Teaching Dossier Dr. Ryan Trelford University of Calgary [email protected]January, 2015 Contents 1 Approach to Teaching 1 1.1 Teaching Philosophy .................................... 1 1.2 Teaching Goals, Strategies, and Evaluation Methods .................. 3 2 Teaching Contributions 4 2.1 Teaching Responsibilities ................................. 4 2.2 Activities Undertaken to Improve Teaching and Learning ............... 6 2.3 Publications and Professional Contributions ....................... 7 3 Reflections on and Assessment of Teaching 8 3.1 Documentation of Results of Teaching .......................... 8 3.2 Reflections on Teaching and Student Learning ...................... 8 3.3 Future Plans ........................................ 9 Appendices 11 A Teaching Responsibilities 11 B Activities Undertaken to Improve Teaching and Learning 13 C Documentation of Results of Teaching 16
B Activities Undertaken to Improve Teaching and Learning 13
C Documentation of Results of Teaching 16
11 Approach to Teaching
1.1 Teaching Philosophy
I discovered my passion for teaching after delivering my very first mathematics tutorial as anew graduate student. I recall feeling a lot of stress and anxiety beforehand, but while I wasdelivering the content to the students, those feelings disappeared and I knew at that moment thatteaching would play an important role in my future academic career. Since that initial contact, Ihave strived to make teaching a priority during my graduate studies. My belief is that studentsshould be exposed to the creation of mathematics rather than just the results. When students seeexplanations and derivations of formulas, they begin to view mathematics as the understandingof ideas and concepts rather than just the memorization of facts. This shift in paradigm canlead students to the realization that one of the main goals of mathematics is to clearly expressan idea in the simplest of terms. My views of teaching have of course been shaped through myown personal experiences running mathematics tutorials and lectures. However, it was the adviceof some exceptional colleagues and mentors that I have been fortunate enough to encounter thatreally guided me to the views that I have today.
During my Master’s degree, one of my committee members, Dr. Wieslaw Krawcewicz, said thefollowing to me in an effort to aid in the reading of my first mathematical paper:
“Every mathematical concept is a very simple idea that has just been dressed up.”
I kept this piece of advice in the back of my mind as I proceeded to struggle through the paper. Itwas only once I was finished that I realized what he was telling me: to understand mathematics,one must get to the heart of the matter. Once one looks past all of the notation and mathematicaljargon, one sees with clarity the simple underlying concept upon which the mathematical expositionis built. My fear of reading advanced papers in mathematics disappeared immediately. I incorporatethis notion into my teaching by emphasizing the idea of each topic before, during and after eachexample.
For instance, students typically struggle when asked to verify that a function is one-to-one; theyeither cannot recall the definition of one-to-one, or they do not know how to begin the verification.To aid in this, I use pictures to show what one-to-one means, and several graphs to show themwhat a one-to-one function looks like, and equally importantly, what a one-to-one function doesnot look like. Only then do I introduce the condition that needs to be satisfied for a function tobe one-to-one. At this point the formula seems obvious to many students, and they can reproduceand even justify the formula when asked. I proceed with several examples, emphasizing not thecomputations, but rather reiterating the idea of a one-to-one function. They now see that a functionis one-to-one if, and only if, the image of distinct points are distinct - a very simple idea.
My beliefs regarding teaching were further brought into focus when a colleague and mentor,Dr. Keith Nicholson, gave me a very important piece of advice as I prepared to teach my firstmathematics course at the University of Calgary:
“You cannot tell students how to do mathematics; you have to create it in front of them.”
This one single statement has had a profound affect on me. It made me realize that teachingmathematics is truly about guiding students to the results rather than simply stating them. It haslead me to view teaching as the act of painting a picture in the minds of students - each lecture
should paint a new piece of the picture in such a way that students understand exactly why thatnew piece belongs in that exact place.
I strive to adhere to this piece of advice every time I teach. To do so, I motivate each topic as Iintroduce it, so that students understand why we are studying it. Once students understand whysomething is being studied, I find they are more open to learning about it. I proceed by explainingthe theory required for mastery in the topic. I am not satisfied with merely giving out formulasand explaining when to use them. My goal is to lead students through the derivation of formulas,allowing them to see exactly why such formulas work. I always follow such a derivation with asimple example which reinforces the concept that was just explained.
For example, in a topic such as Matrix Algebra, students often become so lost in the rules ofcomputing matrix products and inverses that they lose sight of the underlying idea. I motivatethis topic by first showing students that a linear system of equations can be represented as a singlematrix equation, and that by solving the matrix equation, we solve the underlying system. Solvinga single equation is something students understand, and I frequently remind them that behind allof the rules of matrix algebra, we are ultimately trying to solve a system of equations.
My teaching mentor, Dr. Thi Dinh, played the largest role in my development as an instructor.Among the countless lessons he taught me, the most vital was the one that took me the longest torealize the importance of:
“Just be yourself.”
