Teaching Dossier

Ryan Trelford

University of Waterloo

r2trelfo@uwaterloo.ca

October, 2019

Contents

1 Teaching Philosophy 1

2 Teaching Responsibilities 3

3 Activities Undertaken to Improve Teaching and Learning 4

4 Documentation of Results of Teaching 5

5 Service Duties 5

6 Future Plans 6

Appendices 7

11 Teaching Philosophy

I discovered my passion for teaching after delivering my very first mathematics tutorial as a newgraduate student. I recall feeling a lot of stress and anxiety beforehand, but while I was deliveringthe content to the students, those feelings disappeared and I knew at that moment that teaching ata university was the career that I wanted. I have taught many students since that initial contact,and my experiences teaching different topics to students of different mathematical backgrounds atseveral institutions have steadily brought my view of teaching into focus. 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 understanding ofideas and concepts rather than just the memorization of facts. This shift in paradigm can leadstudents to the realization that mathematics is a language itself; a language that allows us todescribe and predict physical systems in the world around us, enables us to express abstract ideasclearly and concisely, and aides us in business, commerce and science. Indeed, it is a language ofsuch beauty that words cannot adequately describe it. Of course, I alone didn’t create my view ofteaching – it was the advice of some exceptional colleagues and mentors that I have been fortunateenough to encounter that helped guide 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 had been 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 to beone-to-one. At this point the condition seems obvious to many students, and they can reproduceand even justify it when asked. I proceed with several examples, emphasizing not the computations,but rather reiterating the idea of a one-to-one function. They now see that a function is one-to-oneif, 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

2

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 concepts that were 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 to not be afraid to show excitement when I discussed aninteresting concept. Over time, my lessons have become less scripted, and more spontaneous. Ihave become comfortable with not over preparing 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 becoming more confident in my teaching.

Normally, when teaching a course, I find I have a few minutes left at the end of at least onelecture. Instead of diving ahead into the next lecture, I often show students the thing that trulyamazed me the most when I learned it, despite it being a bit off-topic. I begin by showing thata point is zero-dimensional. Then in one dimension, I show that two distinct points determinea line segment, and that in two dimensions, two parallel line segments can determine a square.Next, two parallel squares in three dimensions can determine a cube. Now students believe we are“out of dimensions”, but I then show them how two parallel cubes in four dimensions determine afour-dimensional cube. This is truly the best example of when I was being myself: I was so excitedto explain this amazing idea to students. I could tell from their reactions to learning about fourdimensions that they were feeding off of my enthusiasm. My goal is to continue teaching with thislevel of enthusiasm 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 alwaysrequire me to grow and learn, and I look forward to facing and overcoming the challenges that Iwill encounter in the future.

3

2 Teaching Responsibilities

I have been a Definite Term Lecturer in the Faculty of Mathematics at the University of Waterloosince August 1, 2015, but like many instructors, my teaching began during my graduate studies.As both a Master’s Student in the Department of Mathematics and Statistics at the University ofAlberta and as a Ph.D. student in the Department of Mathematics and Statistics at the Universityof Calgary, I taught many tutorials in calculus, linear algebra and discrete mathematics. Asidefrom working through problems on the board with students, I graded assignments and quizzes andwas the first point of contact for students who had issues with online homework systems such asMathXL, WebAssign and Lyryx.

In the summer of 2012, I taught my very first course, MATH 172 (Applied Mathematics II),in the Centre 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. 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.

Shortly after, in January 2013 as I worked to complete my Ph.D, I became a Sessional Instruc-tor at the University of Calgary. Although instructing courses are typically not part of a graduatestudent’s workload, the department has initiated a program whereby students who pass the In-structional Skills Workshop (see Section 3) and obtain higher than average student reviews becomeeligible to instruct mathematics courses. Over the course of two years, I instructed five sections ofMATH 211 (Linear Methods I), and one section each of MATH 271 (Discrete Mathematics) andMATH 249 (Introductory Calculus). With the exception of one Linear Methods course I instructedduring the summer of 2014, all courses were one of several concurrent sections that were run bya course coordinator. My duties as an instructor included preparing and delivering two or threelectures each week, as well as teaching one of the weekly one-hour tutorials attached to each ofthese lecture sections. I was required to suggest problems to the course coordinator for all exams,vet the draft versions of these exams, and supervise both the writing and grading of all exams withthe help of teaching assistants. I have also written solutions for several of these exams so that theycould be used as learning tools in future semesters, and have delivered two 2-hour final exam reviewsessions for all eight sections of Linear Methods in the Fall 2013 semester. I have also instructed thefirst four weeks of AMAT 425 - Introduction to Optimization in the Winter 2015 semester in theabsence of the regular instructor. I lead the students to understand convex sets, convex functionsand introduced linear programming in a flipped-classroom setting.

