Recursive Functions
The following video clips are from a Calculus 1 class at Westfield State University taught by Prof von Renesse in Fall 2016. The materials the students are working on can be found at iblcalculus.com (free download). The particular activity can be found here. Notice that the students discovered the growth patterns and explicit equations for linear and exponential functions during the last activity.
Group Work
Work through the activity yourself. What misconceptions and struggles do you think the students will have?
From the video, what misconceptions and struggles did the students actually have?
Does the group work well together? Would you change anything about the group for the next class?
What did you notice the facilitator do/not do? What could she have done differently?
Whole Class Discussions
After the groups have worked on the activity for a long time, the facilitator calls the attention back to the whole class.
Before you watch the video: What could be goals for the whole class discussion?
At 1:39 minutes none of the students answer the question that the facilitator asks. What would you do next?
At 3:00 minutes, there are several possible solutions and the students are not sure which one (if any) are correct.
Which misconceptions do you see in the proposed solutions? (See proposed solutions below)
What would you do next as the facilitator?
Watching the end of the clip, what do you notice about the choice the facilitator made?
Proposed Solutions:
$P(n+1)=P(n)*m^k, P(0)=a$
$P(n+1)=P(n)*a, P(0)=b$
$P(n=1)=P(n)+x*n$