In this monthly column, we speak with a notable member of the mathematics education community about their work and their perspectives on the teaching and learning of mathematics. This month, we had the pleasure of speaking with Dr. Harley Weston.
Harley was born and raised in Southern Ontario and went to high school in Caledonia, where a Grade 10 teacher taught him geometry using Euclid as the text. This is where he was first introduced to the beauty and lure of mathematics. He received an undergraduate degree from McMaster University and a Masters and PhD from Lehigh University in Bethlehem, Pennsylvania. In 1967, Harley and his wife Marianne moved to Regina, where they lived for almost 50 years. He taught in the Department of Mathematics and Statistics until his retirement in 2005. His research was in Point Set Topology for a few years, after which his interests turned to Applied Mathematics and Mathematical Modelling. Starting in about 1995, his academic interests changed again, this time to Mathematics Education. In 1992, he was awarded the University of Regina Alumni Association Award for Excellence in Undergraduate teaching, in 2007 the annual Education Prize from the Pacific Institute for the Mathematical Sciences, and in 2008 the Adrien Pouliot Award from the Canadian Mathematical Society.
Harley and Marianne have two sons, three granddaughters, and two great granddaughters. They now live in the hamlet of Pasqua Lake in the Qu’Appelle Valley.
Thank you for taking the time to have this conversation, Dr. Weston. I would like to start by asking you about your interest in mathematics education. Your background is in applied mathematics, and this was the focus of your research at the Department of Mathematics and Statistics at the University of Regina from 1967 until 2005. However, you have also spent much time cultivating relationships between mathematicians, K-12 students, mathematics teachers, and Education faculty. In your view, why is it important to establish dialogue between these groups?
Thank you for inviting me to be part of this endeavour.
[perfectpullquote align=”right” cite=”” link=”” color=”” class=”” size=””]”I have always been passionate about the beauty and elegance of mathematics and have used my teaching as an attempt to transmit my love of mathematics and to help others glimpse the beauty that I see.”[/perfectpullquote] When I arrived in Regina in 1967, my academic interest was in pure mathematics, and it wasn’t until about 1980 that I became interested in applied mathematics. I have always been passionate about the beauty and elegance of mathematics and have used my teaching as an attempt to transmit my love of mathematics and to help others glimpse the beauty that I see. At times, however, I have been frustrated by the fact that many people don’t share this view of mathematics or even appreciate how anyone could have this view. I think that part of the reason that so many people have a negative view of mathematics is due to the way that it is taught, and I felt that I had much to learn about mathematics teaching from my colleagues in mathematics education. Fortunately, at the University of Regina there was already a close working relationship between some of my colleagues in the Department of Mathematics and Statistics and faculty in the Faculty of Education, so it was relatively easy for me to build on this.
In my view, those of us who are faculty members in mathematics can learn from a relationship with education faculty, teachers, and K-12 students. Many of the students we teach are students in the Faculty of Education, and it is valuable to know what their faculty expects of them. It is also very valuable to know what we can expect from students as they transition from high school to university. Furthermore, mathematics faculty have much to offer to faculty members in education and the K-12 community, both in their knowledge of the subject area and their passion for it.
In what ways do you suggest that mathematicians reach out to members of the mathematics education community (including students, teachers, and Education faculty), and how did you do so personally? In what ways can the relationships be reciprocal, or mutually beneficial?
In my experience, nothing is as valuable as finding a project to work on with a colleague in education. Before I became involved, members of our department and members of the faculty of education worked together to design a mathematics course that is a requirement for all education students in the elementary program. This course is taught by members of both units, which helps maintain the contact. We also worked together on an annual math camp where we involved mathematics and mathematics education students as volunteers. These students take classes together, but may have little contact otherwise. It is valuable for them to work together, and in particular in our math camp the mathematics students see that the mathematics education students have skills and knowledge that may not be evident in mathematics classes.
