EJC: VINCULUM: JOURNAL OF THE SMTS

vinculum 4(1&2)
(11.5M)EDITORIAL: CHANGE(S), FIVE YEARS LATER Over five years ago, in vinculum 1(1), my first editorial for the Journal of the Saskatchewan Mathematics Teachers’ Society (SMTS) began as follows: Stated as a proverb, change is the only constant. However, and without getting into a discussion of the derivative, how much change is occurring at a particular point may vary. In other words, while change is the only constant, rate of change is not, necessarily, constant. For example, points in time may experience more or less change than other points in time. At the present point in time, and with respect to the teaching and learning of mathematics in the province of Saskatchewan, we are in the midst of major change. (p. 2) For the remainder of that editorial, I detailed the change(s) that was (were) occurring at that particular point in time: Saskatchewan’s recent and pending adoption of new mathematics curricula for grades K12; the potential for a Saskatchewan and/or Western Canadian version of the ‘Math Wars’; the newly elected SMTS executive; and, numerous changes to the Journal of the SMTS (e.g., a new editor; the announcement of associate editors, an editorial board, and an editorial advisory board; a change in the SMTS journal’s name, from The Numerator to vinculum; and, my attempt at a logo for the journal). Looking back over my last five years of editorials, from 1(1) to 4(1), I see, now, that a theme has emerged: I have documented change(s) to the teaching and learning of mathematics in the province of Saskatchewan. For example, in 1(2) I detailed the first semester activities from the members of the newly founded M(ath)Ed Cohort (a Master’s of Education Program for inservice mathematics teachers in the Department of Curriculum Studies in the College of Education at the University of Saskatchewan, with the support of the SMTS). From a wherearetheynow perspective, I am proud of the change(s) exacted by the (official and unofficial) members of the M(ath)Ed Cohort. For 2(1), I foreshadowed how a change in the mathematics curricula, which (arguably) introduced a “new” approach to the teaching and learning of mathematics, would lead to change in related domains (e.g., textbooks, professional development, and others); however, I did not anticipate that these change(s) would lead to a multiyear debate (from September 2011 to present day) over the “new” approaches to the teaching and learning of mathematics, which I collectively refer to now as the ‘Canadian Math Wars’. As another example, in 2(2) I looked back over my first two years as editor and detailed some of the change(s) that I, personally, had gone through after embracing my role as “accidentaleditor” (p. 2) of vinculum. My editorials for 3(2.1960), 3(2.1970), 3(2.1980), 3(2.1990), and 3(2.2000), which were designed to “set the stage” for each decade of our celebration of 50 years of the SMTS, documented major moments that changed world and Canadian history, popular culture, and mathematics. Which brings us to 4(1 & 2). For the remainder of this editorial, in keeping with the theme of documenting change(s) to the teaching and learning of mathematics in the province of Saskatchewan, I will detail some of changes that are occurring at this particular point in time. First, this is my last issue as editor of vinculum. (With apologies to George Costanza: Alright, that’s it for me! Be good everybody!) Second, I am pleased to announce that my close colleague Gale Russell (a past editor of the journal of the SMTS) will, once again, take over as editor of (what is now known as) vinculum (or whatever she decides to name the journal). Lastly, in perhaps the biggest change to the teaching and learning of mathematics in Saskatchewan over the past two decades, Dr. Rick Seaman is retiring from the Faculty of Education at the University of Regina. I am honoured that my final issue as editor of vinculum ...download vinculum 4(1&2) to read the rest of this editorial and more... 
vinculum 3(2.2000)
(87K)This issue is only available in print. 
vinculum 3(2.1990)
(87K)This issue is only available in print. 
vinculum 3(2.1980)
(88K)This issue is only available in print. 
vinculum 3(2.1970)
(46K)This issue is only available in print. 
vinculum 3(2.1960)
(46K)This issue is only available in print. 
