Math Teaching – Page 2 – Journey to the west: from Singapore to Canada

OERs and the Vision of Mathematics Education in the Open, presentation at OCMA Virtual Symposium 2020

I recently gave a talk at OCMA Virtual Symposium 2020 titled “OERs and the Vision of Mathematics Education in the Open“, during which I shared my experience with open education resources and open textbooks in my teaching. Since we shifted to emergency online teaching this March, it has been challenging for everyone: students, faculty and staff. We are living in a time during which we experience the loss of family and friends without much emotional support, overworking is the new norm and the future is uncertain.

How are our students doing? Many of them are not sure whether they can continue their education now that they lost their part-time job without enough income to cover school and textbooks; they are not sure whether they can keep their scholarship because they may not be able to keep their perfect GPAs; they are not sure what is the best way to study now that courses are all online with minimal or even no connections with their peers and instructors; their course load is getting too much: all of a sudden every course they take has weekly check-ins and quizzes; they may not even have stable wi-fi because they are financially disadvantaged and/or live in a war zone; they fell terrified when they are watched by proctoring softwares because even the blink of an eye could signal they’re cheating. This list could go on, and this is the situation our students are in.

Is there anything we could do as instructors to help our students on their learning journey? I believe OERs are part of the solution. As Sean Fitzpatrick pointed out on Twitter, we should use OER because they are just as good, sometimes better than commercial textbooks, and our students can use them any time, any where; we instructors can connect with a passionate community of educators which is exactly what I experienced this semester. We are using Active Calculus for MATH2720 Multivariable Calculus at University of Manitoba in fall semester, and I got to connect with the author of the book: Steve Schlicker who are so supportive and shared a ton of resources with me when he learned that I’m teaching using this book. I also connected with Feryal Alayont from the Department of Mathematics at Grand Valley State University because we both teaching the same course using this book. It’s wonderful to connect with and learn from them. And none of this would be possible without this wonderfully written open textbook. My class and I also use Hypothes.is for social annotation and the discussions students have are another proof that using an open textbook is the right choice.

As I said during my presentation, when teachers work together, students win! Let’s try to build a supportive community for each other so everyone’s life is a bit better, easier and brighter. If you are interested in learning about my experience with OERs, feel free to reach out to me via email xinli.wang@umanitoba.ca and on Twitter: xinli_w. I always love a good chat. Take care for now.

How’s 2020Fall semester going?

It’s been a hectic start to 2020 Fall. We moved to Winnipeg MB from Mississauga ON in Aug and did self-isolation for two weeks due to COVID-19. Shortly after that I got my teaching assignments for Fall semester: MATH1510 Calculus I, MATH2720 Multivariable Calculus, and MATH2030 Combinatorics. I will coteach MATH1510 with another experienced instructor who has been teaching this course for many years and he took on the coordinator role. I’m on my own for the other two courses, which also means I have more liberty as to how to run the courses. For MATH2720, I decide we are going to make the best use of existing OERs for this course, and the textbook I chose is Active Calculus written by Steven Schlicker. This turns out to be a great choice as students love the interactive visualizations and practice exercises in the end of each section. We also use Hypothes.is for social annotation and Piazza for discussions. To see the details of how this course is structured, you can find my course syllabus here. For the weekly videos, I used Zoom’s recording function, and recorded myself working through examples on OneNote, then added interactive questions in all of them using H5P. A complete list of these interactive videos are available: you’re welcome to reuse them as they are all under CC license. For the other course, the instructor who taught it last semester was very kind and shared all his materials with me so I kept the course structure more or less the same except the assessments. A copy of the syllabus can be found here.

This is our 4th week into the semester, and I did a short survey during the synchronous sessions for all the classes to see whether students are happy with their online experience so far. You can see the responses in the pictures below.

MATH1510 class response to the question: How do you find the weekly video lectures for this course so far?

MATH2720 class response to the question: How do you find the live sessions so far?