From August 2015 onwards I have been a Definite-Term Lecturer at the University of Waterloo.I have taught MATH 115 (Linear Algebra for Engineers), MATH 128 (Calculus II for the Sciences)MATH 135 (Honours Algebra), MATH 136 (Honours Linear Algebra I) and MATH 215 (LinearAlgebra for Electrical and Computer Engineers). Although I did not coordinate MATH 128, MATH135 nor MATH 136 in any of the semesters I taught them, I was responsible for checking assignmentsfor typos and ensuring the questions were stated clearly, typesetting solutions for some of theassignments, suggesting problems for the midterm and final exams as well as grading exams andreporting final marks. In the Winter 2016, 2017 and 2018 semesters, I taught all sections of MATH215. I was solely responsible for all aspects of the course: creating practice problems and practiceexams, assignments, midterm exams and final exams in addition to assigning grading duties toTAs and computing final grades. Beginning in the Fall 2018 semester, I became the coordinator

4

of MATH 115. This involved the same level of work as MATH 215, but I was also responsible foroverseeing all 10 sections while teaching two sections. This required having all course materialsprepared well in advance so that the other instructors knew what material to teach and whatlevel to teach at. Also, I created linear algebra applications aimed at engineering students such aselectrical networks, directed graphs, linear dynamical systems and linear regression as part of theMATH 115 curriculum review.

Tables 1 and 2 (pages 7 and 8) summarize the courses I have taught to date

3 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:

• Course Design Workshop (CDW) - 14 hours, completed January, 2014

• University Teaching Certificate (UTC) - 36 hours, completed April, 2013

• Instructional Skills Workshop (ISW) - 24 hours, completed November, 2011

• University Teaching Program1 (UTP) - completed October, 2008

The CDW, UTC, and ISW were offered by the Teaching and Learning Centre2 (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:having one lecture observed by a member of the TLC, who then supplies constructive feedback,which is presented in Figure 1 (page 9). 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 in addition to having a tutorial videotaped andcommented on by a member of the mathematics department.

Figures 2a, 2b and 2c (page 10) shows the certificates of completion for the ISW, UTC andCDW.

1This 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.

2The Teaching and Learning Centre has since been updated and is now known as the Taylor Institute for Teachingand Learning. The University Teaching Certificate program has been changed significantly since I received it.

5

4 Documentation of Results of Teaching

Teaching assessments are an invaluable part of the growth of an instructor. Aside from UTCfeedback (mentioned in Section 3), I have received feedback from students in the form of bothsurveys and questionnaires. The survey results from all courses taught at the University of Waterlooare provided in Tables 3 and 4 on page 11, while all courses taught at the University of Calgaryappear in Table 5 on page 13. Figures 3a to 3d on page 14 are Letters of Recognition from theEngineering Faculty at the University of Waterloo for my teaching of MATH 215 in each of theWinter 2016, 2017 and 2018 semesters and MATH 115 in the Spring 2019 semester.

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 I ambeing recognized by the student, but because I was able to make such a profound impact on theiracademic careers that they took to the time to tell me about it. Samples of such emails and lettersare included on pages 15–17.

