction to the conceptualization of health numeracy and general thinking behind our online health numeracy teaching and learning instrument, we will outline how we created lessons about probability, chance and risk. Our major challenge lied in the fact that although adults do need a good understanding of major probabilistic concepts and ideas (many of which are not intuitive), that understanding should not come from formal definitions, proofs and algorithms, as in mathematics courses. Given the diversity of the background preparation, knowledge and demands of our intended users, we built a long trajectory from the very basic principles (such as understanding what 15% really means), to dealing with data uncertainty, to explaining conditional probabilities and the law of total probability (as they are needed in reasoning about medical testing). We will illustrate this trajectory with sample questions from our online instrument.

University of Lund, Sweden

[STEM-TEC seminar]

Numeracy means, and is, different things to different people. For my university’s call for
improvements of our students’ literacy and numeracy skills, numeracy (or numeric literacy or
quantitative literacy) can be viewed as a combination of specific knowledge and skills, which are needed to function in the modern world. Numeracy involves reasoning from, and about, numeric information (data), which can be presented in a variety of ways (such as numeric, graphic, and dynamic forms). There are many conceptualizations of numeracy, and much debate over the relationship between numeracy and mathematics. Although I will touch upon these--as I am a person who prefers action--I plan to spend most of the time describing the numeracy course (somewhat inappropriately named “Numbers for Life”) that I created and have been teaching at McMaster University. This is a course which allows me to bring important mathematical and statistical ideas together, and apply them in truly relevant contexts, including climate change, population dynamics and environment, money and financial matters, crypto currencies, economic and wealth indicators, and understanding of data.

Auckland University of Technology, New Zealand

[Adults Learning Mathematics conference; with Andrijana Burazin (UTM) (ML presenting)]

The authors have recently integrated computer labs in Python into their first-year courses. At the start of the semester, students showed high levels of anxiety, claiming that they have not done any coding in high school. This obviously being a transitional issue, we designed activities to help high school teachers learn about coding as well. Our hope is that, once they remove their personal barriers, teachers might be better motivated to engage with coding activities in their math classes. Being able to compare, we asked ourselves – What are the differences in views, experiences, and actual learning when two different populations (first year university students and high school teachers), with no or very little prior experience in coding, learn to code in Python? Our preliminary results point to the fact that the two groups show some differences, which will certainly inform how we modify our teaching and learning support.

University of Lund, Sweden

[First Year Math and Stats in Canada]

Three case studies.

University of Alberta, Edmonton

[Welcome Week Faculty Talk]

Suggestions on how to eat an elephant.

McMaster University, BSB 147

[Adults Learning Mathematics conference; with Taras Gula (GBC) (TG presenting)]

with Taras Gula

University of Lund, Sweden

[May at Mac presentation]

McMaster University

[Math Panel Discussion for HWCDSB Conference]

[Digital Education for a Digital World conference; with Taras Gula, GBC (TG presenting)]

TBA

George Brown College

[Fields Math Education Forum day on Learning Mathematics Outside of the Classroom]

Fields Institute, Toronto

Presentation to high school teachers about transition, focussing on academic challenges.

Mentor College, Toronto and Mississauga

[Math at Mac]

Discovering and analyzing patterns; Luhn algorithm for credit cards; modular arithmetics, prime numbers, hash functions and RSA algorithm (two lectures)

McMaster University CIBC Hall

[First Year Mathematics Repository Workshop (19w2256)]

Motivation, successes and challenges in introducing programming to a life science course, with most students haveing no experience working with computer code.

BIRS, Banff, AB

[Dialogie with High School Teachers]

Agenda will include: computational thinking and programming - integration of computer labs in our math for life sciences courses; new numeracy course we have been offering; presentations and Q&A with our students; general discussion.