[perfectpullquote align=”right” cite=”” link=”” color=”” class=”” size=””]”I have found that if you give the students as much freedom as possible, they grow professionally and excel in the work.”[/perfectpullquote] In addition, I work with mathematics education faculty and students on Math Central, Aboriginal Perspectives and Math on the Move. Over the years, I have hired many mathematics education students in these projects and have found it very rewarding; I think that the students found it rewarding as well. I have found that if you give the students as much freedom as possible, they grow professionally and excel in the work.
One of your own ongoing outreach efforts is Math Central (http://mathcentral.uregina.ca), a collection of internet services designed for teachers and students of mathematics at the K-12 level. Created in 1995 and maintained by University of Regina faculty and students ever since, Math Central has earned many awards since its inception, and was cited as one of your major contributions to the advancement of mathematics and mathematics education at the local, regional, and national levels when you received the 2008 Canadian Mathematics Society (CMS) Adrien Pouliot Award and the 2008 Pacific Institute for the Mathematical Sciences (PIMS) Education Prize.
Could you describe what Math Central offers for students and teachers of mathematics, and what sparked its creation? How has it evolved over the years?
In 1995, the World Wide Web was in its infancy and there were very few educational websites. Denis Hanson (a mathematician), Mhairi (Vi) Maeers (a mathematics educator), and I, all at the University of Regina, saw the possibility of creating a mathematics education website for use by K-12 students, teachers, and parents. We also saw this as a way to introduce the mathematics education students at the University of Regina to using the web as a teaching resource. This may seem strange now, but it was before schools, school boards, or the Department of Education had their own websites.
The resulting website, Math Central, began with four services: The Resource Room, a place where teachers could share teaching ideas; Quandaries and Queries, a question and answer service; Teacher Talk, a mailing list for teachers; and The Bulletin Board, which contained, among other things, links to mathematics teachers’ organizations across the country. From the beginning, Teacher Talk and the Bulletin Board were infrequently used, and Teacher Talk was soon dropped and replaced by other services. The material in the Resource Room and in Quandaries and Queries are stored in searchable databases. The initial development of Math Central was supported by a grant from the Multimedia Fund of the Department of Education and support from the Faculties of Education, Science, and Graduate Studies and Research. This and other funding that Math Central has obtained over the years has been used largely to hire students, mainly students in the Faculty of Education, for part-time positions during the academic year as well as for summer positions.
Most of the items in the Resource Room come from Saskatchewan teachers, many from pre-service teacher projects in mathematics education courses. Others were gathered from visits to teachers in their classrooms and from the former SMTS publication, Ideas and Resources for Teachers of Mathematics (see the Math Central website for select issues). When the Stewart Resource Centre at the Saskatchewan Teachers’ Federation went from distributing paper copies of its resources to digital distribution, they gave all of their mathematics material to Math Central for posting in the Resource Room. Approximately 10% of the items in the Resource Room are in French.
Quandaries and Queries has been by far our most active service. The primary goal is to respond to students’ questions with ideas, hints, or links to responses to similar questions to help them solve the problems themselves. The responses are supplied by teachers, university faculty and students across the country. Each response is formatted into a web page and entered into the database by an editor. The fact that many of the responses are read by the responder and an editor gives some degree of quality control to the responses. The majority of questions do come from students, but we also receive questions from parents, especially addressing topics that were not in the curriculum when they were in school. One surprise has been the number of questions received from the general public. These questions are wide ranging for example determining the number of acres in an odd-shaped lot, scheduling foursomes for a golf vacation, questions from artists, questions about carpentry, calculating the amount of fertilizer in a bin, and much more. Using the keyword search, in Quandaries and Queries you can find some of these questions from the general public and our responses by entering the phrase math beyond school. You can also drill down somewhat in the database by adding a keyword. For example, the phrase math beyond school trigonometry will bring up questions where we have used trigonometry in our responses.