As a result of taking advantage of the large number of teaching resources that have beenavailable to me, I was a recipient of a teaching award in each of the first four years of my Ph.D.program. In 2010, I received the Fred A. McKinnon Graduate Teaching Award as the top graduateteaching assistant (see Figure 5a on page 18), and in each of 2011, 2012 and 2013, I receiveda Departmental Graduate Teaching Assistant Excellence Award. I was also the recipient of anEric Milner Graduate Scholarship in 2011, awarded not only for academic excellence, but alsofor being actively engaged in the sharing of mathematical knowledge. Most recently in the Fall2014 Semester, following the nominations from my Linear Algebra students, I received both theOutstanding Teaching Excellence in First Year Engineering Award and the University of CalgaryStudents’ Union Teaching Excellence Award, the latter of which appears in Figure 5b on page 18.At the University of Waterloo, I was nominated for a FEDS Excellence in Undergraduate TeachingAward in Winter 2016 by my MATH 215 students, but I unfortunately did not receive this award.

5 Service Duties

Service is playing an ever more prominent role in my career at the University of Waterloo.Through these duties, I am often able to interact with students outside of the classroom settingwhich allows me to learn about the non-academic problems they encounter. As a result, I gain abetter understanding of our students.

Academic advising is my main duty. I began my advising duties as a First-Year (Undeclared)Academic Advisor in 2016. A year later, I additionally became a Math Studies Advisor. Inthis capacity, I respond to student inquiries about their programs and help them overcome anyroadblocks they may encounter. Often I help students decide what courses they should take in anupcoming semester, remove academic holds on their accounts, discuss options with students beingasked to leave the faculty, discuss graduation requirements and assist students with the paperworkrequired to clear an academic term due to physical or mental health issues. As mental health is agrowing concern to our students, I took part in the Mental Health First Aid workshop last summer(see Figure 2d on page 10) in an effort to make myself more aware of when a student is showingsigns of having a mental health crisis.

My other main duty which I have recently begun involves assigning transfer credits to studentsapplying to the University of Waterloo who have previously taken courses at other universities. As

6

I am new to this position, I attended one of the quarterly admissions meetings to learn more aboutthe admissions process.

Aside from these duties, I have also spent a large amount of time in the Math UndergraduateOffice (MUO) helping the staff with the day-to-day operations during my last two summers. There,I have learned a lot about how the Math Faculty operates, and I have become a more experiencedadvisor as a result of dealing with student requests in the MUO. I have also been given the opportu-nity to travel to China on behalf of the University for the last two summers to meet new incomingstudents and help them prepare for their transition into a new life at the University of Waterloo.

There are many other smaller duties I perform, such as participating in the Pink Tie Ceremonyduring orientation week and assisting with the Ontario Universities Fair and Fall Open House,attending school visits to high schools in Canada and abroad and evaluating the final capstoneprojects for the Masters of Mathematics for Teachers. All of these duties allow me to interact withvarious students and help to give me a better understanding of the challenges our students facetoday.

6 Future Plans

In the Fall 2018 semester, I became the coordinator for MATH 115 – Linear Algebra for Engineers,a position I expect to hold for some time. One of my goals in this position is to create a set ofcourse notes so that the students have an inexpensive text to read that is more closely related tothe course than any published textbook. Another goal is to further develop the set of applicationsthat I created last year to make them even more applicable to each of the engineering disciplines.To aid in this, I would like to opportunity to audit some of the engineering courses to see firsthandhow the concepts of linear algebra are being used in other courses. Some useful courses could be

• PHYS 115 - Mechanics (taken by Chemical and Mechanical Engineers)

• ECE 140 - Linear Circuits (taken by Electrical, Computer and Software Engineers)

• MTE 120 - Circuits (taken by Mechatronics Engineers)

• CHE 102 - Chemistry for Engineers (taken by Mechatronics and Management Engineers)

Given that I have only taught a few courses at the University of Waterloo so far, I would alsolike to have the opportunity to teach some higher level courses in the future. Courses I am mostinterested in are

• MATH 235 – Linear Algebra 2 for Honours Mathematics

• MATH 239 – Introduction to Combinatorics

• CO 227 – Introduction to Optimization

• PMATH 333 – Introduction to Real Analysis

Finally, I hope to continue to learn about the admissions process for the Faculty of Mathematicsand perhaps play a larger role in this process in the future.