Council Chambers, Gilmour Hall 111, McMaster University

[Guest lecture in ArtSci 1D06]

Case studies of true life situations where we use integration (UV index, volume of a heart chamber, Gini index of wealth inequity)

McMaster University

[Fields Math Education Forum day on Computational Thinking]

In this talk we discuss our ongoing project of integration of CT, and in particular, Python programming, into a large math for life sciences course. This project involves many moving parts - from working on changing students’ attitudes toward programming and addressing the anxieties of many who claimed to have never seen computer code, to designing coding activities which are meaningful and complement the material that is taught in the course.
We will focus on coding activities and the way they enriched mathematics instruction. Coding brought forward aspects of calculus that are not covered extensively and which students, lacking adequate exposure, find difficult and confusing. For instance, working with a function as a discrete object naturally introduces the need to approximate derivatives and integrals, and thus shines a bright light onto the secant line approximation and Riemann sums. Using Python, we are able to push biological models farther to make them more “palpable,” and thus more meaningful. As well, Python notebooks (Jupyter) seem to be a good way to introduce, through experimentation, new math material.

Fields Institute, Toronto

[Presentation for visiting high school students from Sir Allan MacNab Secondary School]

McMaster University, BSB/B140

[Fall Preview]

McMaster University, MDCL 1105

[CMESG Topic Session, Invited Talk]

I will report on several attempts at identifying alternatives to present-day teaching of mathematics and statistics to year 1 university students. As a possible theoretical framework to support necessary curricular changes I propose an enhanced version of mathematical habits of mind (Cuoco et al., 1996). My presentation will be informed, in part, by an analysis of data from the newly created First Year Mathematics Courses Repository database. I will discuss my efforts and experiments with year 1 mathematics curriculum, which include: investigating possibilities of replacing calculus for students who have to take only one university mathematics course with a true applications-based, active-learning numeracy course; integrating computational thinking into the two life sciences mathematics courses we are offering at McMaster; and modifying an existing “proofs course” into a user-friendly math survival course, with the help of a MOOC.

Quest University, Squamish, B.C. (room 326)

Ad Hoc presentation

Quest University, Squamish, B.C. (room 326)

[Joint Mohawk-McMaster initiative]

Mohawk College, Hamilton

[First Year University Mathematics Across Canada: Facts, Community and Vision conference]

TBA

Fields Institute and University of Toronto

[May at Mac]

TBA

McMaster University, Hamilton Hall 302

[Math at Mac presentation]

Investigation of patterns with numbers, and their use in applications of mathematics. Error detecting codes and cryptography.

CIBC Hall, McMaster Student Union, McMaster University

[Prof Talks Series; OSSTF District 20 Halton]

Presentation and discussion about academic and social issues of transition from secondary to tertiary mathematics.

OSSTF, 920 Fraser Drive, Burlington, ON

[RUME (=Research in Undergraduate Mathematics Education) Conference]

With Andrijana Burazin (University of Toronto, Mississauga); invited talk

We analyze Calculus textbooks to determine to what extent narratives about limits at infinity and infinite limits align with research in mathematics education. As reasoning about limits falls within the domain of advanced mathematical thinking (AMT), we looked for evidence of appropriate treatment of, and support for, AMT: clear and precise narratives, deductive and rigorous reasoning, intuitive development that does not create or enhance students’ misconceptions, opportunities for “personal reconstruction” (Tall, 1991), adequate representations, and the appropriate use of definitions. In conclusion, both high school and university Calculus textbook narratives do not place infinity in a precise, well-defined context, thus possibly creating or strengthening (novice) students’ misconceptions. We identified very little evidence of the type of support for AMT that we were looking for. This paper concludes with several suggestions for possible modifications of narratives which involve infinity.

Coronado Room, Kona Kai Resort, San Diego, CA

[Presentation for visiting high school students from Assumption College School]

[OMCA Presentation]

Conceptualization of health numeracy and the ways we used it to create an online teaching and learning tool for health numeracy.

George Brown College, Toronto

[Presentation for visiting high school students from Sir Allan MacNab Secondary School]

[CMS Winter Conference]

After giving an outline of a large-scale initiative at McMaster to introduce mandatory literacy and numeracy requirements for all students in Science, Social Sciences and Humanities, I will focus on my experiences with creating and teaching my vision of a numeracy course.

The course “Numbers for Life,” now in its second iteration, is (among other things) my attempt at trying to answer the question many of us are asking – if a student needs to take only one math course at university, what would that course be? Calculus and linear algebra are needed for further math development; however, they place numerous constraints on the content that can be used to discuss applications. We have to admit that many “real life” applications in textbooks for these courses are artificial and not at all real life. In designing my course I worked backward, by looking at quantitative narratives addressing important contemporary issues in books, newspapers and internet, and then extracting (rich!) math content from it.