Dr. Dinh repeatedly said this to me, but I never thought much of it. I instead spent a great deal ofmy graduate studies trying to pre-plan each lesson down to the smallest detail, leading to completelyrehearsed lectures that were essentially devoid of emotion. I slowly learned to become comfortableexplaining things in my own words, and not being afraid to show excitement when I discussedan interesting concept. Over time, my lessons have become less scripted, and more spontaneous.I have become comfortable with not overpreparing my lectures, and I feel less intimidated whenstudents ask insightful questions that require me to expand upon what I have just taught. Beingmyself has lead to me being confident in my teaching.
While teaching a Discrete Mathematics course, I finished one of my lectures early. Instead ofdiving ahead into the next lecture, I decided to show students the importance of one-to-one andonto functions. I explained that if such a function existed between two sets, then the sets have thesame cardinality. I then extended this to infinite sets, and briefly talked about why the integersand rational numbers have the same cardinality, but that there are more real numbers. This waswell beyond the syllabus of the course (which I clearly stated to them), but it was something thatdrastically changed my view of mathematics when I first learned it, and I felt compelled to share itwith them. This was truly the best example of when I was being myself: I was so excited to explainthis amazing fact to the students. I could tell from their reactions to learing these unintuitive ideasthat they were feeding off of my enthusiasm. My goal is to continue teaching with that level ofenthusiasm and excitement.
These three quotations have truly shaped who I am as an instructor, and they will continueto guide me as I gain more experience. I am fortunate to have had such wonderful role models,and I hope that I can inspire my students in the same way that they have inspired me. I knowthat as I continue to teach, my views will change, and that I will encounter new role models, andeven become a role model myself one day. I understand that teaching is a career that will always
require me to grow and learn, and I look forward to facing and overcoming the challenges that Iwill encounter in the future.
1.2 Teaching Goals, Strategies, and Evaluation Methods
Aside from the obvious goal of having my students pass the course I am teaching, I really aimto instill a sense of confidence in the student. I want them to know that they can do mathematics,and that they can even enjoy it. I strive to find ways to involve students in my lectures, and Itry to develop innovative examples that really grab their attention. Preparing for this starts wellbefore the course begins.
I believe that being prepared for a course (and for each lecture) plays a significant role in being asuccessful instructor. Before teaching a course, I spend time researching the students’ background;I see what programs they are enrolled in, and what year they are currently in. Doing so gives mea better understanding of how well the students are prepared for the course, how mature they are,and also gives me an idea of what types of examples I could use to get the students interested inlearning. On the first day, I tell them what I expect of them in the course, and what they shouldexpect of me. I also ask them if I am talking clearly, and if they can read my writing at the backof the room. This serves to show the students that I am willing to work with them to facilitatetheir learning, and helps to put their minds at ease should they have any worries about the course.During the first lecture of one course, I asked students to fill out an anonymous questionnaire tocollect information such as what calculator they were using, what program they were in, and evenwhat their height was. This made them feel like I really cared about them as individuals. I laterused the data on their heights in an example where I computed the mean, median, mode, andstandard deviation, as a way of involving them in the course material.
When teaching a mathematics course, it can be easy to get lost in the theory. As much asI personally enjoy theory, students are often looking for applications to the material. They findapplications more concrete and easier to work with, and they also need to feel like there is areason they are learning the theory. I try to have as much fun as I can with applications whenthe opportunities to cover them present themselves. One instance of this occurred while I wasteaching a Linear Methods class. Students spend a great deal of time fighting with matrix algebra,and one application of this is Markov Chains, where several populations interact with one another,and the student has to figure out the long term behavior. The example I have used is to modela zombie apocalypse, which the students have responded well too. Given the role zombies play inpop-culture, everyone can relate to it, and it makes for a fun and simple illustration of all they havelearned up to that point in the course. Students are quick to answer questions I ask them, and aremore likely to pose questions such as “how would changing the parameters affect the outcome?”and “What would have to change for the zombies to completely wipe out the humans?” Theseinsightful questions are not typically asked by first year students, but when given such an example,they begin asking higher level questions that can ultimately lead to them exploring the problemmore on their own, and even to them answering their own questions.
Outside of the classroom, I typically hold two hours of weekly office hours for each course. Iuse these office hours to meet with students, and try to get to know them a little better. Theseoffice hours also serve as a way for me to see what students are struggling with, and to practiceexplaining key concepts in a different way to help aid the student in understanding. The secondtime I taught Linear Methods, I held a two 2-hour final exam review sessions, open not only to mysection, but to the other seven sections as well. I used what I had learned about the difficulties
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students talked to me about in my office hours to help choose appropriate questions to cover forthe review. During the review, I asked the students how to approach the given question, and aftera problem had been solved, I discussed some common pitfalls students encountered, and askedboth why these pitfalls were indeed incorrect, and how they could be avoided or corrected. Ialso expressed the importance of checking the correctness of their solutions: the accuracy of mostcomputational problems students encounter can be verified in several places, and I showed themhow and when they could check. This led to students be more confident in their answers, and withthe course material itself. Several students thanked me afterwards, saying that I had made thingsmore clear for them.
