Historically, students struggle with determining a limit as independent variable goes to infinite. SP19: 25% (non LC) and 48% (LC) answered this question correctly on final exam.
Limits in calculus are a threshold concept (core concept and foundational to calculus that can transform a student's understanding) and difficult for students.
In Fall 2019, I updated my calculus workbook to include more conceptual understanding of end behavior of functions. This included a ranking problem of functions and their end behavior. I also continually tied this idea of limits going to infinite to college algebra with horizontal asympotes as well as related the concept to investing money for retirement. Students worked collaboratively in groups, held class discussions, and used technology. I gave a small lecturet, too.
For my course alone, 76.9% answered the question correctly! Was this a fluke? Was I left with the best of the best students? From initial review, my activity worked. But, will it always work? We will be receiving the common final results from Fall 2019 in Spring 2020. The results will be reviewed to see if anyone else had improvement in their courses, too. If they did, we will review if they made any changes, too.
Next steps are to incorporate this into my Spring 2020 courses. I am teaching two calculus I classes and will see if I have the same results. The calculus faculty are going to start meeting every semester to review data and discuss activities. We have meet in the past, but not with consistency. We will have a standing meeting at 4pm prior to the all adjunct meeting every semester.
Update: In Fall 2020 and Spring 2021, I continued to use the scaffolding handout that addressed conceptual understanding of limits at infinity (as described in this CATS). This handout addresses EMCC's ILO of critical thinking along with the CLO of choosing the most appropriate tool/technique to solve a problem. In both Fall and Spring semesters, I had similar results with roughly 75% of students (both semesters) answering the limits at infinity question correctly on the final. In several cases, students wrote down their rationale as to why they selected the technique they did to solve the problem (and I didn't ask them to do this), and their rationale was related to the ideas in the handout. I will definitely continue using this for all my courses and will speak to college algebra and calculus faculty about developing conceptual understanding of end behavior. If we can get all college algebra faculty to discuss end behavior of functions in a similar fashion, I hope to see higher success in all calculus classes with this topic.