Here are a few things that work well so far:

Using Excel to track student’s questions: for every class that I teach, I created an Excel document from day 1. Each worksheet corresponds to one lecture, and there are two columns: Questions, and Comments. Students are encouraged to put their questions in the document, and I will address them during live sessions. This turns out to be working really well. I know it’s hard to track what they asked in Zoom chat window because a) I can’t monitor chats all the time while I’m teaching; b) when there are too many questions, older ones get buried pretty fast. Using Excel would solve both issues; and since it’s a collaborative document, it’s nice to see them typing in real time, which tells me they are present. At the end of each worksheet, the link to the recorded Zoom sessions and my lecture notes are posted so they can always go back to a certain lecture and quickly find what they are looking for.
Using Piazza discussion forum: this is a game changer in terms of me communicating with students. I no longer need to reply to the same question multiple times. In the first two week, I had to “force” students asking questions there even if they first sent me emails; I would say “can you please post this question on Piazza and I will respond there”. They get used to posting on Piazza pretty fast. For my courses that adopted Piazza, I almost never get emails: I visit the discussion forum regularly and if students haven’t already answered each other’s questions, I would chime in and clarify doubts. It’s also very easy to create quick polling questions. My first two weeks’ Student Hour has been really quiet so I created a poll on Piazza and pushed it to students’ reading list to determine an alternative timing that works for them. They responded pretty fast.
Using Zoom sessions as Q&A: whenever we meet online synchronously, I use the time to answer students’ questions. I don’t do formal lecturing at all. This has been working well based on their feedback.
Using Hypothes.is for social annotation: since we are using an open textbook that’s online, it makes sense to offer students the opportunity to annotate online. I can take a glance at their annotations and have a pretty good idea of how much they understand the materials and what I should talk about when we are all online.

One thing that didn’t work well and I’d like to know how to fix it is using Break-out Rooms: I tried to send students to break-out rooms for discussions, but it didn’t work. Some didn’t join, some didn’t participate even when they are in a break-out room. My guess is more structures are needed, and some form of collaborative space should be open to them so they can record their progress (google doc? google slides?). If you have good ideas about how to use Break-out rooms, please do share.

Today is mid-autumn day for Chinese in China and overseas. It’s a time of family reunion. I wish my mum is still around. Even though I don’t usually get to spend holidays with them back in China, it still feels like home when she’s around.

Getting ready for Fall

We recently relocated to Winnipeg so I can start my new teaching job at University of Manitoba. In the past few months I have attended numerous webinars about the best practices to teach online, design assessments, engage students, and build communities. While waiting for my teaching assignments, I’ve thought a lot about how to design fall courses and I’m using this space to record my thoughts and put down some ideas for future reference.

LMS: I’m not sure what LMS system is being used for UofM, but do realize the choice of LMS affects course design to certain extent. I plan to continue using the ideas of having a clean layout on the homepage, with icons and texts to guide students where they should go base on what information they are looking for, and on top of the homepage the two most recent announcements populate automatically. I’m debating whether I should include a calendar at the bottom of the page as well.
Weekly structure: I plan to run my courses mostly asynchronously. Every week students will access reading materials and pre-recorded videos, followed by an online quiz before they join me for a synchronous session which serves as Q&A. Discussion forums will be available for them from the start of the course and they will learn how to build a community via posting on discussion forums, and annotating the lecture notes online. I plan to give certain weightage for their community building effort with the following question “Does what I do benefit the community knowledge building?” If the answer is Yes, then students will receive a point. These points can be accumulated and will translate to final grade. As to how they can earn these points, the choices are plenty: they can answer their peers’ questions on discussion forum, share resources that help with understanding a certain topic, share learning strategies, develop review questions and solutions for the cohort, answer questions that are posted on Hypothes.is which is the social annotation tool I plan to use, organize synchronous review sessions etc. Hopefully community building will become a part of the course by the end of the semester. By the end of each week, there will be a set of quiz questions so students know whether they get the main ideas or not. There will be regular written homework assignments which require students to think deeper and write down their ideas in a clear manner.
For student engagement piece, it should be a continuous effort: I will start the semester with a letter to all students to introduce myself and my teaching philosophy, and a general survey about what situation people are in and whether they have what’s necessary to complete an online course. Then they will practice using Hypothis.is by annotating on the course syllabus. They will work together to build a community conduct codes and share their thoughts with me about the syllabus. If most people have strong opinions about certain things there, I’m open to suggestions and happy to make changes.
There will be interactive questions embedded in the pre-recorded videos using H5P to engage students and these questions will help them perform better when they work on pre-lecture quizzes.
As to formative assessments, I’m not sure what’s the common practice in the department. If timed tests/exams are the norm, then we can certainly do that. I won’t rule out oral exams, especially if someone missed a scheduled test due to personal reasons, the make-up test will most likely be an oral exam.

