Mastery Learning for One Exam

Submitted by Becky Baranowski on
What is the Purpose of the Assessment?

The 4th exam in my calculus I course is traditionally has an average of mid F to low D.  The section of the exam that brings student grades down is integration by u-substitution. 

Describe the necessity for this assessment

This technique to integration is needed in future STEM courses such as calculus II, III, differential equations and engineering.  Also, this addresses a learning outcome in MAT22X.

Describe how the practice will be implemented

From teaching the calculus sequence, I enjoy seeing students move onto calculus II and III and seeing how they go from "can't u-sub" to "easy peasy."  This is a solving technique that students need to practice over time. The 4th exam was broken up into four parts. Instead of 1 exam to take an entire class period, students took 4 20-25 minute exams over a period of 4 different days.  The top 3 scores were averaged to give the overall exam score.

Interpret, compare, and describe the results

1. Student scores showed some improvement after each part. Some students started with 0/10 to 7/10 by the 4th part.  2. Student confidence somewhat went up. 3.  Students had time between each part over a 3 week period to see where they had gaps in their integration techniques and practiced more. 4.  Because u-sub requires finding derivatives, their derivative skills also improved  The average on the scores was a D (sigh).  

After analyzing, and reflecting on the outcome, what are the next steps?

An interesting observation of this is that students did much better on the 3rd part than the 4th one. While I am overall frustrated with the average, I was very happy to see improvement for parts I - III. Questions I have about this and next steps: 1. Was 4 parts too much? 2. Did students "check out" after the 3rd one? 3. The 4th part was held the Monday of Thanksgiving week. Was this a bad week to have the 4th part? I will try this again in 2 classes in Spring 2020.


Angela McClure and I worked on this as part of our calc I/phy I learning community.  She and I plan to re-evaluate this in the Spring and I will also try this in the other learning community.  I will be reaching out to some of my calculus colleagues to see if they are interested in trying this with some of our exams that are more "skill" based an not conceptual.  Angela mentioned possibly looking into doing something like this with vectors in PHY121.  Is this worth the time and effort with doing this?  Are students willing to take advantage of this opportunity?  There are quite a few questions Angela and I have about this, so Spring semester will be another opportunity to dive deeper into this.

Note:  This was done with the 4 exam only; all other exams were taken in one class period.   

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Christopher McNeal Thu, 12/05/2019 - 8:29am

Hi Becky,

I would be happy to create a study session for intergrating using u-substitution, similarily to how I did Laplace Day! Also, I do agree that because Thanksgiving was so late this year, it could've had an impact on the timing of the exam. 

Becky Baranowski Thu, 12/05/2019 - 8:47am

Thanks, Chris.  I think having an "Integration Party" would be a valuable event for our calculus students.  We could advertise to all students in the calculus sequence.  Thank you!

Sarah Lockhart Mon, 01/27/2020 - 1:19pm

Were the concepts tested the same on all 4 tries?  

Becky Baranowski Mon, 01/27/2020 - 2:00pm

Hi Sarah - thanks for taking time to comment.  Yes, the concepts were all the same (u-substitution) but the type of u-sub problems were different.