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.

  1. Even/Odd functions: In this app, students can visualize even/odd functions and explore the symmetries embedded in these functions.
  2. Function transformations: In this app, students can explore how different types of function transformations affect the graph of a function.
  3. 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.
  4. 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.
  5. 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.
  6. 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?

Book Recommendation: a list of books that I enjoy reading

Here’s a list of books that I enjoy reading and I believe most of my students will benefit from reading as well. A majority of them are math related: they are meant for the general public to enjoy mathematics so it will be fun!

  1. The Joy of x: a guided tour of math, from one to infinity by Steven Strogatz. The topics that are touched by this wonderfully written book include numbers, quadratic equations, functions, geometry, calculus, vector calculus, differential equations, probability and statistics, group theory and prime number distribution. I especially enjoyed all the examples that stem from real life stories. You will learn how Google’s page ranking works, how many people you should date before settling down, how to look at O.J. Simpson trial from the angle of conditional probability, and so much more. You won’t be disappointed.
  2. Grit: The Power of Passion and Perseverance by Angela Duckworth. It’s a well-researched book and explains why successful people get where they are clearly. I first got to know Angela’s work through one of my favorite Podcast: Freakonomics and I’m in general very interested in learning human behaviors and why we do what we do. In her book she gave perfect explanations of how being gritty is one of the most important factors that lead to success, no matter what field or industry. The good news is grit is not a fixed variable for any individual, so we can all become a little bit more gritty today than yesterday.
  3. Weapons of Math Destruction: How Big Data Increases Inequality and Threatens Democracy by Cathy O’Neil. The first time I heard about this book was on a bus from Montréal-Pierre Elliott Trudeau International Airport to Sherbrooke. It was from a colleague at the University of Waterloo and she was reading this book while we were both on our way to attend STLHE 2018 conference. What a fantastic book! Anyone who has some kind of online presence should read it; anyone who works with data should read it; anyone who ever wonders why you didn’t get into the college/job you applied for should read it. In fact, we all should read it: it offers an authentic view of what is happening with data that are linked to every one of us; how are various algorithms controlling our daily lives even without us being aware of their existence. Can we fight them? Can we protect our privacies? Can we live in an unbiased society? I don’t know the answers, but we should all be asking these questions, and be conscious of these WMDs.
  4. Messy: the power of disorder to transform our lives by Tim Harford. I enjoy orderliness a lot in my life. If I’m going traveling, I make sure air tickets, hotels, maybe even attraction tickets are all booked well in advance. Not knowing what’s going to happen stresses me out greatly. I also like my house to be in order, and I find it more and more challenging now that I have a five-year-old roaming around all the time. This book offers me a new perspective of looking at messiness in our lives and teaches me to appreciate it just enough to not get annoyed so easily any more. I also found out Tim is hosting this great storytelling podcast Cautionary Tales and is now a devoted listener.
  5. Invisible women: Data Bias in a World Designed for Men by Caroline Criado Perez. This is a book that tells us how much costs we women pay when living our lives, in terms of time, money, health and sometimes, life. I have to admit I felt so angry reading all the true stories that reveal the gender bias that put women all over the world, from all walks of like at such a disadvantaged position. The two chapters that I had the deepest connections are The Myth of Mediocracy and The Plough Hypothesis. I work in academia and I’m aware of the biases existing when it comes to student evaluations: we female professors constantly get lower scores due to our gender. And it’s sadly true that we are at child-bearing age when we are at the most critical moment careerwise. How many of us had to choose one over the other? I went through severe post-natal depression which eventually led me to leave my first teaching job. My career was put on hold for an extended period and I’m still struggling to catch up. No man (or almost none) from academia had to go through it. I grew up in a village and was a farmer myself until I left for university. The story in the plough hypothesis is too close to home: my mum spent significantly more time in the field between the time of planting and harvesting because weeding is considered women’s job; after the crops have been harvested and transported home, she’s the one who has to peel the skin of corns and remove corn kernels so they can be consumed later; she’s the one who spent hours everyone cooking in front of a traditional stove; she’s the one who looked after us. None of her work is paid. I wish it is different for the women who still live in my village today but little has changed.