Upon completion of a course, I step back and think about my experience over the semester. Iconsider the things I did well, and I list the things that I felt I could have been better at. I writethese things down in my lecture notes, so that when I teach the course again, I can be aware of whatI felt could be improved. I also take my student evaluations very seriously, and often think aboutways to accommodate any suggestions that students make. I have learned during these reflectionsthat the goal of teaching is not to satisfy every student, but rather to give them the skills necessaryto continue learning and to begin doing their own independent research in their chosen disciplines.This begins with stressing the fact that being wrong is an important part of learning. This is agrowing process for the students, and it can sometimes be met with resistance, but once studentscan be convinced that they can learn from their mistakes, and succeed where they once struggled,they are well on their way to success in their academic careers.
2 Teaching Contributions
2.1 Teaching Responsibilities
I have been a full-time Sessional Instructor in the Department of Mathematics and Statistics atthe University of Calgary since September 2014, but I began teaching mathematics courses there inJanuary 2013 as I worked to complete my Ph.D. Although instructing courses are typically not partof a graduate student’s workload, the department has initiated a program whereby students whopass the Instructional Skills Workshop (see Section 2.2) and obtain higher than average studentreviews become eligible to instruct mathematics courses.
I have instructed five sections of MATH 211 (Linear Methods I), and one section each of MATH271 (Discrete Mathematics) and MATH 249 (Introductory Calculus). With the exception of oneLinear Methods course I instructed during the summer of 2014, all courses were one of severalconcurrent sections that were run by a course coordinator. I had approximately 120-200 studentsenrolled in my classes, most of whom where first-year undergraduates whose majors were in adiscipline other than mathematics. In the Fall 2013 semester, the enrollment of my Linear Methodsclass rose from 120 to more than 150 students, and I was forced to request a larger room in orderto ensure my own students were able to attend my lectures without having to stand in the backof the room or sit on the floor. My duties as an instructor include preparing and delivering twoor three lectures each week, as well as teaching one of the weekly one-hour tutorials attached toeach of these lecture sections. I am required to suggest problems to the course coordinator for allexams, vet the draft versions of these exams, and supervise both the writing and grading of allexams with the help of teaching assistants. I have also written solutions for several of these examsso that they could be used as learning tools in future semesters, and have delivered two 2-hour finalexam review sessions for all eight sections of Linear Methods in the Fall 2014 semester.
In the summer of 2012, I taught my very first course, MATH 172 (Applied Mathematics II),in the Center for Academic Learner Services at the Southern Alberta Institute of Technology.This was the only lecture section currently being offered, and my duties included preparing anddelivering two 3-hour lectures each week, creating and marking the five module tests in additionto the final exam for a class of 27 students. Each lecture was divided into approximately one hourof teaching, and two hours of tutorial where the students would attempt problems from the coursepackage while I circulated around the room offering help as needed, both with the material andwith the use of their scientific calculators. The majority of students had been away from schoolfor many years, and were taking this course to upgrade in order to meet the prerequisites of theirrespective programs.
Tables 1 and 2 (page 11) summarize the courses I have taught to date. In addition to thesecourses, I was employed by the Math and Applied Sciences Centre at the University of Albertato teach a four-hour combined final exam review session for Linear Algebra I and Honours LinearAlgebra I at the end of the 2009 Winter Semester.
Throughout my graduate studies, I have instructed many tutorials in calculus, linear algebra,and discrete mathematics. These tutorials have ranged from solving prescribed example problemson the board to supervising and assisting students’ work on assignments that were due at the endof the tutorial, as well as administering quizzes and midterms. In the Fall Semester of 2012, Iwas the Teaching Assistant Captain for Linear Methods I, which in addition to running a tutorial,involved addressing student concerns regarding Lyryx, the online homework tool used to assessstudent assignments. A summary of the tutorials I have instructed appears in Table 3 (page 12).
Continuous tutorials are drop-in help sessions where students can get one-on-one help withtheir homework from a graduate student. I have frequently run many of these for calculus atthe University of Alberta as well as linear methods and discrete mathematics at the University ofCalgary. These continuous tutorials allowed me to see firsthand which topics the students struggledwith, and I was able to practice and develop multiple ways of explaining important concepts tothem.