Besides presenting “Numbers for Life” course design and showing a few examples, I will discuss related future plans, which include bringing non-traditional math content into level 1 courses for Math and Stats majors.

Delta Hotel (110 Erb St W) and the University of Waterloo, Waterloo, Ontario

[RUME AnnualConference with Ami Mamolo, UOIT]

We report on a mathematician’s perceptions and awarenesses related to incorporating problem-based activities requiring computational thinking into an upper level undergraduate mathematics course. Computational thinking is understood as the thinking, strategies, and approaches for problem solving that parallel the design of computational algorithms which can be followed by a computer. Data from this case study is qualitative in nature, and seeks to present an in-depth account of one professor’s experiences developing and teaching computational thinking in and for mathematics. Analyses highlight the similarities and differences amongst the values and opportunities perceived for computational thinking versus other more ubiquitous mathematical approaches, as well as the perceived tensions and challenges in trying to foster such values and opportunities.

San Diego

[Fall Preview]

McMaster University, MDCL 1105

[OMCA meeting]

George Brown College, Harbourfront Campus

[Presentation for visiting high school stduents from Bishop Reding HS]

HH 102

[OCMA Yearly Conference, Miroslav Lovric and Taras Gula; T.G. presenting]

In teaching foundations mathematics to health sciences students, topics such as calculating rates and proportions dominate. Given that our students have already completed high school mathematics, is it safe to say that they already have the ability to do calculations? When they can't answer what seem like straightforward questions we posit that they aren't numerate, but what does that mean? Is it important for foundations mathematics students to know that zero is not the same as nothing? How do we evoke numerate thinking that resonates beyond the math class? This presentation will try to answer some of these questions by presenting some preliminary findings from a research project entitled “Improving Health Numeracy in Health Science Students and Professionals Through an Online Instrument.”

Huronia room, Fern Resort, Orillia

[George Brown College Applied Research Day; Miroslav Lovric and Taras Gula; grad student presenting]

Progress report on the deveopment of the online instrument.

George Brown College, Waterfront, Toronto

[May at Mac 2017]

Title says it all.

McMaster University, Hamilton Hall 302

[Talk for visiting high school students (Bishop Redding)]

TBA

McMaster University, Hamilton Hall 104

[Math at Mac session for high school students]

In this talk, I will touch upon some amazing aspects of infinity. Through a sequence of mental experiments we will discover concepts which form the basis of modern mathematical understanding of infinity. Georg Cantor (one of the ‘discoverers’ of infinity) exclaimed 'I see it, but I do not believe it,' as he witnessed his discoveries, unleashed, shaking mathematics to its core and changing it forever. Thinking about infinity is not without danger - Cantor died in a mental institution.

McMaster University, CIBC Hall

[Session for high school teachers]

TBA

McMaster University, Gilmour Hall 111

[Fields Mathematics Education Forum]

We will discuss our SSHRC-funded project “Improving Health Numeracy in Health Science Students and Professionals Through an Online Instrument.” Besides academic collaboration, this project involves partnerships with medical programs and hospitals in GTA. There is plenty of evidence suggesting that the lack of adequate health numeracy is a significant problem. Canadian Council of Learning reported that “60% of adults in Canada lack the capacity to obtain, understand and act upon health information and services and to make appropriate health decisions on their own.”This collaborative action research project is guided by two questions: (1) What are the core elements of health numeracy for health sciences students and health care professionals? (2) How might their health numeracy be most effectively improved using an on-line, interactive instrument? The conceptualization of health numeracy that we are presently working on will inform the content of the on-line learning tool. By seeking input from individuals within academia and elsewhere, we will ensure that special attention is paid to the health science contexts and tasks which demand proficiency in numeracy, so that we can develop meaningful learning tasks.

Room 230, Fields Institute, Toronto

[Third Age Learning]

There is so much to look at and admire in Alhambra Palace (Granada, Spain) - exquisite rooms decorated with stone and wood carvings, finest ornaments and calligraphy; night sky represented in ceilings built of thousands of pieces of wood; gardens, courtyards and fountains; monuments, towers, archways - the list is endless. Quite possibly, an immense wealth of ornamental patterns, friezes, mosaics, star designs, and brickwork motifs tops the list. Among those, mosaics are – mathematically – the most interesting and the most intriguing.

