A Case for Portioned Practice
by Felipe Almeida - OAPT Newsletter, May 2021
Portioning Errors
Imagine a parent saying the following:
Hey child of mine, whom I love very much, this weekend is going to be very busy so I’d like you to eat all your food for the next two days right now. Enjoy!
All the weekend's food, at once.
Clearly, this is a bad idea, but physics teachers make an equivalent portioning error by asking am unprepared student to do this:
Solve the following:
A 143 kg penguin, while moving away from the origin, accelerated at 0.14 m/s² [N] and acquired a final velocity of -16 m/s [N]. If the penguin was in motion for 18 s, what was its initial velocity?
The complete solution is simply too much physics to be done at all once:
The responsible physics teacher chunks the problem by only asking for parts of the full solution at a time (e.g. complete sketches and motion diagrams only). But if the problem itself doesn't change, the chunking actually looks like this:
Instead of this:
Portioned Practice
All practice in an introductory physics course like SPH3U should be portioned appropriately in both task and problem. What follows is a description of what the penguin problem from above would look like apporpriately portioned, and why.
The Penguin Problem, Portioned
First Portion
To begin, we recognize that the penguin problem, like many typical physics problems, comes in two parts: setup and question.
A 143 kg penguin, while moving away from the origin, accelerated at 0.14 m/s² [N] and acquired a final velocity of -16 m/s [N]. If the penguin was in motion for 18 s, what was its initial velocity?
Since the question is not necessary to make sketches, motion diagrams or motion graphs, it can be removed.
A 143 kg penguin, while moving away from the origin, accelerated at 0.14 m/s² [N] and acquired a final velocity of -16 m/s [N].
For the same reason, so too the numbers.
A penguin, while moving away from the origin, accelerated north and acquired a final velocity to the south.
To be successfull without a total grasp of the new vocabulary yet (i.e. ‘accelerated’ and ‘velocity’), they can be replaced with more accessible language.
A penguin, moving south and away from the origin, slowed down.
One last detail to consider: penguins have feet. If students, consciously or not, hold the 'misconception of self-acceleration'1 and are met with success with their motion responses, the misconception will be reinforced. Instead, a cubic penguin2 is used:
A cubic penguin, moving south and away from the origin, slowed down.
Second Portion
After practicing sketches, motion diagrams and motion graphs, students should be confident using the motion terms previously removed (and their symbols). With the problem described below, they can be tasked with describing the motion with words, a sketch, a motion diagram and motion graphs.
A cubic panda bear, while moving towards the origin, accelerated at -a [N] and acquired a final velocity +v2 [N].
Third Portion
The third portion marks the return of the question. Is 'algebra first'3 important? With the problem below, students can select an appropriate equations and solve for the unknown algebraically.
A cubic pangolin, while passing the origin, accelerated at -a [N] and acquired a final velocity -v2 [N]. If the pangolin was in motion for a time t, what was its initial velocity?
Fourth Portion
Finally, students are ready for the original problem4, numbers and all.
A 143 kg cubic peacock, while moving away from the origin, accelerated at 0.14 m/s² [N] and acquired a final velocity of -16 m/s [N]. If the peacock was in motion for 18 s, what was its initial velocity?
Same Destination, Different Route
Portioned practice makes it easier for students to engage with traditional physics problems without compromising their depth and complexity. Why lift a car with your hands when you could use a jack? Sure, it takes longer, but chances of success are much greater, as is the liklihood of wanting to do it again and again.
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Much of this article's content was part of a 'Physics Hour' presentation for the Ontario Association of Physics Teachers (OAPT) (March, 2021), as well as separate article written for their newsletter (May, 2021).
1 The belief that an object applies a force on itself to change its motion. What makes a car speed up? Responses typically include: 'Wheels!', 'Engine!', or 'Driver!'- the untrained never say 'ground'. Since training on Newton's third law and all its implications takes time, delaying the use of objects with feet (or wings or fins or wheels etc.) seems the responsible thing to do. back ↑
2 What the heck is a cubic penguin? Well, a cubic penguin (like all cubic animals) is not alive, extremely durable, and happy to participate in the strange situations it finds itself in (maybe its life is tedious otherwise?). We wouldn't want to promote the endangerment or mistreatment of actual animals. It's essentially a memorable cube that:
- slides when in motion (rather than rolling - now is not the time for the how-braking-causes-wheels-to-push-the-ground-forwards-/-ground-to-push-the-wheels-backwards conversation, or for worrying about rolling friction and conservation of angular momentum).
- needs to be pushed or pulled by some other object to speed up (to avoid the 'misconception of self-acceleration' as described in 2. back ↑
3 Algebraic errors can be separated from numeric ones if solving algebraically before subbing numbers into equations. If this is not that important to you, skip to portion 4. back ↑
4 With 'cubic' optional (i.e. are the students ready to make their own assumptions yet?) back ↑