Grading assignments, quizzes, midterms, and final exams has also been a large part of myresponsibilities as both a graduate teaching assistant and instructor, and this task has again givenme a greater understanding of the topics that give students difficulties. In addition, grading hasshown to me the importance of writing clear and concise proofs and solutions, a skill that I nowtry to emphasize in my teaching. My grading duties are summarized in Table 4 (page 12).
On occasion, I have found employment beyond the university walls; most recently I was aninstructor at the Yufeng Chinese School1 where I taught math enrichment to grade 5–6 studentsfor one hour per week during the month of September 2013. The enthusiasm and mathematicalskill of these students was very impressive; they truly enjoyed the subject, and were not scared toapproach a new problem by themselves. This was the first time I had done any teaching where Idid not understand the students’ background, and in hindsight, I feel that I gave them problemsthat were not quite challenging enough. I was also forced to move away from the lecturing stylethat I have become comfortable with, and teach in a completely interactive style. I learned thatthe students focused less on correctly solving a given problem, and more on simply exploring aconcept and experimenting with new ideas.
During my time at the University of Alberta, I was employed by Pearson Canada as a contentdeveloper and reviewer for their online homework system, MathXL, as well as by Nelson Education
where my duties included reviewing content for their online homework system, WebAssign, anddealing with student inquiries and mark adjustments for MATH 101–Calculus II, as part of theUniversity’s pilot program using WebAssign. Working with both publishing companies gave me astronger sense of how one properly poses a mathematical problem concisely, and made me awareof the different types of questions one can ask students: from simple computational questions thattest the students’ ability to reproduce basic calculations to more theoretical questions that forcestudents to take what they have learned and apply it to a new situation.
Finally, I have had the opportunity to assist with some outreach programs during my time as agrad student. Most recently, I was involved with the marking of the Canadian Open MathematicsChallenge of the Canadian Mathematics Society (CMS). In the summer of 2013, I volunteered at the2013 CMS Regional Math Camp where I chaperoned the 28 participants in grades 7–10 in additionto giving a three-hour presentation on techniques for constructing convex polytopes. I have alsovolunteered for “Math Nites” where grades 7–12 students who are passionate about mathematicsattend a weekly two-hour problem solving session held at the University of Calgary. There, theywork in groups to solve several math problems designed to invoke their curiosity and creativity.Many of the problems they encounter have no known solutions. In the past, I was also involvedwith the University of Alberta’s SNAP Math Fairs, which were workshops aimed at getting grades5–6 students excited about mathematics through problem solving.
2.2 Activities Undertaken to Improve Teaching and Learning
As my passion for teaching has grown, I have attended several workshops aimed at helping medevelop as an instructor. These are listed as follows:
• University Teaching Program2 (UTP) - completed October, 2008
The CDW, UTC, and ISW were offered by the Teaching and Learning Center3 (TLC) at theUniversity of Calgary, while the UTP was taken at the University of Alberta through the Facultyof Graduate Studies and Research. During the CDW, I learned how to address issues arising whenone either creates or modifies a course. Topics included developing a course outline and syllabus,deciding upon learner outcomes, choosing appropriate assessment tools, and, upon the completionof the course, evaluating and modifying the design. The ISW serves as a prerequisite for the UTC,and focuses on teaching with the BOPPPS model, and consists of three 10-minute lectures to asmall audience who then supply the presenter with feedback. The UTC expands upon the ideasaddressed in the ISW, with topics including teaching to different learning styles, dealing with issuesthat may arise in the classroom, properly assessing student work, and the importance of a coursesyllabus and a course outline. It culminates with a co-teaching scenario where the presenters explorea topic that was not covered during the workshop. The UTC also has an out-of-class requirement:
2This program was discontinued in 2009. As a result, the 40 hours of required seminars was reduced to 35, andonly one tutorial was required to be videotaped and assessed.
3The Teaching and Learning Center has since been updated and is now known as the Taylor Institute for Teachingand Learning. They do not currently offer a University Teaching Certificate.
having one lecture observed by a member of the TLC, who then supplies constructive feedback,which is supplied in Figure 2 (page 14). The UTP was completed during my time at the Universityof Alberta. In this program, the student is required to attend approximately 40 hours of workshopsand seminars aimed at all aspects of teaching; a list of those I attended is supplied in Table 5 (page15). In addition, a candidate must have a tutorial videotaped and commented on by a member ofthe mathematics department, the results of which are supplied in Figures 3 (page 15).
Some additional seminars offered by the TLC that I have attended are Assessment Tools inBlackboard (August 2013), Blackboard Essentials (August 2013), and Writing a Teaching Philos-ophy (November 2011). The Faculty of Science at the University of Calgary also offers two-hourteaching workshops designed to target issues that arise in science classes. I have attended one suchworkshop, Getting it Right on the First Day of Class (January 2013), which greatly aided me inteaching my first course, and I plan on attending more in the immediate future.
