Integration in Calculus II

Submitted by Becky Baranowski on

While success rates are high in my calculus II courses (85-95%, depending on the semester), students struggle with integrating.  In spring 2008, students were required to write "recipe cards" on integration techniques for trigonometric substitution and integrals involving trignometry.  The average on the quiz was a 75%.  Students presented their steps to the class and worked on these recipes as a group days before the quiz.  In spring 2010, 2011, and 2012, I did not require students to create these cards; I highly recommended them, though.  The quiz average dropped to 69% (2010), 68% (2011) , 61% and 54% (2012).  

In Spring 2013, I decided to spend more time on the recipe cards.  Students spent time in class developing them and working together with them.  Less time was spent on doing actual problems in class.  The quiz average was a 71%.  Thus, from the results in 2008 and 2013, I will continue to require students to write these recipe cards. 

Completed Full Cycle
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f12-81-85-quiz.doc 38 KB
Assessment of the Month
Average: 4 (6 votes)


Bronwen Steele Tue, 02/19/2013 - 8:02am

This looks great so far, can't wait to see what happens.

Marianne Smith Tue, 02/19/2013 - 1:03pm

Are students allowed to use the cards for the quiz, or do you suppose the difference in quiz scores is due solely to the collaborative practice?  It sounds like the cards really reinforce integration strategies for your students.  I wonder if we could use a similar approach for other math classes (i.e. factoring strategies in 121?)

Becky Baranowski Tue, 02/19/2013 - 1:09pm

I do allow students to use their cards, but I have noticed that after they create them and work together - they don't need them for the quiz.  The ones that do use the "recipe" cards are so lost that it doesn't matter if they have the cards or not.  Most of us know that if a student can explain in words what they are doing, then they understand more than the others who cannot explain the process.  This data seems to reinforce this idea.  I really hope that the results after the quiz are what I think they will be!

Peter Turner Tue, 02/19/2013 - 1:58pm

Perfect example of what Action Research is all about, Becky. I too look forward to seeing you close the loop and shareing your results!


Erik Huntsinger Mon, 03/18/2013 - 5:22pm

It is wise to see the value of the in-person class time is the higher level thinking that can occur through collaboration.  I think another interesting measurement besides the average test score is how many students passed the test.  In other words, did the recipe cards allow more students to "get it", as opposed to those that already did to "get it more"?

Bronwen Steele Tue, 03/19/2013 - 3:32am

Rachel has found the exact thing about cards. The ones who are not really prepared but just relying on the card could do just as "well" without a card. 

Holly Dison Tue, 08/13/2013 - 11:21am

Hi Becky, I like your recipe card idea and I think it would work

well in lower level classes too. I think I'll try it for topics like Order of Operations and Problem

Solving (Mixture Problems, in particular) for 091.

Do you have guidelines to give the students to help them create useful recipe cards? 

Becky Baranowski Tue, 08/13/2013 - 11:31am

Hi Holly - I do have guidelines.  We can meet and discuss them, if you would like.  I give them an example one that they can use or follow.  Then they use the sample one to create others for the course.