# Educational

## Changing the Culture 2022 Plenary: Logic in K − 12

We will give examples from grade 1 to through high school where the logical insights of the last century impact classroom teaching. We include both "do's and don'ts". These examples range through such topics as "equals" vs "evaluate" vs "solve", "why multiplication is not JUST repeated addition", "lies my teacher told me", "identities, equalities and quantifiers", and "Is it true that the sum of the angles of a triangle is 90o". We will briefly discuss the place of formal logic in the secondary school.

## Changing the Culture Panel Discussion: How has Coronavirus changed the teaching of Mathematics?

The title for the panel discussion at this year's Changing the Culture conference was "How has Coronavirus changed the teaching of Mathematics?". In the video, each of our panelists addresses that question from their perspective. Following these opening remarks, the panelists respond to questions posed by the Changing the Culture community.

## PIMS Education Prize 2021: Bruce Dunham

PIMS is pleased to announce that the winner of the 2021 Education Prize is Dr. Bruce Dunham, Professor of Teaching in the Statistics Department of the University of British Columbia.

Dr. Dunham is an internationally respected expert in statistics education, and has contributed to education in the mathematical sciences by developing and providing resources for evidence-based teaching. He has also provided training and expert advice on statistics teaching and curriculum. He has served in a range of leadership roles at UBC and at the provincial and national level.

Dr. Dunham has served on the British Columbia Committee on the Undergraduate Program in Mathematics (BCCUPMS) since 2006 and has been the chair of the BCCUPMS Statistics sub-committee since that time. He has played a major role in the new BC Statistics 12 high school course, from defining the vision of the course, to the development of the curriculum and currently, in his continued role in teacher support and training, including offering five training workshops for teachers. At the national level, Dr. Dunham has served in various roles in the Statistical Society of Canada. He has served on the executive committee of the Society’s Education Section, having previously been secretary and president and currently president-elect. He has served on the Society’s Education Committee.

The evaluation committee was particularly impressed by the direct public impact of his curriculum work in the BC school system, and the development of free software for the community. Dr. Dunham is a tremendous advocate for mathematics and statistics, his leadership contributes to public awareness, fostering communication among various groups concerned with mathematical training. We are very pleased to celebrate him, and his achievements with the PIMS Education prize.

Dr. Dunham's prize was awarded as part of the 2021 Changing the Culture event.

## How to fold things into thirds, sevenths, and thirty-sevenths!

Come with something floppy in hand--a string, a shoelace, a tie, or perhaps a floppy zucchini. Not only will we fold the object into strange fractional lengths, but we’ll also see how folding it into fractions leads to famous unsolved mathematics! Can you solve an unsolved problem?

## Math Outreach: Many Needs, Many Ways

Math Outreach: Many Needs, Many Ways

I will present a wide range of math educational outreach activities involving elementary, middle and secondary level students. By expecting children to succeed, introducing new and exciting ways to teach mathematics, and promoting role models, the Pacific Institute for the Mathematical Sciences (PIMS) is making a significant difference in the way students view science and technology and their own mathematical ability. These activities are designed to transform the way students look at mathematics and empower them to see themselves as fully capable of succeeding at math. I will describe PIMS outreach programs specifically designed for First Nations schools in British Columbia.

We have also developed a variety of programs to support teachers, in particular I will describe our must recent one: a 4-week Summer School for Elementary School Teachers. At this camp, teachers work with mathematicians, educators and math specialists to increase their mathematical knowledge and capability and boost their confidence, as well as foster a positive attitude towards learning mathematics.

WORKSHOPS:

1) Bar Model Workshop (Friday, October 27, 1:00 - 2:15 pm)

The main purpose of this workshop is to show how the Bar Model method can be used not only as a problem solving technique, but also to develop in students a deeper understanding of fundamental concepts in mathematics.

2) Kindergarten to Grade 2: An important foundation for success (Friday, October 27, 2:30 - 3:45 pm)

What students learn during these early years will make a significant difference in how they approach mathematics later on. Research is showing that mathematics knowledge and skills are the most important predictors not only for later math achievement but also for achievement in other content areas (Claessens A. and Engel M., 2013). This workshop presents connection of various concepts and ideas, teaching sequencing, and hands-on fun activities for retention.

## Women in Math

See the event webpage for more information on Two Weeks in Vancouver - A Summer School for Women in Math.

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## Juggling Mathematics & Magic

The popular Richard & Louise Guy lecture series celebrates the joy of discovery and wonder in mathematics for everyone. Indeed, the lecture series was a 90th birthday present from Louise Guy to Richard in recognition of his love of mathematics and his desire to share his passion with the world. Richard Guy is the author of over 100 publications including works in combinatorial game theory, number theory and graph theory. He strives to make mathematics accessible to all.

Dr. Ronald Graham, Chief Scientist at the California Institute for Telecommunications and Information Technology and the Irwin and Joan Jacobs Professor in Computer Science at UC San Diego.

Dr. Ronald Graham, Chief Scientist at the California Institute for Telecommunications and Information Technology and the Irwin and Joan Jacobs Professor in Computer Science at UC San Diego, will the present the lecture, Juggling Mathematics & Magic. Dr. Graham’s talk will demonstrate some of the surprising connections between the mystery of magic, the art of juggling, and the some interesting ideas from mathematics.

Ronald Graham, the Irwin and Joan Jacobs Professor in Computer Science and Engineering at UC San Diego (and an accomplished trampolinist and juggler), demonstrates some of the surprising connections between the mystery of magic, the art of juggling, and some interesting ideas from mathematics. The lecture is intended for a general audience.

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## A topological look at the vector (cross) product in three dimensions

The vector product (or cross product) of two vectors in 3-dimensional real space $\mathbb{R}^3$ is a standard item covered in most every text in calculus, advanced calculus, and vector calculus, as well as in many physics and linear algebra texts. Most of these texts add a remark (or “warning”) that this vector product is available only in 3-dimensional space.

In this talk we shall start with some of the early history, in the nineteenth century, of the vector product, and in particular its relation to quaternions. Then we shall show that in fact the 3-dimensional vector product is

notthe only one, indeed the Swiss mathematician Beno Eckmann (a frequent visitor to Alberta) discovered a vector product in 7-dimensional space in 1942. Further-

more, by about 1960 deep advances in topology implied that there were no further vector products in any other dimension. We shall also, following Eckmann, talk about the generalization to r-fold vector products for

$r\geq 1$ (the familiar vector product is a 2-fold vector product), and give the complete results for which dimensions n and for which $r$ these can exist.

In the above work it is clear that the spheres $S^3$, $S^7$ play a special role (as well as their “little cousin” $S^1$). In the last part of the talk we will briefly discuss how these special spheres also play a major part in the recent solution of the Kervaire conjecture by Hill, Hopkins, and Ravenel, as well as their relation to the author’s own research on the span of smooth manifolds.

## It’s All in the Follow Through – what research in math education says ... and doesn’t say

We’ll be examining a few classic cases of how educational research has been handled that explain a lot about how we got where we are in public school math education today.

## Robustness of Design: A Survey

When an experiment is conducted for purposes which include fitting a particular model to the data, then the ’optimal’ experimental design is highly dependent upon the model assumptions - linearity of the response function, independence and homoscedasticity of the errors, etc. When these assumptions are violated the design can be far from optimal, and so a more robust approach is called for. We should seek a design which behaves reasonably well over a large class of plausible models. I will review the progress which has been made on such problems, in a variety of experimental and modelling scenarios - prediction, extrapolation, discrimination, survey sampling, dose-response, etc