vinculum: Journal of the SMTS 3(1)
(5.2M)EDITORIAL: PROBLEMS AND REFLECTIONS The Saskatchewan Mathematics Teachers’ Society (SMTS) is – and actually has been for quite some time – an affiliate of the National Council of Teachers of Mathematics (NCTM), which is the world’s largest professional organization dedicated to the teaching and learning of mathematics. According to www.nctm.org, affiliates “are independent organizations whose missions and goals are similar to those of the National Council of Teachers of Mathematics”. I am telling you about our affiliate status with the NCTM for two reasons. First, if you have not already, I urge you to head over to www.nctm.org and check out their wealth of resources. I have spent many an evening going through the multitude of different sections (e.g., professional development, lessons and resources, conferences, etc.) and always come away with something new to try or think about. Second, in November 2010, I submitted the first three issues of vinculum: Journal of the Saskatchewan Mathematics Teachers’ Society for consideration for the 20102011 NCTM Affiliate Recognition for Outstanding Publication. Before you get too excited, we did not win. We did, however, get some constructive criticism, which is evidence of the symbiotic relationship between the NCTM and its affiliates. According to the NCTM, on the one hand, the strength of our journal is the inclusion of highquality research articles; on the other hand, we were criticized for not having a particularly wide variety of articles for our membership, which we have taken to heart with this latest issue of vinculum. This current issue is the product of the tireless efforts of thirteen practicing elementary and secondary mathematics teachers who, in the fall of 2010, were enrolled in a graduate mathematics education class at the University of Saskatchewan. During the course, one of their main tasks was to take the mathematics problems we discussed during our class and to implement them in their own classrooms during the following week – no excuses! In other words, yes, they knew there was not enough time and, yes, they knew that some of the problems had nothing to do with their grade level or the topic or the curriculum they were currently teaching and, yes, [insert other flimsy, frequently used excuses used here]. Funny thing is, and despite all the wellknown excuses, introducing the problems into their classrooms was a resounding success – for both the teachers and the students. Given the infectious nature of what happened, each of the thirteen teachers has submitted their favourite problem, which you can implement in your classroom tomorrow. Further, each of the problems is followed by insightful reflections from individuals who have already implemented the problem in their classroom. It is now your turn to take these problems into your own classroom and give them a try – no excuses! Switching gears, the SMTS turned 50 this year! As you all know, the teaching and learning of mathematics in Saskatchewan has a long and storied history and an integral part of the past 50 years (19612011) of history has been vinculum: Journal of the Saskatchewan Mathematics Teachers' Society (in its many different renditions). As such, the next few issues will present ten memorable articles from each of the past five decades (i.e., 50 articles from the past 50 years of the journal), which will provide an opportunity to share this rich history with the members of the SMTS. In doing so, we will provide a historical account of many of the trends and issues associated with the teaching and learning of mathematics. These next few issues are meant to serve as a celebratory retrospective on the work of the Saskatchewan Mathematics Teachers' Society. 
vinculum: Journal of the SMTS 2(2)
(5.6M)EDITORIAL: TWO YEARS AND FOUR ISSUES LATER Recently, I looked back over my first two years as editor of vinculum. I would like to take this opportunity and elaborate on some of the trials, tribulations, and triumphs I have encountered and, in doing so, hopefully, help to generate some discussion within the mathematics education community. In October 2008, as the newly appointed liaison between the University of Saskatchewan and the Saskatchewan Mathematics Teachers’ Society (SMTS), I found myself at the society’s annual general meeting. During the meeting it was announced that the SMTS was looking for a new editor for their journal. Once the meeting was adjourned, I mentioned, casually, to a few of the individuals I was sitting with (at the back of the room), that I had, at a point prior, thought about the position of editor. (To be honest, what happened next is still sort of a blur.) Unintentionally, and unexpectedly I had volunteered for the position, had been quickly vetted, and, subsequently, right then and there, was appointed the new editor of the journal! I left the meeting an accidentaleditor. In dealing with the task of producing our first issue, I set three goals. First, I wanted to set up an editorial board. After a few emails to particular members of the SMTS, I quickly had an editorial board filled with local individuals heavily invested in the teaching and learning of mathematics. When given the reins of the journal, I was also given the opportunity (if I wanted) to start from scratch. After deliberating for quite some time, I did decide to start over. Starting with (if you will) a blank slate, I spent a great deal of time reading other journals, however, in a much different fashion than I had before. Instead of “reading the articles,” my focus turned to which types of sections to include and, for the majority of time, layouts. After finally putting together a structure and layout that I considered aesthetically pleasing and adaptable for subsequent issues, I had but one last task left: getting people to write for our journal. Although I had been told that, in the past, previous editors had difficulties procuring submissions from members of the SMTS, I was not concerned. After all, I had a backup plan. Over the past five years, while attending a number of local, provincial, national and international conferences, I consistently received the following message: The mathematics education community (i.e., mathematics educators, mathematicians, mathematics teachers, and other individuals with a vested interest in mathematics education) was a unique collaboration of individuals interested in the teaching and learning of mathematics and, further, mathematics teachers. Having received the message loud and clear, I thought, if I had any difficulties in getting submissions from local members, I would simply rely on the mathematics education community (and their interest in the teaching and learning of mathematics and mathematics teachers) to contribute articles to our journal; if the local mathematics teachers were not going to submit, I would still be able to get submissions from mathematicians, mathematics educators, graduate students, and others....download vinculum 2(2) to read the rest of this editorial and more... 
