On the integration exam in calculus I, students try to perform a specific intergration technique called u-sub on EVERYTHING. They lose sight of simple integration.
To get students using the right integration technique so that they can be successful in future calc, physics and engineering courses. 20% tried u-sub instead of basic integration.
After talking with Dwain Desbien and Jennifer Shannon, Dwain had a theory that students didn't understand the integral operator and the properties of it. After brainstorming with these two, I created a warm up (WU) problem to further investigate a "simple" integration problem. See attached document for the warm up. The 1st and 3rd problem of the WU are the same problem, but the 3rd one is rewritten using properties of integrals.
The results greatly surprised Dwain, Jennifer and me. The answers to 1 an 3 on the WU were so different, and they should have been the same. After further reviewing the results, we believe students do not have a fundamental idea of what an integral means. For example, several made errors of changing an operation of multiplication to addition. Please refer to the attached document for common errors and further discussion of this analysis.
After reviewing the exam, the next steps were to determine why students took a "simple" problem and complicated it. So, with the results of the WU which was used to further investigate where students are going wrong, I will be coming up with more problems to see what misconceptions students have. This is something that needs to be further investigated at different levels. See attached for sample problems I will be asking in the future.
The purpose of this CATS is to really dive into one concept and try to figure out what students don't understand about basic integration. Why is everything u-sub? After each WU, I will use the information to write another WU to go further into the issues students are having. The goal is to come up with a set of questions/problems that students have to do which "attack" a concept from multiple directions. If I can cover the concept in many different ways and variations, I hope to fill any and most gaps students may have in their understanding of basic integration.