Scientists and artists working in the Islamic world pushed geometry to its limits, creating patterns and configurations whose sophistication has not been surpassed. Investigating numerous possibilities, based on experience and long tradition, architects and builders of the Alhambra (14th century) created all possible mosaics – in the sense of the mathematical classification of plane crystallographic groups. Mathematics behind all this is intuitive: we will discuss the concept of symmetry and see how it can be used to analyze mosaics.

* SOLD OUT *

Art Gallery of Burlington, 1333 Lakeshore Road, Burlington

Introducing Mathematics and Statistics (McMaster, October 2014)

Spotlight on Science episode (McMaster, October/November 2011)

Treehouse talk Toronto, 14 October 2011

[McMaster Fall Preview]

Aspects of learning math, and learning math at McMaster. New and interesting courses we offer, plus opportunities for experiential learning and co-op.

MDCL-1309

[Talk for visiting high school students]

Why math and why bother studying math.

ABB-162

[Talk for visiting high school students]

TBA

[Science 1A03 Talk]

Why math and stats matter.

LRW-1007 (new Wilson building)

[MCM program workshop]

Discussion of ideas in math, psychology of math and learning math.

McMaster CCE, Jackson Square

[McMaster Engineering and Science Olympics]

Through case studies, we will see how math, and geometry in particular, help us understand the space that surrounds us. Can we determine whether our Universe is finite or infinite? What is the shortest distance between two points in space? How many dimensions does our Universe have? We will introduce basic mathematical model of a black hole, and develop a reasonable scenario for time travel.

[ICME-13 Conference]

[With France Caron, Université de Montreal] We report on a short experiment that was conducted to explore the potential and feasibility of introducing complex dynamical systems in the mathematics curricula, both in schools and in university undergraduate programs. The use of game design to engage in the modelling of a real-life changing ecosystem brought to light different mathematical habits of mind and provided a new perspective on how to revisit key mathematical ideas in mathematics education.

Hamburg, Germany

[Panel, Workshop on Digital Open Mathematics Education]

TBA

Room 230, Fields Institute, Toronto

[Workshop on Digital Open Mathematics Education]

Based on experiences with python in my problem-solving math class, I will underline the importance of creation of standard(s) in online instructional materials.

Fields Institute, Toronto

[Workshop on Digital Open Mathematics Education]

No, we are not. I plan to touch upon two related issues: understanding the nature of online media from the classroom perspective and instructors' ability to modify the content of an online course.

Fields Institute, Toronto

[Canadian Math Education Study Group]

Computational thinking working group.

BioSci complex, Queen's University

[May at Mac 2016]

Title says it all.

McMaster University

12noon-1pm, Princetonplein 5, room 385

[Freudenthal Institute]

I will try to sketch a broad landscape within which we teach science and mathematics today, at a typical Canadian university, by discussing initiatives that have emerged as attempts at dealing with the inevitable “how to teach math and science in the 21st century” question in the contexts of teaching math, teacher-training and math education. Teaching genuine scientific applications in high school and university and the emergence of interdisciplinary science programs (we have one at my university), demand major adjustments in instruction, teacher-training as well as adjusting expectations of our students. I will argue that the tensions brought by these new demands provide us with great opportunities for creative and productive changes. For potential controversy, I will question some of our common assumptions about teaching math and science.

University of Utrecht, Holland

[Bishop Redding High School visit]

Why math is fun and how to succeed in math.

BSB/B154, McMaster University

[Math at Mac Day]

In this talk, I will touch upon some amazing aspects of infinity. Through a sequence of mental experiments we will discover concepts which form the basis of modern mathematical understanding of infinity. Georg Cantor (one of the ‘discoverers’ of infinity) exclaimed 'I see it, but I do not believe it,' as he witnessed his discoveries, unleashed, shaking mathematics to its core and changing it forever. Thinking about infinity is not without danger - Cantor died in a mental institution.

CIBC Hall, McMaster University

Interesting and fun things about pi.

hh/109, McMaster University

[Fields Math Ed Forum Meeting]

Comments on the book "Vital Directions in Mathematics Education."

