Our calculus toolkit is designed to focus on the problem of the transference of knowledge from a pre-calculus course to a calculus course. In particular, the toolkit addresses transference of knowledge concerning the concept of functions. The toolkit includes a college readiness test focusing on functions and three classroom activities which look at functions from a numerical, graphical and verbal perspective.
Having a deep understanding of functions from multiple perspectives is critical to success in calculus. The college readiness test will help instructors identify areas of concern regarding knowledge of functions and the three classroom activities will help students deepen their understanding of functions from multiple perspectives. This should help students retain their knowledge as they progress to calculus and equip them to deal more complex function situations. Materials could also be used within a calculus course as a just-in-time intervention.
Resources Used to Inform this Toolkit
The articles “Foundational Reasoning Abilities that Promote Coherence in Students’ Function Understanding” by Oehrtman, Carlson, Thompson and “Coordinating Symbolic and Graphical Meanings of Function Notation” by Coomes and Lee introduced us to alternative ways of understanding and assessing the concept of functions and laid the foundation for the development of our three classroom activities. Additionally, the article “The Precalculus Concept Assessment: A Tool for Assessing Students’ Reasoning Abilities and Understandings” by Carlson, Oehrtman, and Engelke introduced our cohort to the Calculus Concept Readiness Test and we used these ideas to construct our assessment.
Key Lessons We’ve Learned
The first lesson we learned was through our experience of observing classrooms at both the high school and college level. Often at the college level it is assumed that the problem of transference of knowledge in mathematics is attributed to “poor preparation” of high school students or “lower expectations in the high school than in college”. Throughout our observations we found ample evidence that this was not the case. Students at both levels seemed to struggle with the same concepts and we concluded the issue of lack of transference of knowledge from pre-calculus to calculus had a deeper and more complex cause.
Comprehensive Guide to Utilizing Our Tool in Your Classroom