Perhaps the greatest experience I have had in my development as an instructor was beingpaired up with my teaching mentor, Dr. Thi Dinh. His passion for teaching mathematics is trulycontagious, and his advice for me while I was his discrete mathematics teaching assistant made mea stronger instructor. The most valuable lessons I learned from him were to be confident in myabilities, to not be afraid to let my passion for what I teach shine through, and most importantly,to simply be myself. Working with Dr. Dinh has played the largest role in my growth as a teacher,and he has set an excellent example for me of what a great instructor should be.
Since I began teaching in the Winter Semester of 2013, I have asked several colleagues to attendmy lectures so that I could obtain feedback from them about my teaching performance. Thecomments I received were incredibly useful, and included spending a little more time introducingthe topic of the lecture, using colored chalk on the board to add clarity to diagrams, and includinga few more examples to illustrate more subtle concepts. I was also invited to attend two tutorialsof another graduate student, and I found that observing what other instructors were doing in theirclassrooms was as beneficial for me as I hope my comments and suggestions were to them.
2.3 Publications and Professional Contributions
At the beginning of each academic year, the Department of Mathematics and Statistics at theUniversity of Calgary holds a Teaching Assistant (TA) Training Workshop, where current graduatestudents and faculty may volunteer to advise the first year incoming graduate students on teachingmathematics tutorials and grading homework assignments before the semester begins. I have beenasked to help out with four of these training sessions. In 2010, I was part of a one-hour panel sessionthat answered student inquiries pertaining to the responsibilities of being a teaching assistant. Iassisted with a tutorial designed to help students learn what was expected of them when theygraded assignments in 2011, and in both 2013 and 2014 I took part in a “good/bad” teachingdemonstration: a colleague gave an example of what would be considered ineffective teaching, andthen I presented an example of what would be considered effective teaching.
In 2006 and 2007, I was invited to give a co-teaching talk at the University of Alberta Mathe-matics Department alongside Dr. Eric Woolgar in a seminar titled “Effective Teaching for ProblemSolving Sessions,” aimed at incoming graduate students in the mathematical and computing sci-ences. We received positive feedback from the students in both years, and I felt that I gained alot of insight into teaching, both from Dr. Woolgar as well as from the students in attendance. Iwas pleased when several students approached me after the seminar, and asked me more specificquestions in addition to voicing the concerns they had about teaching for the first time.
Teaching assessments are an invaluable part of the growth of an instructor. Aside from thefeedback from colleagues (mentioned in Section 2.2), I have received feedback from students inthe form of both surveys and questionnaires. The survey results from all courses taught at theUniversity of Calgary are provided in Figures 4–10 (pages 16–19), while a sample of the studentquestionnaires from the Winter 2014 and Winter 2013 semesters follow in Figures 11–14 (pages 20–23), and some very encouraging comments from the Head of the University of Calgary MathematicsDepartment are given in Figure 15 (page 24). Likewise the reviews for Applied Mathematics IItaught at the Southern Alberta Institute of Technology are supplied in Figures 16–17 (pages 25–26).A summary of reviews from all tutorials taught at the University of Alberta are contained in Table6 (page 27).
On occasion students have contacted me to offer thanks for the work I put in to instructingthem. I personally find this to be the most rewarding part of teaching, not simply because Iam being recognized by the student, but because I was able to make a profound impact on theiracademic careers. Samples of such emails and letters are included in Figures 18–20 (pages 28–29).
As a result of taking advantage of the large number of teaching resources that have beenavailable to me, I have been the recipient of a teaching award in each of the first four years ofmy Ph.D. program. In each of 2011–2013, I have received a Departmental Graduate TeachingAssistant Excellence Award (see Figures 21–22 on pages 30–31), and in 2010, I received the FredA. McKinnon Graduate Teaching Award as the top graduate teaching assistant (see Figure 23 onpage 31). I was also awarded an Eric Milner Graduate Scholarship in 2011, awarded not only foracademic excellence, but also for being actively engaged in the sharing of mathematical knowledge.In 2014 I was nominated for both a University of Calgary Teaching Award and a Students’ UnionTeaching Excellence Award.
The University of Calgary’s Mathematics Department prides itself on ensuring that all graduatesare given the proper training necessary to deliver an excellent presentation. Students receive thistraining in the form a weekly mathematics seminar where they receive instruction on how to preparea presentation, critique their colleagues’ presentations, and practice delivering a talk of their own.As a result of this training, I was awarded a student–voted prize for giving one of the best talks atthe Canadian Young Researcher’s Conference in both 2010 at the University of Alberta, and 2011at the University of British Columbia.
3.2 Reflections on Teaching and Student Learning
I began my graduate studies 2005, and since that time, I quickly realized that I gave a higherpriority to my teaching duties than research, so it is only natural that I now look to obtain ateaching position. This is not to say that I don’t enjoy research. In fact, I believe that researchis an important part of teaching, and conducting even a small amount of research will keep meexcited about mathematics and abreast of current topics. My resulting enthusiasm will be conveyedto my students through my teaching, and I will be able to use my research as a starting point forundergraduate research topics for my more motivated students.
