“To me, mathematics is a way of seeing ad experiencing the world”
Lynda's biography
Lynda Colgan, PhD, is a mathematics educator at The Faculty of Education, Queen’s University. Lynda’s career began in Scarborough, Ontario where she taught at many schools including Sir Oliver Mowat C.I. and Eastview P.S. Since then her roles have been many: district-wide computer consultant and mathematics coordinator; researcher; professor; columnist; textbook author; children’s non-fiction book author and developer of educational television programming. Lynda is the recipient of one international and one national award: The Marshall MacLuhan Distinguished Teacher Award and The Partners in Research Mathematics Ambassador Award, respectively. Her research, creative work and teaching have also been recognized at the provincial, local and institutional level by organizations including The Ontario Association for Mathematics Education, The Ontario Secondary School Teachers’ Federation and The Queen’s Education Student Society. Her current research interests include parents as partners in mathematics education and non-traditional approaches to mathematics instruction. Lynda believes that because parents are children’s first and most important teachers and that positive parental disposition and involvement is correlated to improved student achievement, parents must be given opportunities to be learn the math that they see coming home as homework. Without educative opportunities, her work emphasizes that parents continue falsely to fear and be suspicious of new content and methods and insist that they are ill- equipped to support math learning at the kitchen table. To ameliorate these widespread negative influences, Lynda has developed on-line resources and print materials that scaffold curriculum and focus equally on affect: concretizing current research that shows that affective functions and cognitive ones are inextricably linked. A provincial parent engagement kit will be launched at the Ministry of Education’s annual Parent Involvement Conference in April, 2015. Lynda’s other interests include informal mathematics learning through the arts, children’s literature, and, media, culture and technology. Lynda’s research and community outreach activities have been funded by SSHRC, NSERC, The Imperial Oil Foundation and the MSTE Group at Queen’s.
The most important skill that I learned in university was to collaborate. My fondest recollections of my undergraduate years are those of a small cadre of eager, young mathematicians huddled over a problem set in a local coffee shop. The coffee cup rings on assignments were testaments to the ways in which we engaged in discussing and explaining ideas, challenging and teaching one another, creating and solving each other’s questions and working collaboratively to share methods and results. In our, small, familial groups, we were confronted by our fellow students’ different solutions and points of view. This resulted in what researchers call “socio-cognitive conflicts” that were accompanied by feelings of uncertainty. The high level of trust caused a willingness by group members to reconsider their own solutions from a different perspective: stimulating higher cognitive skills. Our coffee-fueled discussions helped us to conquer the uncertainty caused by different points of view with the help of other members of the group, particularly where difficult or complicated assignments were concerned.
I am happiest when I am in the middle of a raucous gymnasium filled with children and their parents who are active participants in Family Math nights: determining the height of the basketball net using indirect measurement; discovering their body type (perfect square, tall or short rectangle); reassembling a tangram square or making a pizza-cutter trundle wheel. We know that all learning begins with play. Children learn about fluids and buoyancy by “doing the dishes” at the kitchen sink. Similarly, they learn geometry with play about space and shape, forming visual templates of shape categories (e.g., they come to recognize a shape as a rectangle because “it looks like a door”). As children move beyond the kindergarten years, it is crucial that they continue to have many opportunities, outside school hours, to learn through planned play environments in which learning opportunities are deliberately embedded.
At their core, experiential learning activities in informal contexts such as Family Math are designed so that when children play, engage, explore, or interact, they cannot not help but learn science and mathematics because they are doing science or mathematics. Further, initial curiosity in science or mathematics has the potential to evolve into genuine interest. The “wow” factor that first captures a child’s attention is likely to contribute to the development of greater understanding of, and positive attitudes toward, mathematics and science.