OE4BW: Open Education for a Better World 2019

First off, if you are interested in doing OER work and impact a bigger community besides your own institution, do pay attention to their call of new participants for next round.

https://unesco.ijs.si/project/open-education-for-a-better-world/

I had the pleasure of working with Jenni Heyman as the Hub Coordinator and Nkaepe Olaniyi as my Mentor while participating in this project. It’s great to work with these ladies and I’ve learned a lot while I work on the open textbook. You can find my presentation online: OE4BW: open and interactive Linear Algebra textbook for all

If you also happen to work with open textbook on Pressbooks and H5P, I’d love to connect with you. You can find me @xinli_w on Twitter.

Open Linear Algebra Textbook

I have been working on a project since the end of last year: adapting an existing open linear algebra textbook: Linear Algebra with Applications by W. Keith Nicholson to make it more interactive.

You can read or download the adapted version here: https://ecampusontario.pressbooks.pub/linearalgebrautm/

To see the H5P elements, it’s best to view the book using your web browser. Once you download it as a PDF file, you won’t be able to see those H5P interactive elements. Enjoy!

CEEA 2019, Ottawa

We just arrived at Ottawa at 6pm today, ready to attend CEEA 2019. I am impressed by the app Guidebook ( https://guidebook.com/ ) that the organizer chose to use. As long as the app is downloaded to my phone, I can see everything about the conference: speakers, sessions and talks, locations, and I can make my own timetable base on which talk(s) I plan to go. It’s very intuitive to use and such an environmentally friendly idea. I’ll come back to this post after tomorrow. Stay tuned!

First workshop: it’s interesting to hear what challenges people have regarding use of OER: it’s free for users, but how about developers? Who’s going to fund all these projects? Is it possible to find resources other than textbooks? How about projects, free softwares, workshop materials?

http://diy.open.ubc.ca/ and http://www.learncheme.com/ offer a variety of open-licensing materials; the latter focuses on chemical engineering, including videos, interactive simulations, and interactive self-study modules.

Afternoon sessions start with a workshop about active learning. I’m here because I want to know whether it’s possible to use this pedagogy in my large first-year calculus class, especially when I don’t have any TA’s help.

Part I Exploring active learning: flipped classroom; think-pair-share; co-operative learning; reflections; discussion questions; concept mapping; peer instruction. We need to think critically and reflectively about our teaching practice.

What is “active” in active learning? It’s about the level of engagement among learners, and whether learning and progress is happening. We were also given the chance to talk about challenges we face in my teaching, learning or mentorship: personally for me the main challenge is lack of interaction with colleagues, and lack of autonomy when it comes to course design. There seems to be little opportunity built-in the college system that actively promote interactions between course instructors. It could happen that a team of instructors teaching the same course never meet till the moment of final exam. I would love to get to know people better, to learn what people are doing for their teaching and to exchange ideas but I have yet to find an efficient way to achieve that goal. Right now almost all the conversations that happened are point-to-point. It’s challenging for someone new like me who just joined the department and who’s not on a continuous appointment stream. Another point that was brought up is when active learning was implemented through team-based work, there are always students who do not participate and engage in the activities. How to motivate them to be more engaging?

Part II Thinking about care and our role:

Part III Generation of new frames:

Frame 1: create environments and conditions that support learners to construct meaningful……

Frame 2: Think about content, instructional activities, and assessment- and the alignment of all three.

Frame 3: Be intentional about how the active learning exercise can support students in making meaning.

I’ve learned to ask questions about why we do what we do, and always try to learn students’ perspective in their learning journey.

I’m back home from this exciting event and I’m so glad that I made it. The best part of it is all the conversations that I was part of and all the connections that happened in-between talks. People are so generous sharing their own teaching practices with me, including their favorite books for active learning in large classes! Even though I was surrounded by engineers and engineering educators, we have a lot in common when it comes to teaching. Look forward to CEEA2020!

OCMA 2019: Improve student engagement using Geogebra

I presented my talk at The Ontario Colleges Mathematics Association
39th Annual Conference, on May 23rd. The talk can be found here:

I shared what I did in my Linear Algebra class: using GeoGebra to explain and visualize a few core math concepts including linear systems, complex numbers, and eigenvalue/eigenvectors. The audience worked together and created this Padlet during my talk.

I also shared the challenges I encountered while doing this education research project. It’s great to have a conversion with colleagues from all different institutions and learn from them. I appreciate the opportunity and hope to be there again next year.

[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 🙂

  1. 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.

  1. 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!

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