In my summer physics class, I asked students the following question about motion online, in which they were asked to consider a wrong answer, explain why someone might think it, and then explain the incorrect answer away.
Here is a physics problem! Imagine you are driving a car along a long straight. Your friend in the passenger seat is recording where you are every hour of the trip.
Clock Reading Mile-marker
72 4:00 PM
Explain why your friend might reach the conclusion that the speed of the car at 3:00 PM was 24 miles/hour.
Then explain why that answer is probably not correct.
Here are different ways that students responded to the task:
Describe the Mistake Process and Explain the Correct Way
Someone might have tried dividing the mile-marker number (72) by the time on the clock (3pm). The answer cannot be correct because during each hour, the car has advanced to a mile marker 52 miles away. The time on the clock can only be used to determine the interval between time: 3pm-2pm =1hr and to find the speed, the initial mile-marker needs to be subtracted from the final mile-marker: v= (72mi-20mi)/1hr = 52mi/hr
Describe Mistake Only
Because they divided 72 by 3 thinking that they had traveled 72 miles in three hours.
Describe Mistake Process and Underlying Misunderstanding
If they confused 3:00 PM with 3 hours, they might be tempted to divide 72 by 3.
Show that Wrong Answer implies Something Else Incorrect
If the car were traveling 24 miles per hour at 3 pm then from 2:00 pm until 3:00 pm they would have only traveled 24 miles leaving them at mile marker 44 instead of 72.
Identify Hidden Assumption in Process and Explain why Wrong
If someone took the mile marker 72 and divided it by 3pm they would come to 24MPH however this would be assuming that the car had started at noon and had started at mile 0. however we do not know where the car started, only where it is now and where it was an hour ago.
Explain Correct but neither Describe or Explain the Mistake
I don’t know why someone would think that they were moving at 24 mph at 3 pm, but the time is given in increments of an hour. So obtain how fas they are moving you would subtract the mile marker number from the number of the previous mile marker of the previous hour. From 2 pm to 3 pm the car traveled 52 miles within the hour , so the car was traveling 52 mph.
State Correct Answer without Explanation
I don’t know why someone would think the speed of the car is 24 miles per hour. If you look at the data it’s clear that they are traveling at 52 miles/hour.
I’m curious: Which kinds of responses do you think are most productive? Which are the least? How could the task be re-written to encourage more of the productive kinds, and less of the unproductive kinds? OR What feedback would you give to students, or do in class the next day, as to encourage the more productive responses on later assignments?