7

Appendices

Institution TermCourse

EnrollmentNumber Sections Name

University of Waterloo

Fall 2019 MATH 115 3 Linear Algebra For Engineers 116,142,133

Spring 2019MATH 115 1 Linear Algebra for Engineers 39

MATH 225 1 Applied Linear Algebra 2 28

Winter 2019MATH 128 1 Calculus 2 for the Sciences 96

MATH 136 2 Linear Algebra I for Honours Mathematics 60, 177

Fall 2018 MATH 115 2 Linear Algebra for Engineers 101, 109

Winter 2018 MATH 215 2 Linear Algebra for Engineering 126, 120

Fall 2017 MATH 135 3 Honours Algebra 54, 58, 60

Winter 2017MATH 136 1 Linear Algebra I for Honours Mathematics 58

MATH 215 2 Linear Algebra for Engineering 111, 111

Fall 2016 MATH 135 3 Honours Algebra 49, 55, 54

Winter 2016 MATH 215 2 Linear Algebra for Engineering 110, 107

Fall 2015 MATH 135 2 Honours Algebra 52, 54

Winter 2015 AMAT 425∗ 1 Introduction to Optimization 21

University of Calgary

Fall 2014MATH 211 2 Linear Methods I 186, 189

MATH 249∗∗ 1 Introductory Calculus 120

Summer 2014 MATH 211 1 Linear Methods I 53

Winter 2014 MATH 271 1 Discrete Mathematics 120

Fall 2013 MATH 211 1 Linear Methods I 124

Winter 2013 MATH 211 1 Linear Methods I 118

Southern Alberta Institute of Technology Summer 2012 MATH 172 1 Applied Mathematics II 27

Red cells represent a multi-section course where I was the coordinator.

Green cells represent courses where I was the sole instructor of all sections.

∗ Instructed first four weeks while the regular instructor was on parental leave.

∗∗ Additionally, I taught one hour per week for another section, as the regular instructor became unable to teach at that time.

Table 1: Summary of mathematics courses taught to date.

8Course

Number

Course

Nam

eIn

stitution

CalendarDesc

rip

tion

MA

TH

115

Lin

ear

Alg

ebra

for

En

gin

eeri

ng

Un

iver

sity

of

Wate

rloo

Th

isis

aco

urs

eon

lin

ear

alg

ebra

an

dit

sap

pli

cati

on

sto

engi-

nee

rin

g.

Top

ics

tob

eco

ver

edin

clu

de

com

ple

xnu

mb

ers;

vec

-to

rs,

lin

esan

dp

lan

es;

syst

ems

of

lin

ear

equ

ati

on

s;m

atr

ices

,li

nea

rtr

an

sform

ati

on

san

dd

eter

min

ants

;in

trod

uct

ion

tovec

-to

rsp

ace

s;ei

gen

valu

es,

eigen

vec

tors

an

dd

iagon

al-

izati

on

;th

eG

ram

-Sch

mid

talg

ori

thm

an

dort

hogon

al

dia

gon

ali

zati

on

;S

in-

gu

lar

valu

ed

ecom

posi

tion

(tim

ep

erm

itti

ng).

We

ap

pro

ach

the

mate

rial

thro

ugh

ab

len

dof

theo

reti

cal

idea

s,co

mp

uta

tion

al

met

hod

san

dso

me

ap

pli

cati

on

s.

MA

TH

128

Calc

ulu

s2

for

the

Sci

ence

sU

niv

ersi

tyof

Wate

rloo

Tra

nsf

orm

ing

an

dev

alu

ati

ng

inte

gra

ls;

ap

pli

cati

on

tovolu

mes

an

darc

len

gth

;im

pro

per

inte

gra

ls.

Sep

ara

ble

an

dli

nea

rfi

rst

ord

erd

iffer

enti

al

equ

ati

on

san

dap

pli

cati

on

s.In

trod

uct

ion

tose

qu

ence

s.C

onver

gen

ceof

seri

es;

Taylo

rp

oly

nom

ials

,T

ay-

lor’

sR

emain

der

theo

rem

,T

aylo

rse

ries

an

dap

pli

cati

on

s.P

ara

-m

etri

c/vec

tor

rep

rese

nta

tion

of

curv

es;

part

icle

moti

on

an

darc

len

gth

.P

ola

rco

ord

inate

sin

the

pla

ne.