Reflection of my experience moving teaching online

It’s been crazy in the last three weeks when every college and university in Ontario suddenly moved teaching and learning online due to COVID-19. I remember my last face-to-face lecture (which only lasted for less than 3 minutes): it was Friday, March 13th and I have Linear Algebra from 1-3pm. I arrived at my lecture theatre before 1pm and the TA who has been working with me for this semester told me all lectures will be cancelled from that afternoon on. I had a few students who were already in the room and I had to tell them to go home. I stayed on for a few more minutes, just in case anyone who came in late and didn’t know all classes are going to be cancelled till further notice. Back then I didn’t know that would be the last time I talked to my students in person till I don’t know when.

I didn’t even have the opportunity to go back to my office. I headed home right after. I thought grocery shopping might be a good idea so I went to a nearby supermarket. I was utterly shocked by how packed the place was so I left without leaving my car. That’s the starting point of self-isolation and social distancing.

We had the weekend to come up with a plan to move things online. There are still two weeks of teaching before final exam kicks in. I remember frantically emailing colleagues, talking with them on Slack and just refreshing university website to get a vague idea of how to carry one. Eventually here’s what I did for the courses I taught.

MAT223: we have a team of 4 who teach this semester and we eventually divided up the content. This course has already been using a flipped classroom model so content wise it’s relatively easy to shift to remote teaching. However I feel the chemistry we were able to build when students come together and work on in-class activities is lost. For the week that I worked on, I provided PDF worksheet and solutions. I did not make videos, and ran online sessions as Q&A asynchronously. I’m aware how few students were there with me compared with in-person sessions.
MAT202: we almost finished delivering lecture content so that’s good news in this situation. There are two of us who are teaching this course and we both run our online sessions more like drop-in office hours and did not require students’ attendance. Recordings were made and shared later on.
MAT135: the course coordinator made video lectures for the rest of the semester and I helped with the subtitle. It took a lot of time for me to edit the auto generated subtitles from YouTube ( and I’m sure for him to make the videos as well) but we all knew it’s necessary work for accessibility reason. I would not recommend sudden shift from in-person lectures to video lectures if you don’t have sufficient time.
Office hours: I have been running my office hours in two ways since a year ago: in person and online using Zoom. I simply shifted those in-person sessions to online. I’m glad I have experience holding office hours with Zoom and attendance didn’t vary much.

I also ran a survey with my class asking the following questions when we are two weeks into this “new model”:

How are you? How is your family doing?
What are the main challenges for you when teaching and learning switched to online mode?
What could be done differently to improve your learning experience given the current circumstances?

Majority of my students are doing well, and they have been extremely understanding of the work we are doing. I also received so much encouragement and thank you’s which really warm my heart. The main challenge students have in common is staying motivated. It’s hard for them to stay motivated when they are in isolation, with no interaction with us and their peers. Going forward this will be my main focus when redesigning my courses (I assume school won’t be able to open doors till a long time from now).

UofT has been offering ongoing support for faculty members and instructors. I find the drop-in sessions organized by TLC really helpful: they helped me stay connected with colleagues and having the opportunity to talk to a few fellow instructors really made a difference for my mood, thus my teaching. Everyone is anxious, not knowing what’s coming and I came to peace with the fact that I can’t stay as productive as I used to be. If you’re reading this post, hope you and your loved one are doing well. If you are a student of mine, you know I’m only an email away; if you are a colleague from HE, feel free to reach out to me on Twitter @xinli_w: I’m always happy to talk.

