Learning Strategies

This is a collection of evidence-based learning strategies I’d like to share with my new incoming students in 2020 spring. If you are aware of anything else that might be helpful, please feel free to share them with me.  

  • Spaced practice: space out your study over time. You can have your own calendar to plan out how you will review chunks of content. Do not wait till the last minute before your quizzes/exams to study.

  • Retrieval Practice: practice bringing information to mind without help. When you do this exercise, you will need to turn off your devices, put all your notes and books away, then write everything you know about a particular term or topic. You can doodle if you’re more comfortable with that.

 

  • Elaboration: explain and describe ideas with as many details as possible. Ask yourself open-ended questions about the topic, answer in as much detail as possible, then check the materials. 

  • Interleaving: switch between different ideas/subjects while study. Mix the topics you are learning at a given time. Do not keep working on the same topic for long stretch. 

  • Concrete examples: use concrete examples when you learn an abstract topic. I often like to use visualization tools for mathematics concepts. Check out GeoGebra if you haven’t already. 

 

  • Dual coding: combine words and visuals. We learn new information better when there are multiple channels available to us. 

                         

The research can be found here: The Learning Scientists Website You can also find the book Understanding How We Learn: A Visual Guide by Yana Weinstein, Megan Sumeracki and Oliver Caviglioli in our library to read the full research behind these ideas.

Presentations at RTL and CMS winter meeting 2019

Dec 2019 turned out to be a good month: I managed to present a few talks at two conferences: Research on Teaching and Learning Conference and CMS winter meeting 2019. RTL focuses on SoTL research where educators share their teaching and learning scholarship experience. I enjoyed it a lot: the crowd is small enough for people to connect and have in-depth discussions. Even an introvert like myself is able to feel comfortable and I enjoyed all the talks that I attended. This is also the first time I learned about Q-Methodology which is a fascinating way to analyze qualitative data such as students’ course evaluations. I can see a lot of potential in using this method for our future work. I gave two talks at this conference and have enjoyed my interactions with the audience. The slides can be found here:

Design of a classroom-based intervention through technology-enhanced activities

Active Learning Design for Calculus II

It’s a perfect opportunity to get some valuable feedback for the education research projects we have been working on in the past year.

CMS winter meeting 2019, on the other hand, has attracted hundreds of mathematicians from Canada and worldwide and can feel overwhelming. There are so many sessions happening at the same time so one is bound to miss a few that he/she plans to attend. I’m glad I caught the Art of Mathematics talks especially the one given by Gerda deVries during which she talks about quilts and mathematics. I have to admit it gave me a lot of ideas of future painting projects I can work on. I gave a talk TECH for teaching during the special session Teaching Strategies for Increasing Diversity in Math moderated by Sarah Mayes-Tang from University of Toronto. What a lovely audience! I enjoyed the conversations and sharing of all the speakers very much but it’s a pity I couldn’t attend all the talks (and the lunch!) due to a final exam in the afternoon. I’ll make sure to come back next year.

Life does have surprises for us: the first time I attended the same meeting was in 2010 while I was a Ph.D. student in Singapore. I still remember the excitement and nervousness of presenting our work the very first time. That’s also my first time visiting Toronto. Who would have thought we will end up living here after this many years.

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.

  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!

css.php