Our original intent in this project was to create an examination process that would identify which concepts students need to understand deeply in order to succeed in calculus. We felt that the first issue in transference of knowledge was identifying the areas where students had difficulty. So we read and discussed the following articles:
- The Calculus Concepts Readiness (CCR) Instrument Assessing Student Readiness for Calculus by Carlson, Madison and West
- The Pre-Calculus Concept Assessment: A tool for Assessing Students ‘Reasoning Abilities and Understanding by Carlson, Oehrtman and Engelke
- Coordinating Symbolic And Graphical Meanings of Function Notation, Coomes and Lee
These articles introduced us to a calculus pre-assessment called “The Calculus Concepts Readiness Test”. This test was developed by the authors at Arizona State University and was used to at that school to place students in calculus. The assessment focused on reasoning and understanding the concept of a function, instead of solely focusing on procedural skills. We used these articles to help design our in-class assessment of calculus readiness that is included as part of our toolkit. In addition we consulted the article “Foundational Reasoning Abilities that Promote Coherence in Students’ Function Understanding” by Oehrtman, Carlson, and Thompson. This article emphasized the importance of the deep understanding of the function concept as a key to student success, not only in calculus, but also in science and applied science courses in college. The article stressed that we need to change our focus in teaching functions from an action view to a process view. Furthermore, the article stresses focusing on approaching the study of functions from multiple representations including graphical, numerical, analytical and contextual. In addition more time is required for students to gain the depth of knowledge needed to be successful in calculus. We used this article and the Coomes and Lee article to help design our pre-calculus interventions that are included in our toolkit.