vinculum: Journal of the SMTS 2(1)
(6.3M)EDITORIAL: CURRICULAR EDITION I want to take this opportunity to talk about a war being fought – this very moment – on US soil. Don’t worry; the Saskatchewan Council of Social Sciences (SCSS) (another of the Special Subject Councils of the Saskatchewan Teachers’ Federation) has not hijacked this editorial! Here’s the proof: I am not going to talk about the War of 1812, the Civil War, or the American Revolutionary War; but I am going to talk about the Math Wars. The Math Wars is a term used to describe a mathematics education (i.e., research and practice associated with the teaching and learning of mathematics) debate over mathematics curricula, which began, and still goes on today, in the United States. “The immediate origins of the conflicts can be traced to the ‘reform’ stimulated by the National Council of Teachers of Mathematics’ [NCTM] Curriculum and Evaluation Standards for School Mathematics” (Schoenfeld, 2004, p. 253). The NCTM’s (1989) standards document not only acted as the Math Wars powder keg, it also helped define the two sides of the debate: traditional mathematics (curricula) versus reform mathematics (curricula). On the one hand, proponents of the traditional approach, denoted by Schoenfeld (2004) as traditionalists value (note: I am aware I am painting with a broad brush here): skills, procedural understanding, repetition, memorization, algorithms, and direct instruction. In fact, the colloquial phase often associated with traditional mathematics (curricula) is backtobasics. Whereas, and on the other hand, proponents of the reform approach, denoted by Schoenfeld as reformers, value (note: I am still painting with broad strokes): discovery, process, problem solving, inquiry, non standard algorithms, creativity, pattern recognition, group work, conceptual understanding, communication, and alternative instructional methods. You may be wondering what all this has to do with teaching mathematics in Canada. Since 1989 the NCTM’s influence on mathematics curricula has moved out of the United States, into North America, and beyond. Case in point: The NCTM (2000) published the Principles and Standards for School Mathematics, which (in my opinion) has heavily influenced the Western and Northern Canadian Protocol’s (WNCP) Common Curriculum Framework (CCF) for K9 Mathematics (2006) and Common Curriculum Framework for 1012 Mathematics (2008). For example, problem solving, communication, connections, and reasoning concurrently exist as mathematical processes and standards for school mathematics (which are central components both) for the WNCP and NCTM, respectively. Now you may be wondering what this has to do with teaching mathematics in Saskatchewan. As I have detailed in the past, the mathematics curricula in the province of Saskatchewan is in the midst of major change, and will be for the next number of years (see, for example: http://www.education.gov.sk.ca/math curricula). I have also contended that the new curricula, arguably, introduces a new approach to teaching and learning mathematics. Here’s why: If the principles and standards of NCTM are influencing the CCF of the WNCP, which influences the Saskatchewan mathematics curricula, it can be argued, syllogistically if arranged properly, that the NCTM is influencing the Saskatchewan mathematics curricula. But, I don’t want to bury the lead too much...download vinculum 2(1) to read the rest of this editorial and more... 
