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Integrating Calculus and Introductory Science Concepts Abstract

During their first two years, students often fail to make connections between related concepts in their calculus and introductory science courses. This disconnect early in their curriculum can hamper engineering majors in their ability to understand how these courses relate to their discipline and can serve as a “turn-off” for students who fail to engage in these courses. Here we present how we have tried to address this problem by integrating basic calculus concepts into the introductory freshman and sophomore biology, chemistry and physics science laboratory courses. In this paper, we will feature a biology laboratory experiment where students examine a growth curve for algae, a chemistry lab involving an instantaneous rate calculation for a rocket launch, and a physics lab experiment where students approximate the instantaneous speed of a cart on an inclined plane. This work has been sponsored in part by NSF CCLI A&I grant #0311481.

Background

Traditionally, science and mathematics content are taught as discrete courses. Consequently, students often fail to make connections between disciplines. Integration between disciplines has been advocated as a solution for this “mismatch” by NSF advisory committees1, in teacher preparation2, by engineering schools3,4, as well as by mathematics departments5. Our approach has been to integrate content between the mathematics and science laboratory courses in the freshman and sophomore curriculum. The primary focus of our curriculum is a 6-course mathematics sequence and an introductory science (chemistry, biology and physics) laboratory series. The mathematics sequence consists of calculus, differential equations, along with just-in- time algebra and trigonometry topics and a unit on statistics.

One of the primary goals of our project is an improvement in student connections between science and mathematics course content. The science laboratory course materials focus on more complex scientific problems requiring application of concepts/ techniques from each of the science disciplines, as appropriate, and the use of mathematics in context. The science laboratory series (chemistry, biology and physics) operates in a single cooperative, technology supported laboratory designed to make possible appropriate content integration among the three science disciplines, as well as the utilization of appropriate mathematics content. In addition, the laboratory was designed to support the use of student teams.

Because of state limitations on the number of credit hours that can be required for a bachelor’s degree, the specific curricular requirements did not change with the implementation of the integrated curriculum. Instead, the curriculum has focused on revising the content and course materials, as well as implementing minimal course sequencing requirements. Content is integrated based on minimal co- and pre-requisites. For example, students in the introductory science labs should, at a minimum, be enrolled in their first calculus course. Because the integrated science lab series develops common laboratory and research skills that build upon those from previous integrated science lab courses, it is desirable that students take the science lab courses in the correct sequence (biology, chemistry and physics). Some students do interchange the biology and chemistry labs without too much difficulty. Because not all students

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Carpenter, J. (2007, June), Integrating Calculus And Introductory Science Concepts Paper presented at 2007 Annual Conference & Exposition, Honolulu, Hawaii. 10.18260/1-2--2021