Class: Calculus 2 Topic: Applications of Integrals Specific problem: Finding the work required to remove a satellite from Earth's gravitational field
Try to evaluate that integral, does anything seem strange?"
"Yeah, I get zero in the denominator in my final answer, that can't be right"
Student 1: Struggles with mathematics but is eager to correct their mistakes and learn from them Note: Student has taken physics I
"Think about where we're starting in relation to the Earth, would the zero point of the gravitational field be on the surface as you said, or could it be somewhere else?"
Misconception: integrate from zero to infinity Reasoning: "We start at the surface of the earth and then go to infinity"
Well think about it, look at the variables you're given, are you using them all? (student was not using Earth's radius
Exactly! You got it, thats absolutely right.
Well we're starting on the surface... And I realize I haven't used the value they gave me for Earth's radius. Would that mean we have to integrate Earth's radius to infinity?
I'm not really sure. Physics always confused me if we're being honest...
First question, helping the student realize something's wrong
Second question, leading the student in the right direction
Conclusion: The first bridge involved letting the student realize on their own that their answer was incorrect, while the second bridge involved pointing out information that the student had been given but hadn't used