Fields Institute, Toronto

[Science and Engineering Olympics]

Through case studies, we will see how math, and geometry in particular, help us understand the space that surrounds us. Can we determine whether our Universe is finite or infinite? What is the shortest distance between two points in space? How many dimensions does our Universe have? We will introduce basic mathematical model of a black hole, and develop a reasonable scenario for time travel.

Location: McMaster University ITB AB102

[Fall preview at Mac]

Aspects of learning math, and learning math at McMaster. New and interesting courses we offer, plus opportunities for experiential learning and co-op.

[STEM centre seminar]

McMaster University’s Interdisciplinary Science (iSci) program has been designed to “put into practice many of the innovative concepts linking science education and science research” with the aim to present a “holistic view of science through the interaction between various science disciplines.” This four-year program “provides students with an opportunity to specialize in a selected discipline including chemistry, biology, mathematics, physics, […].” In the first year of the iSci program, within a single course (which carries 80% of the full first-year course load) students study five science subjects (mathematics, physics, chemistry, biology, and earth science). I have been teaching mathematics in the iSci program since its inception. Going beyond anecdotes and personal experiences, I have been asking myself — What is the impact of this interdisciplinary approach on learning mathematics? Do students know and understand mathematics better? In what sense are they different from the students who do not have similar experiences? These questions (and others) helped me form a research goal - to determine whether (or not) the rich environment within the iSci program enhances learning mathematics, both in terms of content knowledge (functions of one variable, power series and differential equations) and skills (formation of a precise mathematical argument, problem-solving, communication of scientific ideas, etc.). I plan to discuss results and analyse students’ replies to the survey I have conducted, which lead to some (perhaps) surprising conclusions.

[Western Conference on Science Education]

Numerous published papers, conference presentations and panels attest to the need and importance of teaching applications within mathematics courses. I will argue that there is benefit of teaching applications within any science discipline.
By an “application” I mean any context (within science, or broader) which involves or requires some kind of quantitative thinking. For instance, arguments involving risk, chance, or uncertainty use probabilistic concepts. Every time we interpolate or extrapolate from a given set of data we employ functional relationships. In discussing dynamics of drug absorption we use exponential, or more complex mathematical models. Describing viruses infecting certain bacteria, or studying interactions between species in an ecosystem requires that we use mathematics tools.
Mathematics is an abstract discipline, lot more so than other sciences – and hence the tensions I plan to discuss. Every time we discuss a scientific phenomenon, i.e., an application (say, a climate change) using quantitative tools, tensions inevitably show up. They are present in the ways we formulate the problem of our inquiry, in defining objects we study, in the assumptions we make, in the interpretations of results of experiments and mathematical calculations, and elsewhere.
I will argue that, by contrasting the ways these tensions exist and function within each science discipline, we can create rich teaching and learning situations that will deepen our understanding of both math and sciences. Instead of being very abstract, I plan to discuss numerous examples to illustrate these situations.

[Western Conference on Science Education]

Many introductory science courses have very high enrolment, particularly at large universities. For mathematics, teaching large classes is particularly challenging, since the course material rarely lends itself to slide-show presentations, and typically involves extensive and careful writing, both by instructor and student. While teaching a large section of such a course (300 or more students) thus has unique challenges, offering high enrolment courses in numerous smaller sections can also be problematic. In this panel, we will discuss contrasting experiences in coordinating and instructing large introductory courses, with an emphasis on mathematics courses. We do not plan to discuss institutional and other constraints that are beyond what we as instructors can change. Instead, we will focus on ideas, pedagogical approaches and teaching strategies. After brief introductory remarks from the panelists, we will host a moderated discussion and question and answer session. From this session, we plan to create a list of recurring topics and issues, then gather in small groups focussed on each issue. In this way instructors facing similar issues will have a chance to meet, share and brainstorm. Our aim is to provide participants with fresh ideas that will allow each of us to improve the first-year math experience at our home institutions, for example by connecting lectures to current research topics and raising expectations for serious, independent learning.

[CMESG = Canadian Math Education Study Group conference]

Presentation and discussion.

[May@Mac presentation]

Title says it all.