vinculum: Journal of the SMTS 1(2)
(4.9M)EDITORIAL: STUDENTCENTERED EDITION Do you remember last winter? I certainly do. In fact, I will forever remember the winter of 2008/2009. Having moved from V ancouver in August of 2008 (stop laughing), our last winter was my first winter. (As the saying goes, you never forget your first time.) While walking over the university bridge in 50 below temperatures, I began to panic about a course I was offering in the summer. Given the conditions people had to put up with in the winter, surely no one was going to spend two weeks of their summer (vacation) stuck in my classroom. To my surprise, and delight, 24 individuals, interested in the teaching and learning of mathematics, and from all over the province, converged on the University of Saskatchewan campus to discuss trends and issues in mathematics education. As our discussions continued, a theme began to surface: research findings, trends, and issues related to the teaching and learning of mathematics seldom spread beyond the mathematics education community. While ruminating over the theme that emerged, I revisited the SMTS objectives, which were outlined in the January 1979 SMTS Newsletter (and are found on the inside cover of each edition of vinculum). My attention was drawn to the first and second objectives of the SMTS, which are, respectively, “to improve practice in mathematics by increasing members’ knowledge and understanding” and “to act as a clearinghouse for ideas and as a source of information of trends and new ideas.” I also recalled, the main objective of vinculum is to provide a venue for SMTS objectives to be met. With the abovementioned objectives in mind, the main purpose of the course became the dissemination of the students’ newly gathered knowledge, through vinculum, to those individuals involved with the teaching and learning of mathematics in Saskatchewan (i.e., the members of the SMTS). (Enough with the backstory.) In this edition you will find 24 articles, focusing on trends and issues in mathematics education, written by the 24 students who converged on the University of Saskatchewan campus in the summer of 2009. In other words, welcome to the studentcentered edition of vinculum. To be clear, and as you are about to read, the views expressed in each article of the studentcentered edition of vinculum are those of its author, and not, necessarily, the views of the SMTS, the SMTS executive, or the SMTS Editorial Board. However, the abovementioned declaration was not made for hedging purposes. In fact, the declaration was made to document the fact that the studentcentered edition of vinculum embodies a central tenet of our new mathematics curricula: Students are curious, active learners with individual interests, abilities and needs. They come to classrooms with varying knowledge, life experiences and backgrounds...Students learn by attaching meaning to what they do and need to construct their own meaning of mathematics (WNCP’s CCF, p. 2) One last thing, the SMTS executive welcomes two new members to the Editorial Advisory Board here at vinculum: Gale Russell (former editor) and Murray Guest. As most of you are aware, Gale and Murray are heavily involved in the teaching and learning of mathematics in our province. Their knowledge and experience will play a key role in shaping the purpose and direction of your journal. 
vinculum: Journal of the SMTS 1(1)
(4.2M)EDITORIAL: CHANGE(S) Stated as a proverb, change is the only constant. However, and without getting into a discussion of the derivative, how much change is occurring at a particular point may vary. In other words, while change is the only constant, rate of change is not, necessarily, constant. For example, points in time may experience more or less change than other points in time. At the present point in time, and with respect to the teaching and learning of mathematics in the province of Saskatchewan, we are in the midst of major change. Saskatchewan’s recent adoption of WNCP (Western and Northern Canadian Protocol for collaboration in education) Mathematics’ Common Curriculum Framework has introduced new mathematics curricula to the province for grades K9. Further, the province will adopt new mathematics curricula for grades 10, 11, and 12 in 2010, 2011, and 2012, respectively. Major change to mathematics curricula brings change to related domains (e.g., textbooks, lesson plans, university entrance requirements, etc.). However, and perhaps more importantly, adoptions of the new K12 curricula this time will, arguably, introduce a new approach to the teaching and learning of mathematics for elementary and secondary school mathematics classrooms. With the overwhelming change (detailed above) ahead of us, and not wanting to recreate a Western Canadian, nor Saskatchewan, version of the “Math Wars” occurring in the United States, our society, the Saskatchewan Mathematics Teachers’ Society (SMTS), is committed to a smooth transition. Our newly elected President, Stephen Vincent, details in his column PRESIDENT’S POINT (p. 3) how the SMTS and its executive (also in the midst of major change) is proactively dealing with the change that is and will be occurring. Change is also occurring here at the Journal of the Saskatchewan Mathematics Teachers’ Society. On behalf of the SMTS members, I want to thank Jennifer Von Sprecken, former Editor, for her tireless efforts with The Numerator. Personally, I want to thank Jennifer for (1) a smooth transition, and (2) unlimited access to all things related to The Numerator. Further, I want to welcome Karen Campbell, Ryan Banow, and Cynthia Sprung as Associate Editors of the journal. Their knowledge, insight, and direction—displayed in our conversations over the past few months—has demonstrated our journal has a strong Editorial Board, further supported by Evan Cole, a member of our (ever growing) Editorial Advisory Board. Perhaps the most obvious change to our journal is the name: The Numerator is now vinculum. Vinculum is defined as “a horizontal line placed above multiple quantities to indicate they form a unit” (Weissten, 2009). As such, and as demonstrated on our new cover, vinculum (i.e., our journal) symbolizes the horizontal line placed above multiple quantities (i.e., members of the SMTS) to help form a ‘unit’ (i.e., the SMTS), which, as mentioned, is important in this time of change(s).