Experience First

In this activity, students work in groups of four on whiteboards to solve four distinct, but related problems. After each group member has completed their problem, all four answers will be summed and the final answer presented to the teacher. If the sum is incorrect, group members must work collaboratively to find each others’ errors.

 

To prepare for this activity, we suggest printing each of the six problem sets on different colored cardstock. You may wish to make multiple copies of each problem set as groups will finish at various times and will need a new problem to work on. Arrange students in groups of four. Have students assign each group member a letter A-D which they will stick with for the whole activity.

 

Hand out one problem set per team (the order in which they complete the sets doesn’t matter). Using a large whiteboard, each group member will work on their part of the problem (Player A does part a, Player B does part b, etc.). The problem sets  are specifically designed so that each student will see a variety of problem types (finding derivatives analytically, reasoning from a derivative equation, reasoning from a derivative graph, justifying differentiability, etc.). When all group members are finished, have students sum up their four answers and call you over to check. If the sum is correct, hand them a new problem set. If the sum is incorrect, group members must work collaboratively to find each others’ errors. Do not tell them which of the four responses are correct or incorrect. Suggest to students that they turn the whiteboard 90 degrees so they can look at the work of another group member or discuss as a group which parts are likely to contain errors.This activity promotes excellent discussion among students! In our experience, working on whiteboards allows students to clearly see each other’s work and thus enhances discussion and accountability.

 

One modification is to write the correct sum on the middle of the whiteboard when you hand out the problem set, allowing students to continue working until they arrive at the correct sum, without having to call the teacher over. 

​

Formalize Later

Our students struggled the most on Problem Sets 3 and 4 which both had students reason about the behavior of a function given information about the derivative. An affordance of this activity is that students naturally help each other to make sense of problems and clarify questions, making a whole group debrief unnecessary.

 

Continue to give problems where students must deal with parameters (like a and b) as these are common in AP Calculus as well as on the SAT. The absence of actual numbers proves challenging for students, but ultimately helps them see the underlying structures and build conceptual understanding.