[Fields Math Education Forum meeting]

The agenda of this meeting is to discuss constructive attempts at answering important questions about teaching mathematics at all levels (with a focus on secondary and tertiary education). We feel that many things are broken, and need to be fixed. Today’s speakers will try to identify what some of these broken things are, and suggest ways of changing and improving them. In my presentation, I will try—as an introduction to the day—to sketch a landscape in which we teach mathematics today. I will mention several ideas and projects that have emerged as attempts at dealing with the inevitable “math in the 21st century question” in the contexts of teaching math and math education. For some potential controversy, I will question of our common assumptions about teaching math, both in high school and in university.

[Guest lecture]

Case studies illustrating how math helps us understand the world around us, and how the unsolved questions in other disciplines stimulate further development of mathematics.

[Lecture for visiting highs school students]

[Lecture for visiting highs school students]

[Lecture, Math at Mac Day]

In this talk, I will touch upon some amazing aspects of infinity. Through a sequence of mental experiments we will discover concepts which form the basis of modern mathematical understanding of infinity. Georg Cantor (one of the ‘discoverers’ of infinity) exclaimed 'I see it, but I do not believe it,' as he witnessed his discoveries, unleashed, shaking mathematics to its core and changing it forever. Thinking about infinity is not without danger - Cantor died in a mental institution.

[Plenary, Canadian Math Society Winter Meeting]

I plan to discuss several ideas and projects that have emerged as attempts at dealing with the inevitable “21st century question” in the contexts of teaching math and math education. I will mention new initiatives that we have been working on at McMaster, including our new first-year math programming course. For potential controversy, I will question (and suggest alternatives to) some of our common assumptions about teaching math, both in grade 12 high school and in university.

[Plenary, Canadian Math Society Winter Meeting]

Tensions between mathematics done by mathematicians and that done by life scientists will be explored during this discussion of the place of calculus in multidisciplinary programs and the future of calculus courses

[Science and Engineering Olympics]
Quite often, we use mathematics to predict events related to our near future - for instance, we calculate a weather forecast for the following week, or study the spread of some infectuous disease, or try to figure out the effects of invasive species on the flora and fauna of Lake Ontario. But how about long-term predictions? What will the population of humans on Earth be 500 years from now? Is it true that there will no more oil in 300 years? Universe (as we know it) was created about 13.7 billion years ago. What will it look like 10 billion years from now? In this presentation, we will see what math can do - and cannot do - to answer these, and similar questions.

[General interest lecture for high school students]

Selection of case studies of present-day research afforts in mathematics: error correcting codes and computer security, data compression and transmission of large amounts of data; learning from animals; weather forecasting and understanding disasters (tsunami, freak waves).

[General interest lecture for high school students]

The idea is to demonstrate – using colourful examples drawn from my experience as a university professor – that the beliefs, skills and attitudes we need to succeed in mathematics are exactly the same as those that we need to succeed in any other aspect of our life.

[Time 2014 Conference]

In this presentation I will report on the classroom experience (from both students’ and instructor’s perspectives) in an advanced mathematics problem-solving course (called Math 3G3), in which students were asked to investigate mathematical problems using computers. In this case, ‘using computers’ means writing one’s own computer code, as opposed to using ready-made software where users manipulate parameters, change settings, etc., but are not (in most cases) aware of underlying mechanisms that control the software.

[Canadian Math Society Summer Meeting]

Math majors take many math courses, but can they actually DO mathematics? To provide my third-year students with an opportunity to think, hypothesize, investigate and problem-solve (as opposed to listen and take notes), I designed a sequence of problems that they had to work on, individually or in small groups. After briefly describing the design of the course, I will discuss my students' experiences with this (for many) different approach to working with new math material.

[Canadian Math Education Study Group]

Modelling complex interactions of four species in Yellowstone National Park: wolves, elk, berries, and bears. The aim is to figure out the long-term effects of introduction of wolves into the park in 1980s.

[TedX St Mary S School May 2014]

The idea is to demonstrate – using colourful examples drawn from my experience as a university professor – that the beliefs, skills and attitudes we need to succeed in mathematics are exactly the same as those that we need to succeed in any other aspect of our life.