From 1995 to 2002, Vi Maeers and I hired mathematics education pre-teachers to work on Math central, visited schools to invite teachers to share their lessons in the Resource Room, and presented our work to mathematics teachers’ conferences in Canada, the United States, and Europe. Other mathematics education web sites came into existence over this period that allowed teachers to share their work, and Saskatchewan teachers were at the forefront of this movement.
Over the years, additional services have been added to Math Central. One is Mathematics with a Human Face. A quilt of photographs of people with a degree in mathematics was created, and clicking on a face on the quilt brings up a PDF file that profiles that mathematician and his or her career. These pages are designed to be printed on an 8.5” by 11” page so that a teacher can post them in his or her classroom. As part of this initiative, we also produced a poster, titled Mathematicians At Work, which was mailed to every high school and public library across the country. A pamphlet was also developed and distributed at teacher conferences and math camps. The quilt, poster, and pamphlet were produced in both English and French.
In 2000, a Problem of the Month section was started by Chris Fisher with help from Claude Tardif and later from Martin Argerami. A problem was posted at the beginning of each month with an invitation for solutions from anyone interested; at the end of each month, a solution was posted, with credit given to all who correctly solved the problem. From the beginning, the problems and solutions appeared in both English and French, and in 2005 a Spanish version was added. In 2012, Chris Fisher retired and our Problem of the Month section ceased to be active. However, the problems and solutions still exist on the site.
One more service I want to mention is Math Beyond School. This is our attempt to help answer the question “When will I ever use this?” The articles span a wide range of topics and mathematical concepts. Their purpose is to provide some examples of how math is used in everyday living and in specific occupations.
Two companion sites to Math Central are Aboriginal Perspectives and Math on the Move. These are mathematics education projects undertaken with Kathy Nolan, a colleague in the Faculty of Education at the University of Regina.
Math Central, and in particular Quandaries and Queries, is not as active as it was a few years ago. My feeling is that part of the reason for this is the advent of social media. Facebook, Twitter, and the other social media networks provide students and parents a more immediate way to obtain responses to their mathematical questions than we can supply, and the responses come from people they know and trust. Our site is still very active, but most of the hits are to items in our databases that come from searches using Google, Bing, or other search engines.
In recent years, you have also been involved in work and research in the interface between mathematics and Aboriginal culture, perspectives, and ways of knowing. In 2009, for example, you worked with students from the Saskatchewan Urban Native Teacher Education Program (SUNTEP) to develop mathematics activities with a distinctly Aboriginal focus, an initiative which has since then been expanded (see Nolan & Weston, 2015). More recently, you have been involved with the development of Aboriginal Perspectives (http://aboriginalperspectives.uregina.ca/), a companion site to Math Central featuring videos, lessons, games, and other information for incorporating Aboriginal culture, perspectives, and ways of knowing in the teaching and learning of mathematics.
How did you become involved in this effort? Has your work and research in the intersection of mathematics and Aboriginal culture changed, or added, to your understanding of the nature of mathematics and what it means to “do” mathematics? (If so, how?)
I don’t really know how I first became interested in mathematics and Aboriginal culture, but I have been interested in anthropology for a long time, so it is natural that I would look at the relationship between mathematics and culture. In 2001, Karen Arnason (an instructor at SUNTEP in Regina), Judith (Judi) McDonald (a fellow mathematician), Vi Maeers, and I presented a paper entitled “Interweaving Mathematics and Indigenous Cultures” at a meeting of New Ideas in Mathematics Education, and then in 2002, Judi and I presented a paper at a meeting of the Second International Congress on Ethnomathematics. These two papers led me to look at the work by the entnomathematics group in North America to see what had been done on the mathematics of the First Peoples of the Americas. I found many references to the mathematics of the Indigenous people in South America and in the southern United States, but very little concerning the mathematics of the First Peoples in our part of the world. This gap became significant to me when I began to hear concerns from teachers in trying to meet the curriculum requirement that they include an Aboriginal perspective in their mathematics classes. The Aboriginal Perspectives web site was an attempt to address these concerns.