To date, I have participated in a variety of teaching activities, and have always strived toobtain feedback regarding my performance. This feedback most often appears in the form ofteaching evaluations and constructive criticism from peers and mentors. I have spent a great deal
of time contemplating all aspects of my teaching, from why I love teaching to how I can improveupon my performance as an instructor. I have realized that my strengths lie in my ability toprepare clear and organized lectures, and to deliver the lecture material in a direct and concisefashion. Many students have commented that they enjoy my lectures because I am able to distillthe course content, present material in a logical order, and give illustrative examples that helpstudents understand the important concepts in the course. On the other hand, I am aware thatthere is always room for improvement. I was very fortunate to find that teaching with a lecturingstyle works very well with me, and I have had much success because of this. However, this hasled me to become more resistant to changing my style for fear that I won’t be as successful. Asa first step in overcoming this, I would like to begin asking the students more questions, and givethem sufficient time to respond. I also have a habit of only making eye-contact with students inthe first few rows, and would like to correct for this as well. I would like to continue workingon conveying my excitement about mathematics, particularly in the more theoretical areas of thesyllabus. Despite my love of teaching theoretical concepts, I have yet to find a way to truly capturethe students attention with this material. Despite my best attempts thus far, students often findtheoretical notions uninteresting and lacking any real application.
I have found that working with other instructors to be both a rewarding and a humbling expe-rience. Seeing others explain their thoughts and opinions about education makes me understandjust how much room there still is for me to grow. For instance, hearing a fellow instructor ex-plain why they are including or excluding material from lectures or exams, or seeing the varietyof questions and examples they can effortlessly create is intimidating to witness, but at the sametime, inspires me to continue learning. The teaching workshops that I have attended (see Section2.2) have greatly impacted every aspect of my teaching; from how I prepare and deliver lectures,to how I assess student work, to how I reflect upon and assess my own teaching. I appreciategreatly the opportunity to meet other participants of these workshops and hear both their viewson teaching, and hear about their struggles as they too strive to become better instructors. Thefeedback I received from all observed lectures was instrumental to my growth as an instructor, andthe excellent mentoring I have received thus far has played a major role in shaping my ideas andvalues as an instructor.
Possibly the most enjoyable part of teaching is the profound sense of accomplishment I feelwhen I see a student who has worked so hard on a subject finally “get it”. This reward is fargreater than any teaching accolade, and it is moments such as these that make me so incrediblysatisfied with my chosen career path.
3.3 Future Plans
My immediate future plan is to obtain a full-time instructor position in the mathematics depart-ment of a post secondary institution with the option to do part-time research. Duties of particularinterest to me include becoming a course coordinator for multi-section service course, teaching areal analysis course and a course in convex geometry, designing a new course (or taking part inredesigning a current course), and taking a leadership role in a mathematics outreach program forjunior and senior high school students. My long term goals involve learning how to advise newstudents on which mathematics courses would be best for their academic program, and advising asummer student in independent research. Coming from a geometry background, there are a wealthof problems that I could lead a motivated student to explore. General topics include developingconstruction techniques for convex polytopes, classifying the number of combinatorial types of con-
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vex polytopes satisfying a given property, while more specific topics like verifying the Illuminationand X-Raying Conjectures for three-dimensional convex bodies with rotational symmetry could beconsidered. Ultimately, I would enjoy the opportunity to become a teaching mentor myself; to passalong my knowledge and experiences to another instructor who shares my passion for teaching.Wherever my career takes me, I hope that I can continue to be fortunate enough to have accessto the valuable teaching resources that I have had thus far, and I am excited at the prospect ofcontinuing to grow as an instructor.
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Appendices
A Teaching Responsibilities
Term InstitutionCourse
EnrollmentNumber Name
Winter 2014 University of Calgary AMAT 425∗ Introduction to Optimization 21
Fall 2014 University of CalgaryMATH 211 Linear Methods I (2 sections) 186, 189
MATH 249∗∗ Introductory Calculus 120
Summer 2014 University of Calgary MATH 211 Linear Methods I 53
Winter 2014 University of Calgary MATH 271 Discrete Mathematics 120
Fall 2013 University of Calgary MATH 211 Linear Methods I 124
Winter 2013 University of Calgary MATH 211 Linear Methods I 118
Summer 2012 Southern Alberta Institute of Technology MATH 172 Applied Mathematics II 27
∗ Instructed two weeks as regular instructor was on parent leave.
∗∗ Additionally, I taught one hour a week for another section, as the regular Instructor was unable to teach at that time.
Table 1: Summary of mathematics courses taught to date.
