October 28, 2019 Filed in: Articles

President, Ontario Association of Physics Teachers

Hybrid Teacher-Coach for Science, Toronto District School Board

Once classes have settled down and our students are trained (see the Quick Guide for Introduction Lessons), we are now ready to focus on teaching some physics! The first unit often taught is motion, both in the grade 11 and 12 courses. Most teachers feel pretty confident with this unit, but I hope to share some tips that might help you out in a few tricky spots. Read on!

**Motion**: Never use this as a synonym for “velocity” because in your next sentence you will use it to mean “every characteristic or feature of the object’s movement”, as in “describe the motion of this object”. Call it “constant velocity” and not “uniform motion”.**Uniform**: This is something people wear when bowling. The word “constant” is absolutely clear. Say “constant velocity” or “constant acceleration”.**Deceleration**: No other vector quantity gets a different name when its direction changes. Students will equate “deceleration” with “negative acceleration”, which is incorrect. Say “slowing down” instead, which is 100% clear.**“Speeding up east”**: The phrase “speeding up” describes what is happening to the magnitude of the velocity. Magnitudes don’t have a direction, so the “east” just doesn’t make sense: is it describing the velocity or the acceleration? Instead say “traveling east and speeding up”.**At rest**: Ask a person on the street to picture something at rest. Are they picturing a ball at the highest point in its trip? Nope! Don’t use “at rest” to describe something with a velocity of zero for an instant of time — it’s counterintuitive. Use “at rest” for velocity of zero over an interval of time.

**“The velocity is increasing”**: Words that work well to describe scalars can be meaningless for vectors, which are a different breed of mathematical object. “The speed is increasing” is unambiguous, as is “the magnitude of the velocity is increasing”. Students have the concept of the integer number line (hopefully) deeply ingrained, where movement to the right along the line means larger or greater than. However, if a one-dimensional vector is represented on an integer number line, movement to the right does not have a clear interpretation (speeding up or slowing down are both possible).**“The velocity +3 m/s is bigger than -7 m/s”**: this misinterprets a vector as an integer number (scalar). Also, don’t say “the velocity 5 m/s is bigger than -2 m/s”. Instead, be specific by saying the speed or the magnitude of the velocity is bigger. We must talk about vectors in a different way than scalars.- Never say two vectors are equal unless their magnitudes and directions are equal. “Equal” has a strict mathematical definition. Otherwise, clearly state which parts of the vector are equal (same direction or same size).
- We only use full vector notation when labelling vector diagrams or working with two dimensional quantities (6.7 m/s [N30°E]); otherwise we are always using scalar notation (Δ
*x*or*v*_{1y}) for a one-dimensional quantity or component. I find a religious use of the arrow notation for one dimensional quantities cumbersome and not reflecting of expert practice. There is a danger to this, however: symbols Δ*x*or*v*_{1}could represent a vector or scalar. Students need to practice deciding which based on the context. Luckily, good questions usually include lots of context. - Provide helpful rubrics for grade 12 vector work.

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**ath is different between a physics class and a math class**: Make these differences clear instead of expecting student to pick up on them on their own (most won’t). Examples: use of units, functional notation, “x” as the only thing you ever solve for, and many more. **Use exemplars**: Even for the simplest math work, have clear exemplars with detailed criteria.**Sense-making is key**: Develop a work procedure that helps students to make sense of their work before, during and after the mathematics.**Give them the equations on tests**: Experts (including you and I) routinely look up equations, facts and data — this is normal. High school tests should have a strong focus on the physics rather than memorization or mathematical acrobatics. Fluency and automaticity come from regular use and reinforcement over time.**Explore the concept before the equation**: The physics should always come first.