2019 Winter MAT102: Intro to Math Proof

The main topics that we cover in this course are:

  1. Numbers, and Inequalities.
  2. Sets, functions and fields.
  3. Informal logic.
  4. Mathematical Induction.
  5. Bijections and cardinality.
  6. Integers and divisibility.
  7. Relations.

The course note is available: MAT102

The slides for weekly lectures can be found here:

  1. MAT102_Week1-2
  2. MAT102_Week2-3
  3. MAT102_Week 4-5
  4. MAT102_Week 6
  5. MAT102_Week 7
  6. MAT102_Week 8
  7. MAT102_Week 9
  8. MAT102_Week10
  9. MAT102_Week 11-12

Below are a few short video clips I made to explain certain questions upon students’ request.

  1. 2.5.29 Part a) Prove or disprove if two functions f and g are bounded, then their sum f+g is bounded.
  2. 2.5.29 Part b). Prove of disprove if two functions f and g are bounded, then f^2-g^2 is bounded.
  3. 2.5.50. Show that in any field F, the equation x^2 = 1 can have at most two solutions.
    Can you think of a field in which the equation x^2 = 1 has exactly one solution?

CV, Teaching dossier and more

Here’s a copy of my recent CV (edited in Sep 2022)

Here’s a copy of my teaching dossier (edited in Dec 2021)

Here are a few gems I collected during my journey as a math educator: letter1, letter2, letter3, letter4, letter5, letter6, letter7, letter8, letter9, letter10, letter11, letter12

Research has shown student teaching evaluations are biased. Teaching evaluations evaluate gender, race, and attractiveness. Men are favored. White people are favored. To see a collection of resources that discuss the issues associated with teaching evaluations, see Rebecca J. Kreitzer’s post: EVIDENCE OF BIAS IN STANDARD EVALUATIONS OF TEACHING

If you are still interested in reading the full version of my recent teaching evaluations, they are here:

MATH1500 Calculus I (2021 Spring)

MATH2150 Multivariable Calculus (2021 Spring)

MATH2720 Multivariable Calculus (2021 Spring)

MATH1510 Applied Calculus I (2020 Fall)

MATH2720 Multivariable Calculus (2020 Fall)

MATH2030 Combinatorics (2020 Fall)

MAT202 Discrete Mathematics (2020 Spring)

MAT135 Calculus I (2020 Spring)

MAT135 Calculus

MAT102 Intro to Math Proof

MAT102 Intro to Math Proof

MAT223 Linear Algebra

Are you a Repeat Learner?

Disclaimer: Repeat Learner here refers to someone who can’t stop learning new things. I don’t believe the definition: a Repeat Learner is a student who has outstanding modules from previous years gives it justice. I’m a proud Repeat Learner who repeats the activity of learning new things all the time.

My life as a student lasted long. When I looked back, I spent almost twenty-two whole years (Y6-Y28) as a full-time student. At some point when I was near the end of my student days, I thought the learning part of my life was about to be done. How wrong was I! Once I started teaching as a full-time mathematics lecturer at Singapore Polytechnic, I quickly realized there were so many things I needed to learn: how to write a lesson plan that makes sense; how to communicate with students; how to write on the whiteboard/blackboard which minimizes the chance of anything getting erased during an one-hour lecture, how to navigate the LMS (we were using Blackboard back then), etc. I had a great officemate when I started my job, and she taught me new skills everyday in the first few months. I didn’t even know how to order textbooks! Once I settled on my new role as a lecturer and knew what I was doing, I found myself learning how to use Camtasia to make video lessons; taking online courses to learn about the newest edtech tools,  and even a cool visualization software for statistics: Tableau. All these learning experiences keep my day exciting. They have brought much frustration and struggle, but also joy, satisfaction and fun. I’m in love with learning new things! It helps me master skills that make me a better teacher.

What I didn’t realize back then is learning new things can also help me stay humble and connected to my students. Sometimes I found myself quietly complaining things in my head while teaching: How can you not know this? How can you forget something that we just learned last week? How can you not get it? You see, I forget what it’s like to be a student, to be a learner who struggles. I took up painting two years ago, and whenever I can’t get things right, which happens to each one of my paintings, I tell myself this is what it’s like to be learning new things. Those quiet complaints in my head gradually go away. I’m able to put myself in my students’ shoes and see things in a different angle now. I’m more empathetic because I also struggle when I learn new things and I know that’s the good thing: without making mistakes and struggling, progress and growth won’t happen.   I’m not suggesting every teacher to go out and learn something new today, but it’s important to remind ourselves what it’s like to be a beginner, a learner.

Now I’m challenging myself to learn how to play piano, which I figured might take years, especially after my first lesson. I’m not giving up just yet. The learning part is too good to walk away from. I guess I’ll never quit being a student.

Should we all become edtech gurus?

I’m pleasantly surprised by how well-organized eCampus Ontario extend mOOC is, and hoping to make some meaningful and long-lasting connections with the community here.

As I’m going through the materials of module 2: Technologists, I started thinking of why digital literacy matters, and how much does it matter to “good teaching”.

Being digital literate starts with knowing the problems we want to solve. Is it about improving student’s engagement? Is it about deepening understanding of key concepts? Is it about communicating more effectively? Or is it about having a fun and open learning environment? While I was teaching in Singapore, every faculty member from my department took part in the popular Coursera online course: Powerful Tools for Teaching and Learning: Web 2.0 Tools.

That was the first time I took some time thinking about what exactly are digital literacies and why they are important. Our students today are different from students decades ago; in fact they are probably more digital literate than us in many aspects. In order for us to improve our teaching and reaching our students, being aware of what tools are available becomes very important.  On the other hand most edtech tools have their own limitations. Before we use any new tool, it’s a good practice to try to understand what they are meant to help with, and what potential issues we may run into. 

I believe most of the problems we are trying to solve have low-tech or no-tech solutions. Using digital tools is just one way of solving it. Perhaps before we dig in the endless list of “cool” tools that are out there, we should ask ourselves can we come up with a no-tech solution to address the issue at hand, focusing on the students, and what’s best for them.

I find the most useful way to adopt new tools effectively is by discussing it with colleagues and the bigger teaching community (we have a wonderful teacher community here: teacherforlearning channel! ). It comes to each one of us to share our experiences and spread it out, especially what don’t work. Don’t hesitate to share something that you tried and didn’t work. It might save someone else plenty of time and frustration in future. I stopped using Mentimeter a while ago because I didn’t like the paid version, and it’s hard to edit mathematics there. 

For those who are taking the same course with me, you can find my extended activities of Module 1 here:

https://docs.google.com/document/d/1zqokoWhrpin3XtxNA6S3L0BvPbQccsAEQMo6zgJ0zIQ/edit?usp=sharing

I joined the math department at University of Manitoba in 2020 Fall. Before that I taught math at University of Toronto Mississauga part-time since 2016 when my family moved to Canada from Singapore. I also taught part-time at two local colleges: Seneca College and Humber College while working at UTM. I taught math full-time at Singapore Polytechnic from 2012 to 2016. This is the space where I explore and share my journey of teaching  mathematics, conducting education research projects, and learning about OER.

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