2019Fall/BMTH100/120 Mathematics of Finance, Humber College

After teaching part-time at Seneca College for almost three years, I decided it’s time to move on due to the commute: we moved to where UTM is, and I find it very challenging to travel to Seneca on a regular basis. Usually, one-way travel takes me at least one hour, and being stuck in traffic along 401 makes it worse than it already is. I did enjoy my teaching at Seneca very much, and my teaching there reminds me a lot of my previous institution in Singapore: Singapore Polytechnic. Even the structure of the buildings on Newnham campus is almost the same with SP: all the buildings are connected through bridges and tunnels. My guess is at both places, the building structure is to accommodate the harsh weather: Canada’s winter is too cold for people to walk outdoor; while Singapore is too hot to walk outside.

I’m fortunate to start teaching at Humber College right away: this semester I’m teaching a course that I used to teach: Mathematics of Finance. For those who are interested in taking a look at what we do, here are the slides. A major learning objective for this course is to teach students how to understand a real-life scenario/story and translate it into mathematical language. After that the can use a financial calculator to find the solutions. Most of my students agree that this course, surprisingly, is not so much about mathematics, but rather about comprehending the stories.

2019Fall/MAT135: Differential Calculus

If you are currently taking this course with me, you can find all the course slides here: MAT135 Differential Calculus

The clicker questions we use in class can be found here:

Below are a few GeoGebra activities that we did in class.

Even/Odd functions: In this app, students can visualize even/odd functions and explore the symmetries embedded in these functions.
Function transformations: In this app, students can explore how different types of function transformations affect the graph of a function.
Inverse trigonometric functions: In this app, students can see how the graphs of inverse sine/cosine/tangent are related to the original functions and see the reason for the choice of domains of these functions geometrically.
Limits of functions: In this app, students can explore the limits to two given functions: $f(x) = \frac{x^2-1}{x-1}$ and $f(x) = \frac{x-1}{x^2-1}$ , and visualize removable discontinuity, vertical asymptote and horizontal asymptote.
The derivative of a Function as Slope of Tangent Line: In this app, students can explore what is a tangent line to a curve at a point, and how the slope of the tangent lines changes when a point is travelling along a given curve.
Derivative as a function: Students get to explore what happens to the derivative function based on a given one and they are related to each other geometrically. They can learn how to identify which curve is $f(x)$ and which one is $f^\prime(x)$ .

2019Fall/MAT102: Introduction to Mathematical Proofs

This is not my first time teaching this course, but the level of excitement and nervousness doesn’t seem to go down at all at the beginning of this semester. I’m fortunate to have a whole class of students who engage fully during the lectures so far and make the teaching so enjoyable.

If you’re a current student enrolling in this course, or just want to take a look at what’s happening in class, you can find all the slides here:

https://drive.google.com/open?id=1i2ltPgAfRQs6rf2FSY0yRMKXDvmwzSUs

This week we were talking about logic symbols and how quantifiers work, and how by changing the order of quantifies, we can tell completely different stories. Here’s one example we did in class:

$(\forall x \in \mathbb R)(\exists y \in \mathbb R)(y \geq x)$

$(\exists y \in \mathbb R) (\forall x \in \mathbb R) (y \geq x)$

While the first statement is saying “for any real number x, we can always find a y such that $y \geq x$ ” which is a true statement, because we can simply make $y =x$ , the second statement is saying “we can find a real number y which is greater than or equal to all real numbers” which is a false statement. This is equivalent to say real numbers have an upper bound.

Can you tell the difference here?

[2019SMAT102] Videos for AM-GM inequality, inequality and set related proofs

I made several videos explaining a few topics that we cover in this course. Some of them came up during my office hours. If you’d like me to explain a certain concept/question covered in our course, feel free to drop me an email and you might see it here 🙂

AM-GM inequality: the statement, how to prove it and its application.