MA

TH

135

Hon

ou

rsA

lgeb

raU

niv

ersi

tyof

Wate

rloo

An

intr

od

uct

ion

toth

ela

ngu

age

of

math

emati

csan

dp

roof

tech

-n

iqu

esth

rou

gh

ast

ud

yof

the

basi

calg

ebra

icsy

stem

sof

math

-em

ati

cs:

the

inte

ger

s,th

ein

teger

sm

od

ulo

n,

the

rati

on

al

nu

m-

ber

s,th

ere

al

nu

mb

ers,

the

com

ple

xnu

mb

ers

an

dp

oly

nom

ials

.

MA

TH

136

Lin

ear

Alg

ebra

Ifo

rH

on

ou

rsM

ath

emati

csU

niv

ersi

tyof

Wate

rloo

Syst

ems

of

lin

ear

equ

ati

on

s,m

atr

ixalg

ebra

,el

emen

tary

matr

i-ce

s,co

mp

uta

tion

al

issu

es.

Rea

ln

-sp

ace

,vec

tor

space

san

dsu

b-

space

s,b

asi

san

dd

imen

sion

,ra

nk

of

am

atr

ix,

linea

rtr

an

sfor-

mati

on

san

dm

atr

ixre

pre

senta

tion

s.D

eter

min

ants

,ei

gen

valu

esan

dd

iagon

ali

zati

on

,ap

pli

cati

on

s.

MA

TH

215

Lin

ear

Alg

ebra

for

En

gin

eeri

ng

Un

iver

sity

of

Wate

rloo

Syst

ems

of

lin

ear

equ

ati

on

s;th

eir

rep

rese

nta

tion

wit

hm

atr

ices

an

dvec

tors

;th

eir

gen

erali

zati

on

toli

nea

rtr

an

sform

ati

on

son

ab

stra

ctvec

tor

space

s;an

dth

ed

escr

ipti

on

of

thes

eli

nea

rtr

an

s-fo

rmati

on

sth

rou

gh

qu

anti

tati

ve

chara

cter

isti

cssu

chas

the

de-

term

inant,

the

chara

cter

isti

cp

oly

nom

ial,

eigen

valu

esan

dei

gen

-vec

tors

,th

era

nk,

an

dsi

ngu

lar

valu

es.

MA

TH

225

Ap

pli

edL

inea

rA

lgeb

ra2

Un

iver

sity

of

Wate

rloo

Vec

tor

space

s.L

inea

rtr

an

sform

ati

on

san

dm

atr

ices

.In

ner

pro

du

cts.

Eig

envalu

esan

dei

gen

vec

tors

.D

iagon

ali

zati

on

.A

p-

pli

cati

on

s.

MA

TH

211

Lin

ear

Met

hod

sI

Un

iver

sity

of

Calg

ary

Syst

ems

of

equ

ati

on

san

dm

atr

ices

,vec

tors

,m

atr

ixre

pre

senta

-ti

on

san

dd

eter

min

ants

.C

om

ple

xnu

mb

ers,

pola

rfo

rm,

eigen

-valu

es,

eigen

vec

tors

.A

pp

lica

tion

s.

MA

TH

249

Intr

od

uct

ory

Calc

ulu

sU

niv

ersi

tyof

Calg

ary

Alg

ebra

icop

erati

on

s.F

un

ctio

ns

an

dgra

ph

s.L

imit

s,d

eriv

a-

tives

,an

din

tegra

lsof

exp

on

enti

al,

logari

thm

ican

dtr

igon

om

et-

ric

fun

ctio

ns.

Fu

nd

am

enta

lth

eore

mof

calc

ulu

s.A

pp

lica

tion

s.

MA

TH

271

Dis

cret

eM

ath

emati

csU

niv

ersi

tyof

Calg

ary

Pro

of

tech

niq

ues

.S

ets

an

dre

lati

on

s.In

du

ctio

n.

Cou

nti

ng

an

dp

rob

ab

ilit

y.G

rap

hs

an

dtr

ees.

