Students were given the following problem:

A dense stone is tossed vertically into the air with an initial speed of 25 m/s.  Represent how ball’s motion changes in a “step-by-step” diagram. By elaborating and specifying aspects of your diagram, determine the maximum height.

Students had some brief direct instruction on what it means to do make “step-by-step” diagram and then to elaborate the diagram to solve a problem. The work below represent the first time students are practicing the approach, so keep that in mind. I’ve included a good example from a student of what this method might look like when done well, followed by two others that aren’t quite able to work it out.

Good Example

 

Student Approach #1

Student Approach #2

 

#1 How do you think students #1 and Students #2 were thinking about the problem and/or the their approach to the method they were asked to practice? In what way does their work “make sense” to them?

#2 What questions would you like to ask student #1 and student #2 to probe into their thinking?

#3 What questions would you like to ask student #1 and student #2 to*nudge* their thinking along?

A cart speeds up with a constant acceleration along a track. The table below shows the cart’s position at different times as read by a stop-watch.

What is the speed of the cart at the instant when the stopwatch reads 2.0s?

Some classic stuff here, but I wanted to try to bring this back alive.

• What were these students thinking? How did they decide to make these particular marks on the page?
• What do this work seem to suggest about what the students know? What ideas are they likely still struggling to make sense of?
• What kinds of instruction would be warranted if such mistakes were limited to a few individuals?
• What kinds of instruction would you want to have in place if a significant fraction of your students were making these mistakes?

This is from an online pre-class assignment:

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
2:00 PM	20
3:00 PM	72
4:00 PM	124
5:00 PM	???
6:00 PM	228

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.

Student Response:

Well someone might get 24 miles/hour by dividing the mile marker (72) and the given time (3:00 PM) and think that would be the miles traveled in that hour. But just because you are at a given mile marker that does not tell you speed because you are at that mile marker for only an instant, so it would be calculated as no speed.

1. What is the student thinking? Why do think it made sense for the student to write this answer?
2. What other knowledge and experiences might we presume the student has for thinking about this question? Why do you think the student failed to draw on this knowledge when answering the question?
3. What question or problem would you pose next to help the student make the next step toward understanding?

Actual student work re-created. These are just three of a large variety of errors made.

 

1. What were the students’ thinking? How did they decide to make these particular marks on the paper?
2. What other mistakes do you think were prevalent? Why would student make those mistakes?