When I am not reading mysteries or working on my traditional rug-hooking projects, I can be found with my camera looking for photographic evidence that mathematics is ubiquitous. For my latest project, I have photographed my dog Ailsa’s pawprints in the sand to record the seven symmetries of frieze groups. I am also a prolific letter writer. For example, I have written to the Governor of the Bank of Canada and the Prime Minister to complain about the discontinuation of the penny. How can children understand five cents when they have no referent: one cent, on which to base the ratio? Five is an anchor number, but it is based on the unit (in this case, the penny). Without the unit, children’s understanding of place value is compromised: the victim of a monetary, not educative decision. I also scour newspapers, magazines and news broadcasts for math errors. Recently, I wrote to a weather forecaster who said that because there was a 50% chance of rain on Saturday and a 50% chance of rain on Sunday that the probability of rain for the weekend was 100%. I hope that he understood my explanation of his egregious error. I also write to popular radio personalities who proclaim their hatred for or weakness in mathematics. This is unacceptable: negative images and myths of mathematics (and mathematicians) are widespread among the public, especially in North America. The majority of people today are scared of mathematics (and mathematicians) and feel powerless in the presence of mathematical ideas. Sadly, many adults of most Anglo-American countries are not embarrassed to proclaim their ignorance or poor performance in mathematics, unlike in other subjects. Many adults buy into mathematical myths that are false beliefs (e.g., there is a math gene), most of which are negative and are always harmful in distorting the image of mathematics to children. Public figures must not contribute to the perpetuation of negative stereotypes and assignations. I consider it my job to “call” journalists, politicians, entertainers and others when they make “throwaway” comments that denigrate math or the people who “do” math in the service of mankind.
I have been the recipient of generous support throughout my career. My mentors, all of whom were my former teachers, provided opportunities to present my nascent work in small, supportive environments in which peers provided constructive feedback and enthusiastic encouragement. Over time, the mentorship relationship, with former high school math teachers, administrative and academic peers became a two-way transfer of experience and perspective. My mentors helped me through periods of self-doubt and self-directed assignations of the “imposter syndrome” during which I attributed my successes to external factors out of my control, like luck or coincidence, but at the same time internalizing any mistakes or failures as my own fault. My mentors guided me by explaining that it was quite normal to feel overwhelmed by new responsibilities and roles that one must take on for the first time. They talked me through the hazards of over-preparation for classes and background research for a paper. My mentors have shared the wisdom of their experience, but they also always emphasized that it was up to me to create —whether it is a class, scholarly article or administrative policy—what I want to do, build or implement. In the end, I appropriated their constructive suggestions and emulated their public personas.
Never. My career path is illustrative of the “butterfly effect,” captured so eloquently by Lorenz, i.e., The scientific theory that a single occurrence, no matter how small, can change the course of the universe forever.For example, the flap of a butterfly’s wings changed the air around it so much that a tornado broke out two continents away. My career path is the result of small steps: the little things in life, the little decisions, the opportunities followed, the people who sat beside me in math class, the emails I read, that made all the difference. I am so fortunate that I switched from teaching high school to teaching Grade 5, where I received the first Apple II computer in the board, along with the Logo programming language. That led me to graduate studies, opportunities to influence provincial curriculum and assessment and a position at Queen’s that opened the gates fully to research funding and provincial, national and international connections and collaborations. To quote Lewis Carroll, “If you don’t know where you are going, any road will take you there.” I have learned that taking action (however small) will get the momentum going, and many times, as a result, I have found myself with a renewed sense of direction.
I suppose that I would say, “Keep flappin’ those wings.” It may sound trite, but when opportunity knocks, answer the door. I would also advise young women to stay grounded and be true to the fundamental tenets that define them—you must believe in what you do with every gram of your being. My personal and professional goal is to dismiss the myth that math is the “bad guy.” This drives everything that I do with children, parents, teachers and the public. This single aim is my raison d’etre and it has sustained me through three decades.
Mathematics, to me is . . . a way of seeing and experiencing the world. Mathematics should be considered to be one of our basic “senses” because if we use our receptors (i.e., our mathematical eyes, ears, finger tips, nose and tongue), we can see, feel, hear, touch, and even taste mathematical wonders in the world around us. Today, we focus so much on language and literacy: speaking, listening, and reading, and yet, mathematics is the other, often ignored side of the literacy coin. We cannot go about our daily lives without mathematics – it is an essential vocabulary, skill and process set and lens. Mathematics is practical from the kitchen and garden to the construction site and hospital. But we cannot go without mathematics in our creative and informal lives either: art, dance, sports, and photography are not only math-dependent but math-illuminative and illustrative. As a teacher, I have re-learned almost all math concepts through the eyes of a child and I have been challenged to explain key notions using words, objects (such as blocks, tiles, counters and paper-folds) and diagrams, and, as a result, I have found my enjoyment for math has increased as the depth of my understanding has grown.