Course Number Course Name Calendar Description
MATH 172 Applied Mathematics II Matrices and pathways, statistics and probabil-ity, finance, cyclic, recursive and fractal patterns,vectors, and design.
MATH 211 Linear Methods I Systems of equations and matrices, vectors, ma-trix representations and determinants. Complexnumbers, polar form, eigenvalues, eigenvectors.Applications.
MATH 249 Introductory Calculus Algebraic operations. Functions and graphs.Limits, derivatives, and integrals of exponential,logarithmic and trigonometric functions. Funda-mental theorem of calculus. Applications.
MATH 271 Discrete Mathematics Proof techniques. Sets and relations. Induction.Counting and probability. Graphs and trees.
Table 2: Description of mathematics course taught to date.
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Course Number of TimesInstitution
Approximate
Number Name Instructed Enrollment
MATH 211 Linear Methods I 8 University of Calgary 30
MATH 249 Introductory Calculus 1 University of Calgary 25
MATH 251 Calculus I 8 University of Calgary 25
MATH 271 Discrete Mathematics 5 University of Calgary 100
MATH 273 Honours Mathematics: Numbers and Proofs 1 University of Calgary 30
AMAT 307 Differential Equations for Engineers 2∗ University of Calgary 50
MATH 349 Calculus III 1 University of Calgary 25
MATH 100 Calculus I 2 University of Alberta 30
MATH 101 Calculus II 1 University of Alberta 30
MATH 113 Elementary Calculus I 12 University of Alberta 25
∗ I taught two sections of AMAT 307 tutorials for two weeks in the absence of the regular Instructor.
Table 3: Summary of mathematics tutorials taught to date.
CourseRole Grading Duties Institution
Number Name
MATH 249 Introductory Calculus Instructor Midterms and Final Exams University of Calgary
MATH 271 Discrete Mathematics Instructor Midterms and Final Exams University of Calgary
MATH 211 Linear Methods I Instructor Midterms and Final Exams University of Calgary
MATH 172 Applied Mathematics II Instructor Assignments, Module Tests, Final Exams Southern Alberta Institute of Technology
MATH 271 Discrete Mathematics Teaching Assistant Assignments and Quizzes University of Calgary
MATH 374 Nonlinear Optimization Teaching Assistant Assignments University of Alberta
MATH 201 Differential Equations Teaching Assistant Assignments University of Alberta
MATH 120 Linear Algebra I Teaching Assistant Midterms University of Alberta
MATH 113 Elementary Calculus I Teaching Assistant Quizzes University of Alberta
MATH 101 Calculus II Teaching Assistant Assignments University of Alberta
Table 4: Summary of grading duties to date.
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B Activities Undertaken to Improve Teaching and Learning
(a) Course Design Workshop (b) University Teaching Certificate
(c) Instructional Skills Workshop
Figure 1: Teaching Workshop Certificates of Completion.
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Figure 2: Teaching and Learning Center classroom observation feedback for MATH 211, Winter2013.
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Figure 3: University Teaching Program videotape feedback.
Session Title Hours Session Title Hours
Preparing for Successful Lectures 1.5 The First Class 1.5
Can Learning Objectives Help my Teaching? 1.5 Leading a Balanced Life 2.0
Sequencing Learning 1.5 Creating a Positive Classroom Atmosphere 1.0
Effective Teaching for Problem Solving Sessions 1.0 Integrating Teaching and Research 1.5
Delivering a Successful Lecture 1.5 Humour in the Classroom 2.0
Preventing Plagiarism 1.5 Communication as Part of A Professors’ Practice 1.0
Evaluating and Marking Students’ Work 1.5 Teaching Calculus and Calculus Labs 1.0
The Code of Student Behavior 1.0 Teaching Math to Undergrads 1.0
How Good is Your Memory? 1.5 Teaching Math to “Mathophobes” 1.0
First Line of Contact 1.0 Some Thoughts on Teaching Math 1.0
Building a Culture of Respect 1.5 ICT in Teaching and Learning Mathematics 1.0
Graduate Students and Supervisors 1.5 Strategies for Teaching Large Math Classes 1.0
Teaching Large Classes 1.5 Strategies of Teaching as a Graduate Student 1.0
The First Sixteen Weeks 1.5 Some Thoughts on Teaching 1.0
A Crash Course in Copyright 1.0 “Tell Me and I Forget...” 1.0
Table 5: University Teaching Program seminars attended.
16
C Documentation of Results of Teaching
UNIVERSAL STUDENT RATINGS OF INSTRUCTION (REPORTING ONLY)
Overall Section Rating
MATH211 LEC 01 -- Linear Methods I Fall 2014
Survey Instructor: R. Trelford
Number of times the instructor has taught this course (last 10 years including the current term):
5
USRI enrolment: 180
Valid instruments received: 146
Response rate: 81.11%
Mean Rating (Out of 7)
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
1. O
verall I
nstru
ction
2. E
noug
h deta
il in c
ourse
o...
