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  Programs

The Power of Calculus When Applied to
Chemistry and Allied Sciences

G. Wesley Childress
Department of Mathematics and Applied Mathematics

Objectives

  • In recent years the mathematics department at Virginia Commonwealth University has seen an increase in the number of students enrolling in calculus who are likewise enrolled in chemistry courses. Some of this increase can be attributed to the addition of a school of engineering and a  forensic science program. Calculus textbooks have long had applications in physics, economics, biology and statistics but lacking in chemistry based problems. This project, in part, is to address this discrepancy.
  • Many individuals who take courses in calculus seem to lack an adequate understanding of where and how calculus might be applicable to their future. This is probably due, in part, to the fact that most exercises in traditional calculus programs are tied to equations which are furnished by either the textbook or the instructor. The student often dismisses or overlooks how this might apply in a world where formulas and equations are now handed to them. This project addresses the concepts in calculus through tables of data which students are very likely to encounter rather than through given equations.

Parameters

  • Because scheduling is a priority and roadblock in creating any new program, this project attempts to limit any and all such impeding factors. To facilitate this no constraints are applied to the students who might participate in the program other than that they be “calculus ready students” in the traditional sense. No background in chemistry is assumed, no particular major or curriculum is required, the project can be carried out in any or all calculus classes - no perquisites beyond that of meeting the requirements to enroll in calculus is needed.
  • One of the goals of this project is to insure that students participating are not exposed to less or different material than that covered in our other calculus classes. The problems are in a laboratory format and are included as an addendum to particular assignments. These labs parallel the existing curriculum.
  • Realizing that some students may feel intimated by the fact that the exercise (labs) are not traditional calculus problems, students are allowed and encouraged to work with a partner. If a student works with a partner, each partner is required to turn in a lab of their own with their partners name included.
  • The intent is that the student’s final grade is neither inflated nor impacted downward through participation in the project. One point is added to the final test for the year for each lab completed. This, in reality, increases the individual’s average by a maximum of 0.8 percent. Realizing that some students might be inclined to turn in a lab based on their partner’s work, bonus questions worth one point each are added to tests and quizzes  throughout the semester. Thus students  need to have some understanding of the lab results in order to answer these questions successfully. Through these bonus questions individuals can add an additional 0.8 percent to a semester average. Hence, active participation could add 1.6 percentage points to the final grade which could affect borderline grades. No grades, however, are affected adversely - which is the intent of the program. (A discussion of this will be included in the results portion of this document.)

Assessment

  • Six labs were assigned during throughout the course of the semester. (Eight were prepared but due to the newness of the study, it was decided to err on the side of too few rather than too many.
  • Titles of Laboratories
    • Fahrenheit vs Celsius Temperature Scales (As Inverse Functions)
    • Average and Instantaneous Rate of Change (the Derivative) in a Chemical Reaction
    • Applying the Definition of the Derivative to Gas Laws
    • Effect of Arterial Radius on Blood Flow - dV/dr  (First - the Physiology)
    • Related Rates and the Gas Laws
    • Effect of Arterial Radius on Rate of Blood Flow - dV/dt  (Now - the Chemistry)
    • Conditions Leading to Optimization (Maximum/Minimum) Through Chemistry *
    • Related Rates and the Chain Rule Applied to the Ideal Gas Law and Arterial Blood Flow *

      *  These labs were not included (due to time constrains  in the initial semester) but should be in the future.
  • Graphs of results
    • Graph A - Number of Students who participated in Lab (out of 35 students)
    • Graph B - Number of Students who picked up Bonus Points per Lab (out of 35 students)
    • Graph C - Number of Students whose grade improved due to Labs (out of 35 students).
    • Graph D - Final Grade Distribution of Class (class of 35 students)

Graph A


Graph B

Note: No bonus questions were associated with Lab 6

Graph C


Graph D

Summary

The motivation for the assessment portion of the project is not to actually measure the affect on student grades; in fact, improving student grades is not a goal of this project. Points are assigned  to each lab in the same manner they are assigned to most class assignments - to motive student participation. The student scores are really most critical as a vehicle to

  • determine whether students are willing participants
  • to see if the level of the labs are proper for the students’ background
  • establish a baseline with respect to length of labs and if they can be completed in a timely fashion.
  • try and establish whether this project merits further field testing and if so, what fine tuning needs to be done to incorporate it into the curriculum.

Projects Future

Considering the fact that not a lot of preliminary work was done to mentally prep students for the incorporation of the labs into the course, I was well pleased. Student participation was at the minimum what I had hoped for; and, as expected, students with the higher averages were more inclined to put forth a much more concerted effort to do their best. The number of students who attempted the last lab was much less than for the others and  may be attributed to the fact that it came just prior to exams.

I believe part of the success of the pilot labs was the fact that they (the labs) were prepared prior to the project which meant that most of  tedious work was done in advance leaving time during the project for instructor energy to be focused towards motivation of the students and insuring that the curriculum paralleled the labs.

The following labs have been written since  this trial was conducted in Calculus I and will be added to the curriculum as time permits:

  • Related Rates and the Chain Rule Applied to the Ideal Gas Law and Arterial Blood Flow
  • Conditions Leading to Optimization (Maximum/Minimum) Through Chemistry

The following labs have been written which are appropriate to the Calculus II curriculum:
           

  • Exponential Grow and Decay Models
  • Calculating the Center of  Mass (Center of Data Values) for the Product in a Chemical Reaction Using Numerical Integration

Note - If this project is continued into Calculus II (which is the intent), students will not be required to have participated in the program in Calculus I - in fact - if they have, it will be merely coincidental.

Addendum

Attached (PDF) to this report is an example of one of the labs used in this project.

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Last modified: June 20, 2013
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