MA

TH

172

Ap

pli

edM

ath

emati

csII

Sou

ther

nA

lber

taIn

stit

ute

of

Tec

hn

olo

gy

Matr

ices

an

dp

ath

ways,

stati

stic

san

dp

rob

ab

ilit

y,fi

nan

ce,

cycl

ic,

recu

rsiv

ean

dfr

act

al

patt

ern

s,vec

tors

,an

dd

esig

n.

Tab

le2:

Des

crip

tion

ofm

ath

emat

ics

cours

esta

ugh

tto

dat

e.

9

Figure 1: Teaching and Learning Centre classroom observation feedback for MATH 211, Winter2013 as part of the University Teaching Certificate

10

(a)

Inst

ruct

ion

alSkil

lsW

orksh

op

(b)

Un

iver

sity

Tea

chin

gC

erti

fica

te

(c)

Cou

rse

Des

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11

UniversityofW

aterlooM

ath

FacultyCourses

Sem

este

rF

15F

16W

17F

17W

19

S19

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Cou

rse

MA

TH

135

MA

TH

135

MA

TH

136

MA

TH

135

MA

TH

128

MA

TH

136

MA

TH

225

MA

TH

136

Sec

tion

L00

7L

008

L00

7L

014

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L00

7L

008

L023

L024

L00

6L

001

L007

L001

L??

?L

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Loca

tion

MC

4063

MC

4063

MC

4058

MC

4058

MC

4063

SJ1

3014

MC

4058

PH

Y150

MC

406

3M

C40

61M

C2065

ST

J3014

MC

4040

RO

OM

RO

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den

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5254

4955

5458

5458

6096

180

60

23

9999

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cent

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din

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.281

.579

.669

.179

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290

.781

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00

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74.

74.8

4.6

4.6

4.8

4.8

4.7

4.4

4.5

4.5

4.5

Org

aniz

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n4.

784.

824.

874.95

4.84

4.7

24.

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04.7

04.6

9

Exp

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ns

4.86

4.64

4.77

4.65

4.70

4.8

24.37

4.76

4.59

4.5

64.7

34.8

34.6

7

Qu

esti

ons

4.76

4.84

4.85

4.95

4.74

4.7

74.

844.

854.

784.6

74.6

54.7

34.58

Vis

ual

Pre

senta

tion

4.68

4.80

4.82

4.82

4.74

4.7

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804.

804.84

4.4

74.6

54.6

94.46

Ora

lP

rese

nta

tion

4.84

4.84

4.79

4.92

4.81

4.7

74.92

4.89

4.82

4.68

4.7

04.7

74.92

Ava

ilab

ilit

y4.55

4.76

4.80

4.77

4.58

4.6

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4.85

4.8

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dIn

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583.4

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4.28

4.12

3.06

3.3

53.4

93.5

8

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ven

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4.81

4.89

4.85

4.95

4.79

4.7

44.

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914.

874.7

04.7

44.7

24.62

Tab

le3:

Stu

den

tE

valu

ati

on

sfo

rco

urs

esta

ugh

tfo

rth

eM

ath

emat

ics

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sity

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;blue

scor

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All

score

sare

outof5

.

12

UniversityofW

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Sem

este

rW

16W

17W

18F

18S18

F19

Cours

eM

AT

H21

5M

AT

H21

5M

AT

H21

5M

AT

H11

5M

AT

H115

MA

TH

115

Sec

tion

L00

1L

002

L00

1L

002

L00

1L

002

L00

7L

008

L001

L00

6L

007

L008

Loca

tion

MC

4020

MC

4020

EIT

1015

RC

H10

3E

IT10

15E

IT10

15R

CH

103

RC

H103

RC

H30

5R

CH

103

RC

H302

RC

H302

Stu

den

tsE

nro

lled

110

107

111

111

126

120

109

101

3911

6142

133

Per

cent

Res

pondin

g60.

957.

968

.579

.358

.751

.792

.784

.281

.6

Pro

fSco

re4.8

4.8

4.7

4.8

4.8

4.7

4.6

4.6

-

Org

aniz

ati

on&

Cla

rity

4.9

15.00

4.88

4.94

5.00

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4.80

4.78

4.88

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ponse

toQ

ues

tion

s4.9

15.00

4.90

4.91

4.97

4.94

4.57

4.75

4.84

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lP

rese

nta

tion

4.9

34.9

64.