In 2009 I hired a student from SUNTEP, a second a student from the Faculty of Education, and a third from our School of Journalism to create lesson ideas built around video clips from both interviews with individuals in the Aboriginal community and traditional Aboriginal activities. In the summers of 2010 and 2011, Kathy Nolan and I worked with students from SUNTEP and the First Nations University of Canada to develop workshops to aid teachers of Grades 3 to 6 with including an Aboriginal perspective in their mathematics classes. The students facilitated these workshops to teachers in Regina in 2010 and 2011 and since then, Kathy and I have delivered these workshops to teachers in various parts of Saskatchewan and in Yellowknife.
[perfectpullquote align=”right” cite=”” link=”” color=”” class=”” size=””]”We tend to see mathematics as procedural, “algebraic”, and acultural, but I now see it as much more than that.”[/perfectpullquote] This work on Aboriginal Perspectives and my contact with the ethnomathematics group has changed my understanding of the nature of mathematics. We tend to see mathematics as procedural, “algebraic”, and acultural, but I now see it as much more than that. I love the beauty and elegance of abstract mathematics, but I also now see mathematics through the lens of the holistic nature of Indigenous knowledge. Kathy Nolan and I saw the challenges and opportunities that this can create for teachers in our work in Yellowknife. There is a document in the Northwest Territories called the Dene Kede Curriculum, which was developed by elders and teachers across the territories. Teachers are expected to link their mathematics lessons to outcomes in the Alberta curriculum as well as to articles in the Dene Kede curriculum.
Do you foresee a danger of activities, such as playing Aboriginal games of chance, being decontextualized and used simply as an “add-on” (and a curriculum requirement), rather than an element of a greater effort to incorporate Aboriginal culture, perspectives, and ways of knowing in the classroom? In your view, what would the latter entail, and how might teachers grow in their capacity to do so?
[perfectpullquote align=”right” cite=”” link=”” color=”” class=”” size=””]”I encourage teachers to invite Aboriginal elders into their classes and to listen carefully to what they say.”[/perfectpullquote] Yes, I do worry about our activities being used as an “add-on” to satisfy the curriculum requirements. In our workshops, we implore the teachers to read the background information we have collected, encourage them to search out other background information, and to share it with their students. I am not an expert on Aboriginal ways of knowing and I encourage teachers to invite Aboriginal elders into their classes and to listen carefully to what they say.
In wrapping up this interview, I’d like to ask you about your current work and interests. For nearly 20 years, in addition to maintaining the Math Central website, you were active in responding to students, teachers, and the general public who sent in mathematics questions to Math Central—and are still doing so! In what other ways do you continue to be involved with the mathematics and mathematics education communities in Saskatchewan? Have you pursued any new interests (mathematical or otherwise) since your retirement?
Much of my work, particularly in Aboriginal Perspectives and Math on the Move, has been done since I retired in 2005. I still respond to questions that come to Quandaries and Queries, many under the pen name Penny Nom, and I continue to work on the maintenance of the websites. One of the challenges of retirement is that I miss the contact with students, but I have been able to maintain it somewhat through Aboriginal Perspectives and Math on the Move. The enthusiasm and ingenuity of our students is a resource that I have relied on to my benefit and to the benefit of the students. In all of my mathematics education endeavours, most of the work has been done by students.
Other than mathematics activities, I am the treasurer of a retirees group at the University of Regina. This group has raised a substantial amount of money for a scholarship fund and I chair the scholarship committee. We have recently moved from our house in Regina to a lakefront property in the Qu’Appelle Valley, where I spend time gardening and woodworking. I am also an avid knitter.
Thank you, Dr. Weston, for taking the time to share your experiences and perspectives. We look forward to continuing the conversation in the future.
Ilona Vashchyshyn
References
Nolan, K., & Weston, H. (2015). Aboriginal perspectives and/in mathematics: A case study of three Grade 6 teachers. in education, 21(1), 13-22.
