Scaffolding Handout: Convergence/Divergence Series

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

In calculus II, one concept of infinite series utilizes 10 tests to determine convergence. Students struggle with CLO#3 determining most appropriate tool to solve a particular problem. 

Describe the necessity for this assessment

1. I typically cover this topic through lecture and not following my preference of active learning.  2.  Average on this assessment ranges from 65%-78% each semester.

Describe how the practice will be implemented

I have struggled with how to get students actively engaged in the learning process for this specific topic. For the last 10 years, I have lectured and did lots of practice with students.  Each lecture was modified to attempt to help students determine the most appropriate test to use. In Fall20, I created a handouts with scaffolded questions and activities. Students worked on the handouts, presented their findings to the class as a whole, and I become more of a coach. 

Interpret, compare, and describe the results

Observations: Students were more engaged and had rich conversations about the topic. Students seemed to grasp the concepts much faster than in previous semesters.  On homeworks, I saw more pictures and explanations than in previous years; students didn't do this in the past.  Exam: The average on the exam was 85%.  Students were able to pick the most appropriate tool to determine convergene; this is helps address CLO #3. 


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

I will continue to use these handouts and may modify them using feedback from students. I also want to see if this was a "fluke" semester.  Is this an exeptually mathematically adept class? I will talk to my calculus colleagues to see if any of them are willing to use the handout.  The key thing with having other faculty use my handouts is that this must fit their teaching style, and the faculty member must know what questions to ask students.  


Update (1 week after CATS was originally submitted): After submitting this CATS, students began learning about Power Series (which is one reason to learn Convergence/Divergence of series discussed in this CATS).  WIth the scaffolding handout, they were able to come up with how to deteremine convergence/divergence of Power Series on their own!  Again, I typically have to do a lot more lecture, but I didn't.  The scaffolding handouts layed the ground work for this next section, and the students were highly engaged, talking, collaborating, and coming up with concepts on their own. This not only addresses my CLOs, but also Critical Thinking and Communication with ILOs. I am hoping this continues to align to our next set of handouts - Taylor Polynomials.  I am excited to see how students do with all of this.  

Completed Full Cycle
Course Number
Average: 4 (6 votes)


Catherine Cochran Wed, 01/13/2021 - 8:56am

Hi Becky,

I love your honesty and willingness to use this new active learning assignment with your students.  I do believe our students have learning styles that are more prodominant than others.  This scaffolding assignment helped meet all your different type of learners.  Your data showed the improvement.  In addition, the repetative review of the assignment helped students who need this.  I believe engaging and learning with your peers is another layer of shared knowledge too. 

Great Job!