New hashtag, folks! #physicsteacherprobz. And entry #1 is the student who solves a problem by substituting values first.
What do my kids do when they encounter this?
A simple pendulum has a period of 2 seconds and length of 1 meter. What is the acceleration due to gravity in this environment?
Kids are gonna solve for g like so:
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To me, that’s so ugly. Substituting numbers in at the beginning and calculating intermediate answers. Kills me to read tests solved this way.
I prefer my physics students solve equations algebraically before substituting numbers for two reasons. One: compounded rounding errors can blow the result. Two: algebra errors are really hard to spot, making the justification of this answer harder to follow. [Of course, the reason “because your teacher wants it that way” isn’t sufficient. -MHG]
There is long term value is in describing a relationship in terms of any variable, no matter how the relationship was stated when you were introduced. Right? (Right?)
Solving the pendulum equation for g requires a student to apply algebraic rules of inverse functions. Maybe the kids aren’t comfortable with this symbol manipulation. Numbers are concrete, so kids like to plug ’em in soon as possible.
In all my time in the math classroom, we never had equations of more than one variable, so I think the kids are stunned when they see that simple pendulum equation.
How do I get the kids to see value in solving an equation algebraically before substituting values? #physicsteacherprobz