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Session 3565

The Deflected Beam in Differential Calculus: Bringing engineering into the mathematics classroom

G.V. Loganathan1, Bill Greenberg2, Lorraine Holub2, Craig Moore1 1 Departments of Civil and Environmental Engineering / 2 Department of Mathematics, Virginia Tech, Blacksburg, VA 24061

Introduction

First year calculus is a hard course for the freshmen students and is sometimes considered as a weed out class by the students. However, as Malcom and Triesman1 convincingly argue, the calculus course is the pump for all other classes and should not be treated as a filter. In addition, the time varying/hidden cognitive abilities of beginning college students require proper nurturing to come to fruition, especially through cooperative learning and guided instruction (Malcom and Triesman1; Wankat and Oreovicz2; Felder and Brent3). The two emerging crucial considerations are: (1) calculus must be learned as a foundation for all modern science and engineering, and (2) it is not that the students lack ability, it is that their talents are quite different than earlier generations and, consequently, misplaced priorities interfere with the didactic presentation. While the first commitment is the strategic goal, the second one requires formulation of action items to achieve the goal.

Curriculum Change and Instructional Methods

Universities all over the country have embarked on various plans for better teaching of calculus. These may be grouped into three categories: (1) introduction of innovative instructional methods/aids, (2) reordering and in general minor additions and deletions of topics to serve a wider class of students, and (3) integration of mathematics, physics and chemistry with focus on a particular field such as engineering. Categories 2 and 3 deal with alteration of the syllabus whereas category 1 focuses mainly on instructional methods.

Barrow and Fulling4 and SimCalc (http://www.simcalc.umassd.edu/simcalc/curriculum) curriculum are two good examples for category 2 content modification. Barrow and Fulling argue for introducing vectors and line integrals in the first calculus course along with the derivatives. Simcalc curriculum supports accumulation and integrals before rates and derivatives. The IMPEC (Integrated Mathematics, Physics, Engineering and Chemistry) curriculum (Felder et al.5) points out the compartmentalized nature of the science, mathematics, and engineering courses. In this regard Townsend et al.6 have also noted the impracticality of introducing Engineering/Science word problems and explaining them in a short period. In the IMPEC curriculum elements of engineering design and operations are brought into the first year and

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Holub, L., & Loganathan, G., & Moore, C., & Greenberg, B. (1999, June), The Deflected Beam In Differential Calculus: Bringing Engineering Into The Mathematics Classroom Paper presented at 1999 Annual Conference, Charlotte, North Carolina. 10.18260/1-2--8135