934.

974.98

4.90

4.94

4.96

4.96

Vis

ual

Pre

senta

tion

4.8

14.9

04.

804.91

4.88

4.88

4.72

4.68

4.80

Ava

ilab

ilit

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14.8

44.

724.85

4.83

4.77

4.76

4.50

4.78

Expla

nat

ions

4.4

24.6

94.

314.

634.71

4.29

3.42

3.81

4.48

Enco

ura

gem

ent

4.2

54.3

34.

284.

224.20

4.35

4.44

4.22

4.44

Enth

usi

asm

4.93

4.8

64.

854.

864.

834.78

4.90

4.91

4.92

Cla

ssR

elati

onsh

ip4.8

74.9

04.

824.93

4.86

4.69

4.83

4.85

4.92

Quality

of

Tea

chin

g4.8

74.98

4.75

4.83

4.92

4.80

4.58

4.60

4.96

Tab

le4:

Stu

den

tE

valu

atio

ns

for

cou

rses

tau

ght

for

the

En

gin

eeri

ng

Fac

ult

yat

the

Un

iver

sity

ofW

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loo.

Red

scor

esd

enot

eth

elo

wes

tsc

ore

inea

chca

tegor

y;blue

scor

esth

eh

igh

est.

All

score

sare

outof5

.

13

University of Calgary Math Courses

Semester W13 F13 W14 S14 F14

Course MATH 211 MATH 211 MATH 271 MATH 211 MATH 211 MATH 249

Section L003 L007 L002 L001 L001 L003 L005

Students Enrolled 104 103 105 48 180 176 109

Percent Responding (%) 78.85 89.32 64.76 75.00 81.11 64.77 96.33

Overall Instruction 6.55 6.66 6.81 6.87 6.52 6.64 6.88

Enough Detail in Course Outline 6.16 6.33 6.59 6.72 6.19 6.20 6.47

Course Consistent with Outline 6.33 6.47 6.57 6.72 6.38 6.42 6.61

Content Well Organized 6.52 6.56 6.78 6.84 6.52 6.68 6.76

Student Questions Responded to 6.69 6.75 6.79 6.89 6.57 6.70 6.82

Communicated with Enthusiasm 6.40 6.89 6.83 6.90 6.74 6.85 6.88

Opportunities for Assistance 6.57 6.61 6.72 6.93 6.30 6.41 6.69

Students Treated Respectfully 6.69 6.88 6.86 6.97 6.67 6.71 6.89

Evaluation Methods Fair 6.07 5.78 6.28 6.77 6.02 6.29 6.40

Work Graded in Reasonable Time 6.50 6.49 6.50 6.75 6.42 6.52 6.53

I Learned a lot in this Course 6.29 6.29 6.54 6.80 6.40 6.50 6.36

Support Materials Helpful 5.53 5.73 5.83 6.30 5.65 5.75 6.23

Table 5: Student Evaluations for all courses taught at the University of Calgary. Red scores denotethe lowest score in each category; blue scores the highest. All scores are out of 7.

14

(a) MATH 215 - Winter 2016 (b) MATH 215 - Winter 2017

(c) MATH 215 - Winter 2018 (d) MATH 115 - Spring 2019

Figure 3: Letters of Recognition regarding my teaching

15

Student Emails Regarding Teaching

Hi Ryan,

I wanted to let you know that you are an exceptional lecturer. Your lectures are always wellplanned out, and I loved how you would use additional props such as markers to illustrate abstractexamples to make them easier to understand. As ECE students, we often encounter professors thatare either indifferent towards teaching or are too invested in their research. You were the oppositeof that. I can tell that you truly care about your students. Your enthusiasm for teaching is clearlyreflected in the amount of work you put into teaching the course. I really appreciate all the extrahours you spent in creating the review problems and practice exam before both the midterm andfinal exam. I have spoken to many of my classmates, and MATH 215 was definitely the most welltaught the course we have taken so far in our undergraduate career. Any class would be lucky tohave you teach them.