2. Given $x > y >z$ , prove $xy+yz > \frac{(x+y)(y+z)}{2}$ .

3. If $A \cup B \subseteq C \cup D, A \cap B = \Phi, C \subseteq A$ , then $B \subseteq D.$

[BAB210] Business Statistics

I’m teaching this course during the summer semester at Seneca College. The course outline can be found here:

https://apps.senecacollege.ca/ssos/findOutline.do?subjectCode=BAB210

We are into our second half of the semester now and being able to use Excel is an important part for the successful completion of it. I made several short videos explaining how to use certain built-in functions in Excel. More will be coming up as our course progresses.

How to draw a bar chart for categorical data:

2. How to build frequency distribution table and draw histogram:

3. How to do cross tabulation:

4. How to use descriptive states tool in Excel:

5. Excel functions to find mean, median, mode,variance and standard deviation:

6. How to find covariance and correlation for two sets of data:

7. How to draw a box plot:

8. How to draw comparative box plot:

9. Continuous Probability Distributions part I:

10. Continuous Probability Distribution II:

11. how to select random samples

12. How to construct confidence interval for a population mean with population $\sigma$ known:

13. How to construct confidence interval for a population mean with population $\sigma$ unknown:

14. How to construct confidence interval for a population proportion:

15. Hypothesis Testing of population mean with $\sigma$ known: $H_0: \mu=295, H_a: \mu \neq 295$ : two-tail test

16. Hypothesis Testing of population mean with $\sigma$ unknown: $H_0: \mu \leq 7, H_a: \mu > 7$ : upper tail test

17. Hypothesis Testing of population proportion: $H_0: p \leq 0.20, H_a: p 0.2 7$ : upper tail test

18. Regression Analysis:

[2019SMAT102] A letter to my students

Dear all,
Welcome to the Introduction of Mathematics Proof!
We want your experience this semester to be successful and rewarding. Math 102 is a challenging course that demands consistent hard work throughout the semester. Here are some tips for you to succeed in this course and some common mistakes you want to avoid.
• Expecting to be graded in the same way as high school
In a university level math course, your grade is based primarily on tests. You cannot pass this course without achieving passing grades on tests. The only way to do this is to master the skills and concepts through careful completion of the homework exercises, review of the textbook and class notes, and extra practice whenever needed. If you get a low grade on any quiz or test, you are in danger of not passing. See your instructor immediately for tips on improving.

• Mistaking recognition for mastery
Students think that because they’ve seen the material before, they “know it”. This can lead to laziness at the beginning of the semester. Many students wait until they get a poor grade on a quiz or test before they get serious about the course. By then, it may be too late. Work hard from the first day to avoid this. Remember, you only “know it” if you can do it. This means you must be able to write out correct solutions for every homework exercise without referring to your textbook or notes.

• Believing that with mathematics, you either “get it” or you don’t
This is a myth. Every student can have success in mathematics with enough hard work. How much depends on the individual’s background and experience. However, it is important to realize that you can earn the grade you want with sufficient hard work.

• Not setting aside enough time for homework
Many students are over-committed with work, school, and family responsibilities. Without time to devote to homework and studying you cannot learn mathematics. You must adjust your schedule to allow sufficient time for your math class. While there are some classes where you might be able to take shortcuts, mathematics is not one of them. If you don’t have a minimum of 15 hours per week to study outside of class, you are setting yourself up for failure.

• Misunderstanding how mathematics is learned
Learning algebra involves skill acquisition. It is analogous to the physical training involved in music and sports. You would never expect to learn to play piano by going to a concert two or three times a week. Likewise, you should not think you have learned some mathematics just because you went to class and understood your instructor. Your real learning begins when you try to do the homework exercises on your own. You have “learned” a section of material only when you can write out the solutions to all the homework exercises without aid from your textbook or notes.

• Not addressing lack of preparation
College Algebra is Pre-Calculus (without trigonometry). It is expected that you have a working knowledge of Algebra 2 from high school, or Intermediate Algebra from a community college. If you don’t, you must get to work immediately to fill in the gaps. There are many resources at your disposal to help you review. Use them! Your instructor will describe all of the available options.

Have a great semester!