Engaging Math Students using Online Discussion Board Math Problems

My name is Mandy Lam. I’m a math professor of The Business School at Centennial College. I teach Mathematics of Finance, which is a course that is designed to prepare students with the math skills they need in their accounting and finance programs.

I have a highly diverse group of math students. They come from all walks of life, and they’re studying different programs here at Centennial, and they have very different math backgrounds, and there’s a wide range of confidence level in math. For many students, learning math at a distance could be challenging. That’s why I would like to encourage my students to be active learners. I’m using a discussion board, and assigning discussion board math problems, to engage students in the online learning environment. To encourage meaningful discussions, the discussion board math problems I created were the types of problems with open-ended responses. That means these were the kinds of problems that, even though there’s only one correct answer, there are many different ways to solve the problem and arrive at the answer. And that’s the beauty of mathematics!

In the past, I have used these questions during an in-class, face-to-face discussion. These pictures show two of my classes in the winter 2019 semester. During these discussions, my students practiced their mathematical reasoning skills. They communicated their strategies, described their thinking, and expressed their mathematical conjectures, which means making informed guesses.

My goal is to create a similar learning experience for my students in the online environment. Here are some examples of what I’m trying this semester. We have five discussion board math problems throughout the semester. Each of these problems invite open-ended responses. For example, in this problem, I ask students to explain why the equation holds true, rather than simply asking them what the answer is when they multiply x cubed and x to the power of seven.

Here are some examples of my students’ work this semester. In this discussion board math problem, I ask students to identify the correct answer and explain their thought process of how they identify the correct answer. One of the skills we teach students is to communicate effectively, and students communicated their thinking using mathematical concepts and terminologies. In their explanations, they use terminologies like factorize, greatest common factor, coefficients, distributive law, etc. In the weeks coming up we will also have the following discussion board math problems. This one is similar to the previous problems. While there’s only one correct answer, there are multiple ways for students to explain the strategy and thinking they use to identify the correct answer.

In this math problem, students have to use concepts of ratios, proportions, and percents to identify the best deal when buying a small coffee. When I gave students this exercise in an in-person class, I saw so many different strategies that they used to solve this problem. I had students who calculated the price per one milliliter volume to make a comparison amongst the brands, and I had students who calculated the volume per dollar value instead, and I had students who made estimations first and then did the calculations after.  There was a large variety of solutions that students came up with, and I thought this would be a nice problem to assign for an online discussion board math problem as well.

This is a similar problem in which students would have to explain their strategies and show their unique thinking process.

What would I do differently next time? Right now, the discussion board problems account for a small percentage of their grade. It is graded as a participation mark. We can perhaps look into using rubrics to grade students’ work, so that this could be an evaluation that’s worth a little bit more of their grade. Also, right now, it’s optional for students to respond to other students’ posts, but next time I think I would try to make it mandatory for students to respond to at least two other students’ comments, because I would like to enhance the richness of the discussions and build more of a connected learning community.

Thank you for watching! To continue the conversation, feel free to contact me at mandylam@centennialcollege.ca