Keep up the great work and I really hope that I can have you again for a future course!

(a) MATH 215 – Winter 2016

Good evening sir:

Thank you for your wonderful lectures and always being patient with my questions. I feel reallylucky to be in your section and I actually learnt something useful. Also it?s my first term to learnmath in English, thank you for helping me in the transition between two different ways of learningmath.

I think math 135 is quite interesting. We aimed on proof techniques and we introduced manyaspects of mathematic, mostly focused on numbers. It is quite amazing that we can learn so manyaspects of math and can combine them together in a single exam. Sometimes I even confused aboutwhether we are learning the actual material or just use the material to introduce a technique.

(b) MATH 135 – Fall 2017

Thanks for perfect lecture with inspiration and passion throughout the whole semester! It’s mygreat pleasure to be assigned to your class in my first year. Think you should know what a goodteacher you are (unless you already do lol). I will certainly choose your course if I have the choice.Oh and btw, good luck on learning Chinese! Hope you have a nice life too

(c) MATH 135 – Fall 2017

16

Hi Professor Trelford,

I’m a 2A CE student who just finished Linear Algebra with you this past winter. I just wantedto let you know how much I appreciated your teaching this semester! Every lecture had a focusdriven purpose with exactly the amount of examples, theories, and questions answered to makeus understand the difficult topics. Your online posted notes were second to none in concisenessand legibility and really helped us study and learn the topics well past the exams! Even theassignments were excellent at testing what we knew and helping us learn what we didn’t.

I really appreciate how approachable and helpful you were in every class! Even now I’m usinglinear algebra in coop and it is really satisfying to see these real world applications!

I hope you feel encouraged that you are really good at what you do and I know we all appreciateyour work this term!

(d) MATH 215 – Winter 2018

Hello Prof. Trelford,

I’m one of your students in Mechatronics Stream 4. I’m writing this email simply to appreciatethe fantastic learning experience you’ve brought to our class throughout the entire term. Honestly,linear algebra is extremely abstract. The definitions of terminology and some theorems arecomplex and hard to imagine. It really shocked me how different the linear algebra was from themath we learned in high school. Although I love math and the logic behind it, the concepts in thiscourse were constantly challenging me.

This course would have been much more difficult and stressful if you were not the one teaching us!I have been hearing from my roommates (also Engineering students) that how they were sufferingfrom both the course itself (MATH115) and their professor’s explanations. One time, by a chance,one of them told me that the only way for them to get lin alg better understood was to lookthrough the course note uploaded by “the Section 8 professor.” Then I checked it on Learn and,not surprisingly, found you were the very one he referred to.

Frankly speaking, there were several times I found this course annoying, but I carried on learning itas soon as I thought of how all the lectures were well-organized and how thoroughly you explainedevery single definition and theorem. Therefore, in the end, no one in our class could complainanything because of the amazing learning experience you’ve been trying to create over this term.Anyway, thank you again for all of these, Prof. Trelford. Best wishes to you for the future!

(e) MATH 115 – Fall 2018

17

Dear Ryan,

I am one of the students who attended your Linear Algebra (Math 136) class last winter (Jan-April)and I wanted to say thank you for your incredible teaching style and support throughout the term.

I have always been passionate about studying mathematics, but I haven’t been able to fully graspthe material taught in lectures until I attended your class. Your simple notes and frequent use ofexamples made difficult concepts so incredibly easy to understand and allowed me to concentratemy time outside of class to reviewing the material rather than having to reteach it to myself again.You explained every concept in simple English and I thank you for that.

I also wanted to say thank you for always answering my questions in full detail and providing methe time that I needed to fully understand a concept. Whether it was after class or during officehours, you always had patience for all of my questions and made sure that I never left withouthaving a complete and thorough understanding of the material.

I genuinely enjoyed attending each lecture and I look forward to any more courses that I can takewith you. I wish you all the best in the coming year.

(f) MATH 136 – Winter 2019

18

(a) Fred A. McKinnon Graduate Teaching Award

(b) University of Calgary Students’ Union Teaching Excellence Award

Figure 5: Teaching awards received