Assessing Allegheny College’s introductory
calculus and precalculus courses
Appendix A

Ronald Harrell and Tamara Lakins
Allegheny College
December 30, 2003

Appendix A:  Details of student performance in Math A, Math 155/156, and subsequent courses, as of academic year 2001-2002.

Data on the effectiveness of Math A.  The distribution of grades received by students enrolled in Math A during the fall semesters from 1997 through 2000 is given in Table 1 below.  Only students in the Fall 1997 through Fall 2000 cohorts, respectively, are considered.   Grades of C or higher are considered successful grades, while grades at the level of C- or lower are considered unsuccessful.

Table 1.  Grades in Math A

Tables 2-5 give the distribution of grades received by students who went on to take introductory chemistry (Chem 101), introductory computer science (CS 101), Math 155, or the research design and statistics course in the psychology department (Psych 206) at some point after passing Math A with a grade of C or higher during one of the fall semesters listed above.  Only the first attempt for each such course was considered; i.e., the grades of those students retaking any of these courses were eliminated from consideration. 

Tables 6-9 compare the distribution of grades for students taking Chem 101, CS 101, Math 155, and Psych 206 with respect to whether they placed in Math A or below and took Math A or Math 155 before taking the course, or placed in Math A and did not take Math A before taking the course.  The Fall 1997 through Spring 01 semesters are considered, and the sample consists only of students in the Fall 1997, 1998, 1999, 2000 cohorts.  Only the first attempt for each such course is considered; i.e., the grades of those students retaking any of these courses were eliminated from consideration.

Data on the effectiveness of Math 155/156.Table 10 indicates the number of students taking Math 155 or Math 160 during the fall semesters from 1997 to 1999, who later went on to take Math 170 (Calculus II), either at Allegheny College or elsewhere.  Only students in the Fall 1997 through Fall 1999 cohorts, respectively, are considered.  Since students in the Fall 1998 and Fall 1999 cohorts were still attending Allegheny College when the data were examined, and because the last semester included in the data is the Spring 2001 semester, the numbers for these cohorts could be incomplete.

The last table compares the grades of students who went on to take Math 170 at Allegheny College at some point after passing Math 155 or Math 160 with a grade of C or higher during one of the fall semesters listed above.  Only the first attempt for Math 170 was considered, and only those students in the respective cohorts were considered.

Appendix B:  Detailed course descriptions and learning goals.

Math 110 (Elementary Mathematical Models) is an algebra-based elementary modeling course intended for students who need a mathematics course but who do not need calculus.  Linear, polynomial, exponential, and logarithmic functions are studied.  The emphasis is on real-world problems and models, and rates of change.  Algebra is reviewed as needed.  Upon completing the course, the student will be able to

• work with functions and data represented graphically, numerically, analytically, and verbally;
• use technology appropriately in mathematical problem solving, and recognize its limitations;
• accurately perform algebraic manipulations; work with formulas;
• communicate mathematical information in written form;
• choose, implement, refine, and interpret appropriate mathematical models for various real-world problems.

Math 150 (Precalculus) is a traditional precalculus course intended solely for students who need extra preparation before attempting Math 160, the first course in the regular calculus sequence.  The mathematical concepts that are a prerequisite to the study of calculus (functions, domains, ranges, graphs, equations, and inequalities) are covered. Upon completing the course, the student will be able to

• manipulate algebraic expressions easily;
• work with polynomial and rational functions, including finding their values, graphing them, understanding their basic properties, and solving equations and inequalities;
• work with trigonometric functions, including finding their values, graphing them, using trigonometric identities, understanding their basic properties, solving equations, and solving problems in triangle trigonometry;
• work with exponential and logarithmic functions, including finding their values, graphing them, understanding their basic properties, and solving equations;
• communicate mathematical information in written form.

The courses Math 157/158 (Calculus I and II for Social/Life Sciences) form a two-semester terminal calculus sequence that gives primarily a conceptual treatment of calculus and is less theoretical than the regular calculus sequence.  The intended audience is economics, biology, and environmental science students. 

Math 157 (Calculus I for Social/Life Sciences) is an introduction to the differential calculus of algebraic, logarithmic, and exponential functions.  The emphasis is on the concept of the derivative and its applications of calculus to the life and social sciences.  Precalculus topics are covered as needed.  Upon completing the course, the student will be able to

• work with functions and data represented graphically, numerically, analytically, and verbally;
• demonstrate an understanding of the concept of the limit of a function and the rules for showing the existence of and finding limits; 
• demonstrate an understanding of the concept of the derivative of a function: the definition, as well its connection to the slope of  tangent lines and instantaneous rates;
• accurately perform the algebraic and calculus computations associated with algebraic, logarithmic, and exponential functions;
• communicate mathematical information in written form;
• choose, implement, refine, and interpret appropriate mathematical models for various real-world problems.

Math 158 (Calculus II for Social/Life Sciences) is a continuation of the differential calculus begun in Math 157, and an introduction to integral calculus of one variable and the differential calculus of multivariable functions involving algebraic, logarithmic, and exponential expressions. Applications of these topics in the life and social sciences are considered.  Upon completing the course, the student will be able to

• demonstrate how the derivative can be used to determine monotonicity, concavity, points of inflection, and maximums and minimums of functions;
• demonstrate an understanding of the definite integral as representing area and accumulated change, antiderivatives, and the Fundamental Theorem of Calculus;
• demonstrate familiarity with functions of several variables, partial differentiation and the information partial derivatives reveal about functions;
• accurately perform the algebraic and calculus computations with functions of several variables that involve algebraic, logarithmic, and exponential expressions;
• communicate mathematical information in written form;
• choose, implement, refine, and interpret appropriate mathematical models for various real-world problems.