Enhancing the Mathematical Understanding of Students in Chemistry

The goal of the project is to increase chemistry students' knowledge of mathematics and its role in chemistry. In particular, we want to enable the students to use the tools and language of mathematics to solve scientific problems.

The project has the following specific components:

• We developed a new placement exam to identify students who cannot solve multi-step non-algorithmic word problems at the precalculus level.
• We developed a math course which teaches problem solving in the sciences.
• We developed lab materials for Organic Chemistry which reinforce mathematical skills and skills they have learned in General Chemistry.
• We developed modules on Linear Algebra and Differential Equations in Physical Chemistry
• We developed an interdisciplinary course on Chirality for mathematics and chemistry students.

Principal Investigator:
Erica L Flapan, Pomona College
Enhancing the Mathematical Understanding of Students in Chemistry

Co-Principal Investigator(s) : Fred J Grieman; Daniel J O'Leary; Adolfo J Rumbos; Shahriar Shahriari
Assessment Consultant : Barbara Gonzalez
Graduate students : Julie Pomerleau; Macy Shen
Undergraduate students : Maile Bay; Cindy Nguyen; Chanda Strom; Di Trang; Bao Trinh; Christopher DuBois; Saki Miwa; Margaret Norris; Erin Dillon

Primary contact: Erica L Flapan
Email: eflapan@pomona.edu
Fax: 909.607.1247
Phone: 909.621.8711
Address: 610 N. College Ave.
Claremont, California 91711

We believe the main difficulty facing beginning chemistry students is their mathematics skills. We identified the following areas of mathematics which are used in General Chemistry:

1. Logarithms and anti-logarithms
2. Percentages, proportions, and averages
3. Scientific Notation
4. Factoring, solving equations and systems of equations
5. Functional relations, proportionality, linear relations

We have developed a new Chemistry placement exam which tests students' ability to do multi-step non-algorithmic problems involving these areas of mathematics. This exam contains no questions on chemistry.

Our assessment consultant, Barbara Gonzalez, together with her students evaluated the effectiveness of the materials we developed. Their findings may be downloaded below.

Download Overall Assessment
Learning Theory Presentation
(evaluation of placement exam begins on page 22)
Presentation on the Effectiveness of Placement Exam
Master's Thesis of Julie Pomerleau Analyzing Placement Exam

For a copy of the exam, interested professionals may contact Kathy Sheldon with your name, institution, and department. Some conditions will accompany use of the exam, such as keeping the exam confidential.

We developed a new Math course entitled 'Problem Solving in the Sciences.' The course was geared for students who performed poorly on the Chemistry placement exam. The course taught the students to use precalculus level mathematics to solve problems that occur in the sciences. The course was organized around scientific rather than mathematical themes. Students in the course learned to use their own mathematical reasoning rather than relying on algorithms that they were taught.

We developed a collection of 11 worksheets for this class, which teach the students to use mathematical techniques to solve hard real world problems related to a variety of scientific disciplines as well as economics and psychology.

Download Problem Solving Syllabus
Download Problem Solving Worksheet 1
Download Problem Solving Worksheet 2
Download Problem Solving Worksheet 3
Download Problem Solving Worksheet 4
Download Problem Solving Worksheet 5
Download Problem Solving Worksheet 6
Download Problem Solving Worksheet 7
Download Problem Solving Worksheet 8
Download Problem Solving Worksheet 9
Download Problem Solving Worksheet 10
Download Problem Solving Worksheet 11

In order to reinforce and strengthen the Organic Chemistry students' ability to use mathematical and scientific reasoning together, we developed a sophomore organic laboratory in which students first derive the calculus of a kinetic rate process and then use the expression to study a series of alkyl halides being subject to a dehydrohalogenation reaction.

Download Organic Laboratory Protocols

We have developed three mathematical modules for the physical chemistry course: one preliminary module on background material (Preliminary Module), one on differentiability of functions of several variables (Module I), and another on partial differential equations and boundary value problems (Module II).

The Preliminary Mathematics Module for Physical Chemistry is focused on Calculus and Approximations. Calculus is a powerful tool for working with functions when only partial information about the function is known. In this module, the students review basic ideas of differential calculus by focusing on local approximations of functions. Linearization and Taylor polynomials are introduced as methods for using calculus to approximate unknown quantities, functions, and solutions to differential equations.

Module I is intended to be a refresher of multivariable calculus concepts on differentiability. Its focus is on the chain rule and its consequences (differentials and change of variables). The main goal of the first module is to enhance students' understanding and competence on these concepts so that when they encounter them in thermodynamics and quantum mechanics, they have enough confidence when applying them.

Module II is more advanced and more difficult. It introduces the students through the development of the vibrating string problem to the method of separation of variables and eigenfunctions expansion which are crucial in dealing with problems in quantum mechanics.

Download Preliminary Math Module
Download Physical Chemistry Math Module 1
Download Physical Chemistry Math Module 2

Dan O'Leary (Chemistry) and Erica Flapan (Mathematics) developed and co-taught a new interdiscilinary course on chirality. The syllabus for this new course may be downloaded below. For more information contact Erica Flapan.

Download Syllabus