3. C
ourse
cons
isten
t with
ou...
4. C
onten
t well
orga
nized
5. S
tude
nt qu
estio
ns re
spon
d...
6. C
ommun
icated
with
enth
usia.
..
7. O
ppor
tunit
ies fo
r ass
ista..
.
8. S
tude
nts t
reate
d res
pectf
...
9. E
valua
tion m
ethod
s fair
10. W
ork g
rade
d in r
easo
nable
...
11. I
learne
d a lo
t in th
is co
...
12. S
uppo
rt mate
rials
helpf
ul
6.526.19 6.38 6.52 6.57 6.74
6.306.67
6.026.42 6.40
5.65
Rating Item
Mea
n
Rating Item
1. Overall Instruction
2. Enough detail in course outline
3. Course consistent with outline
4. Content well organized
5. Student questions responded to
6. Communicated with enthusiasm
7. Opportunities for assistance
8. Students treated respectfully
9. Evaluation methods fair
10. Work graded in reasonable time
11. I learned a lot in this course
12. Support materials helpful
Figure 4: MATH 211 L01 Fall 2014 student survey results.
UNIVERSAL STUDENT RATINGS OF INSTRUCTION (REPORTING ONLY)
Overall Section Rating
MATH211 LEC 03 -- Linear Methods I Fall 2014
Survey Instructor: R. Trelford
Number of times the instructor has taught this course (last 10 years including the current term):
5
USRI enrolment: 176
Valid instruments received: 114
Response rate: 64.77%
Mean Rating (Out of 7)
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
1. O
verall I
nstru
ction
2. E
noug
h deta
il in c
ourse
o...
3. C
ourse
cons
isten
t with
ou...
4. C
onten
t well
orga
nized
5. S
tude
nt qu
estio
ns re
spon
d...
6. C
ommun
icated
with
enth
usia.
..
7. O
ppor
tunit
ies fo
r ass
ista..
.
8. S
tude
nts t
reate
d res
pectf
...
9. E
valua
tion m
ethod
s fair
10. W
ork g
rade
d in r
easo
nable
...
11. I
learne
d a lo
t in th
is co
...
12. S
uppo
rt mate
rials
helpf
ul
6.646.20
6.426.68 6.70 6.85
6.416.71
6.296.52 6.50
5.75
Rating Item
Mea
n
Rating Item
1. Overall Instruction
2. Enough detail in course outline
3. Course consistent with outline
4. Content well organized
5. Student questions responded to
6. Communicated with enthusiasm
7. Opportunities for assistance
8. Students treated respectfully
9. Evaluation methods fair
10. Work graded in reasonable time
11. I learned a lot in this course
12. Support materials helpful
Figure 5: MATH 211 L03 Fall 2014 student survey results.
17
UNIVERSAL STUDENT RATINGS OF INSTRUCTION (REPORTING ONLY)
Overall Section Rating
MATH249 LEC 05 -- Introductory Calculus Fall 2014
Survey Instructor: R. Trelford
Number of times the instructor has taught this course (last 10 years including the current term):
1
USRI enrolment: 109
Valid instruments received: 105
Response rate: 96.33%
Mean Rating (Out of 7)
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
1. O
verall I
nstru
ction
2. E
noug
h deta
il in c
ourse
o...
3. C
ourse
cons
isten
t with
ou...
4. C
onten
t well
orga
nized
5. S
tude
nt qu
estio
ns re
spon
d...
6. C
ommun
icated
with
enth
usia.
..
7. O
ppor
tunit
ies fo
r ass
ista..
.
8. S
tude
nts t
reate
d res
pectf
...
9. E
valua
tion m
ethod
s fair
10. W
ork g
rade
d in r
easo
nable
...
11. I
learne
d a lo
t in th
is co
...
12. S
uppo
rt mate
rials
helpf
ul
6.886.47 6.61 6.76 6.82 6.88
6.696.89
6.40 6.53 6.36 6.23
Rating Item
Mea
n
Rating Item
1. Overall Instruction
2. Enough detail in course outline
3. Course consistent with outline
4. Content well organized
5. Student questions responded to
6. Communicated with enthusiasm
7. Opportunities for assistance
8. Students treated respectfully
9. Evaluation methods fair
10. Work graded in reasonable time
11. I learned a lot in this course
12. Support materials helpful
Figure 6: MATH 249 L05 Fall 2014 student survey results.
UNIVERSAL STUDENT RATINGS OF INSTRUCTION (REPORTING ONLY)
Overall Section Rating
MATH211 LEC 01 -- Linear Methods I Summer 2014
Survey Instructor: R. Trelford
Number of times the instructor has taught this course (last 10 years including the current term):