[Canadian Math Education Forum CMEF 2014]

In the article “Bureaucrat's Math Makes Dizzy Dozen,” written by P. Rolly and J. Jacobsen- Wells and published in The Salt Lake Tribune on 11 October 2002 (Article ID: 100DF2EEC6A2847B) we read:

The menu at the Coffee Garden at 900 East and 900 South in Salt Lake City has included a scrumptious selection of quiche for about 10 years. The recipe calls for four fresh eggs for each quiche. A Salt Lake County Health Department inspector paid a visit recently and pointed out that research by the Food and Drug Administration (FDA) indicates that one in four eggs carries salmonella bacterium, so restaurants should never use more than three eggs when preparing quiche. The store manager asked the inspector whether throwing three randomly chosen eggs from each dozen, and then making 4-eggs quiches from the remaining eggs would work equally well. The inspector gave no answer.

Starting with this story, we devlop and interesting (and challenging) set of math problems.

[Integrated Science Symposium - Synthesis] Keynote address

Using math to make long-term predictions of human population behaviour and usage of resources.

[Math@Mac Presentation]

Through case studies, we will see how math, and geometry in particular, help us understand various features of the space that surrounds us. Can we determine whether our Universe is finite or infinite? What is the shortest path between two points in space? How would our mundane three-dimensional existence change if we were suddenly pulled into the fourth dimension? What is a dimension? How many dimensions does our Universe have? We will introduce basic mathematical model of a black hole, and, as a fun application, will develop a reasonable scenario for time travel.

Interview in the series of 3M teaching fellows interviews, conducted at McMaster University in summer 2010: Talking About Teaching [Youtube] part 1 [parts 2-5 linked to part 1]

To view my lecture Infinity: the Most Fascinating of all Ideas that I gave at Royal Canadian Institute on Sunday, 22 January 2006, click here [will open in new window/tab; it is now a podcast [I have no control over type of media used] and you might need an appropriate plug-in to view/listen; your browser will either start playing the video or else will probably identify the plug-in that you need to download]

[Fall preview at Mac]

Aspects of learning math, and learning math at McMaster. New and interesting courses we offer, plus opportunities for experiential learning and co-op.

[Science and Engineering Olympics]

Certain patterns of behaviour in animals are far from random - as a matter of fact, they can be explained and understood using mathematics. It turns out that animals are lot smarter than we think they are. More than that - scientists can learn a lot by observing how animals do certain things.

[HISTReENet]

How does the life of a 21st century scientist differ from the lives of Galileo, Archimedes or Newton? By examining case studies and interesting stories in math and elsewhere, we will discuss the ever-changing relationships between a scientist and her/his science, and between the sciences and other areas of human endeavour.

[Fall preview at Mac]

Aspects of learning math, and learning mat at McMaster. New and interesting courses we offer, plus opportunities for experiential learning and co-op.

[HISTReENet Panel]

TBA

[Western Conference on Science Education 2013]

McMaster University’s Interdisciplinary Science (iSci) program has been designed to “put into practice many of the innovative concepts linking science education and science research” with the aim to present a “holistic view of science through the interaction between various science disciplines.” This four-year program “provides students with an opportunity to specialize in a selected discipline including chemistry, biology, mathematics, physics, […].” In the first year of the iSci program, within a single course (which carries 80% of the full first-year course load) students study five science subjects (mathematics, physics, chemistry, biology, and earth science). I have been teaching mathematics in the iSci program since its inception. Going beyond anecdotes and personal experiences, I have been asking myself — What is the impact of this interdisciplinary approach on learning mathematics? Do students know and understand mathematics better? In what sense are they different from the students who do not have similar experiences? These questions (and others) helped me form a research goal — to determine whether (or not) the rich environment within the iSci program enhances learning mathematics, both in terms of content knowledge (functions of one variable, power series and differential equations) and skills (formation of a precise mathematical argument, problem-solving, communication of scientific ideas, etc.). I plan to discuss results and analyze students’ replies to the survey I conducted, which lead to some (perhaps) surprising conclusions.

[York Region PA Day]

Most teachers are interested in knowing whether or not students are well prepared for university and college. The math curriculum has changed quite extensively in the past 8 years and there is some uncertainty that students might be overwhelmed after high school. Topics like working with matrices, integration, and some other calculus topics have been removed from high schoolcourses. Some teachers still take the time to teach these concepts, but not all. Which concepts need to be solidified, how should they be taught?