Reflection: Connection to Prior Knowledge Creating Velocity Graphs from Position Graphs - Section 3: Pride Points Problem: Non-linear Position Graphs

 

It is clear from the Pride Points work that students are right on target with the idea of using slopes to create velocity profiles. In addition, every team of students hit upon the strategy of approximating small curved sections of the position graph with short, straight segments whose slopes could be assembled. This is new to me - in previous years, students were not as ready to do this. Before considering why this might be, I want to examining two sample student products.

In the first image, the velocity graph is a staircase function - constant for a segment with quick transitions from interval to interval.

 

Most teams produced graphs like the one above with only minor variations. One team produced this graph which looks continuous:

 

While this is closer to the truth, their thinking (not shown here) reveals that they followed exactly the same strategy as others but decided to simply plot the midpoint of the the velocity value for each interval! 

I think there are two reasons why students were so ready to move to straight line approximations. I overheard many students refer to earlier approximation methods (like estimating the area under nonlinear force functions to get work) as a way to convince teammates that "getting close" was preferable to struggling, perhaps in vain, for a perfect answer. This is very rewarding to me as it indicates a level of sophisticated thinking that we've been striving for and a comfort with uncertainty that is admirable. In addition, students engaged with a simulation in the last lesson that previewed this kind of nonlinear position graph. Both influences likely played a huge role in their comfort with approximating in this problem.

  Examining Student Thinking
  Connection to Prior Knowledge: Examining Student Thinking
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Creating Velocity Graphs from Position Graphs

Unit 5: Objects in Motion
Lesson 3 of 10

Objective: Students will incorporate the idea of slope as an essential idea in studying motion, applying it to create velocity graphs based on position graphs.

Big Idea: The slope of a position versus time graph is the velocity.

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simple pos graph
 
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