Math

July 22, 2024 Filed in: Articles

A while ago when I taught high school my grade 10 Science class came into my classroom after my grade 11 physics class had left. I had just done a lesson on the development of the kinematic formulae using graphing. One of my grade 10 students seemed mesmerized by the boards covered in figures and diagrams. They turned to me and asked what was on the board. I said kinematics, which is part of the grade 11 physics course. Their response was “I guess it will be biology next year for me.” What makes kinematics like this? Is it the mathematics? Is it the lack of relationship to the real world (ignoring friction)?

I began playing with alternatives to present the topic. I recognized it was not the authentic or real-world connections, it appeared to be the arithmetic. Notice, I did not say the mathematics or physics. Many times, a simple arithmetical mistake (even to the point of a miss-written minus sign), might cause them to believe that their whole solution, and therefore their understanding of kinematics, is wrong.

When a student approaches a kinematics problem, they usually draw the sketches and list what’s given and what’s required. Then they choose the formula. That is where the physics ends, and the arithmetic starts. As physics teachers, do we assess physics or arithmetic? Read More...

March 18, 2023 Filed in: Articles

Often, we ask students to do an experiment, gather a set of two-variable data, make a scatter plot, and then try to find the curve of best fit, along with its equation. Historically, Microsoft Excel was the go-to for doing something like this, however nowadays I find my students are most comfortable using Desmos to graph things, because it’s free, simple to use, and doesn’t require any installation or logging in. Desmos is great for making scatter plots and fitting curves, and it can even fit curves beyond Excel’s ‘Add Trendline’ functionality, which is limited to exponential, power, logarithmic, and polynomial-types of curves (Excel can do additional curves, but it's tricky, check out my previous article for instructions on how to do that if you like). In this article, I’d like to go over how you can do a curve of best fit in Desmos, even for complicated curves like what you would find with a damped harmonic oscillator experiment, or with Kepler's third law of planetary motion. Read More...

February 02, 2022 Filed in: Review

There’s a lot of good physics (and math) embedded in the grade nine space unit, if you know where to look for it. David Butler is a retired computer scientist who is fascinated with space, and he’s applied his mathematical background to explaining, in simple terms, what’s behind the fancy pictures we see from NASA, and how we know what we know about the universe. To do this he’s created a series of video books focusing on different topics, as well as hundreds of short classroom-ready video clips on topics ranging from astronomy to quantum mechanics. Read More...

October 19, 2018 Filed in: Articles

In science, it’s always nice to be able to do a hands-on experiment. While there are many experiments you can do in class, there are some you can’t. Sometimes a particular experiment may require expensive equipment that you don’t have, may take too long to set up, may yield data that is too imprecise to analyze properly, or an experiment may be too dangerous for a classroom setting. At the latest annual OAPT conference Andrew Moffat showed us several websites with video libraries filled with experiments that I wouldn’t be able to recreate myself (skip to the end of this article for those links). To give you a taste of what kinds of videos are available, and how you might build a lesson around one of them for your students, I’d like to analyze one of my favourite videos from the collections. Read More...

September 09, 2017 Filed in: Articles

How should we improve math instruction in our province? Pundits and politicians are worked up about the recent, discouraging math scores from the provincial standardized EQAO tests. Luckily, our premier, Kathleen Wynne, is coming to the rescue with an announcement of “sweeping changes”, or maybe a “refresh”, for education in our province. But how will we know if any new changes are going in the right direction? The field of education is littered with the wreckage of pedagogical fads driven by experts who have little connection to functioning classrooms. To navigate this debris, the best maps are those that have been informed by the science of learning and the effective practices of our most successful teachers. These maps will help answer the questions we should be asking as we try to solve the math teaching problem. Read More...