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Chapter 4

First-Year Courses: Calculus and Statistics

Data Highlights

By and large, this chapter contains data not previ-ously collected in CBMS surveys. It shows that, in PhDdepartments, just under half, 48%, of mainstreamCalculus I enrollment was taught in the large lec-

ture/recitation format. Considering only the enroll-ment in the regular section format of mainstreamCalculus I, tenured/tenure-eligible taught justunder 50% of the enrollment in these sections at PhDdepartments, as compared to 77% of the enrollmentat MA departments and 84% of the enrollment at BAdepartments.

On the other hand, there is little difference amongdepartments in the percent of enrollment in main-

stream Calculus I that were taught from a "reform" text:27% for PhD departments, for MA departments,and 29% for BA departments. However, MA depart-ments have the largest percentage of mainstreamCalculus I enrollment using graphing calculators, 44%,followed by departments at 39%, and PhD depart-ments at 33%. All of these numbers represent sub-stantial increases over the 1990 percentages. Forexample, in 1990 graphing calculators were used by

no more than 3% of the sections of mainstreamCalculus I, no matter the type of department.All of the percentages in the above paragraph are

somewhat lower for mainstream Calculus II and quitea bit lower for non-mainstream Calculus I

ments the corresponding percentage is 46%. Finally,42% of the students enrolled in this course in PhDmathematics departments have required computerassignments, while this figure rises to 61% for PhD sta-tistics departments.

Explanation of the Tables

This chapter contains six tables, all in a landscapeformat, that present data on mainstream and non-mainstream Calculus I and II, elementary statistics, andprobability and statistics with no calculus prerequisite.

These tables present data by the different types ofdepartments: PhD, MA, and BA. Whenever one of thesetables gives data on the percentage of enrollment

taught by various kinds of faculty, the percentages foreach type of department total 100%. For example, inTable in the first row of data titled "Large lec-ture with recitation", the percentages given for PhDuniversities: 76, 17, 5, and 2, total 100% (except forrounding errors). The 100% enrollment for this largelecture course at PhD mathematics departments is40,500. The actual enrollment, not percentage ofenrollment, taught by tenured/tenure-eligible faculty

is computed by multiplying 76% (expressed in decimalform .76) and 40,500, which gives an actual enrollmentof 30,780. Tables FY.l, FY.3, FY.5, and FY.6 have sim-ilar presentations.

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a bit lower for non mainstream Calculus I

TABLE FY.1 Percentage of enrollment in Mainstream Calculus I and Mainstream Calculus II taught by tenured/tenure-eligible, other full-time, part-time, and graduate teaching assistants in Departments of Mathematics by size of sections and type of school: Fall Also total enrollments (inthousands) and average section sizes.

Course

Mainstream calculus

Large lecture with recitation

Regular section

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students, but 63% for those regular sections with 30 or more students. A second example is, again, in the use of graphing calculators in main-total enrollment was 48,000 for the smaller enrollment sections and stream Calculus this time in PhD universities. The percentage of stu-

18,000 for the larger enrollment sections. This means that nearly 14,000 dents varies greatly according to the instructional format, but the actualstudents enrolled in the smaller enrollment sections used graphing number of students in each format who use graphing calculators variesculators, as compared to a little over students in the larger enroll- little, ranging between 8400 and 10,100.ment sections who used graphing calculators.

TABLE FY.2 Percentage of enrollment in Mainstream Calculus I and Mainstream Calculus II taught using various refo rm methods in Departments ofMathematics by s ize of sections and type of school: Fall Also total enrollments (thousands) and average section sizes.

Course

Mainstream calculus I

Large lecture withrecitation

Regular section

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74 1995 Survey of Undergraduate Programs

Graduate TAs

Part-time

Other full-time

tenure-eligible

Univ (PhD) Univ (MA) Coll (BA)

FIGURE Enrollment in Mainstream Calculus I inDepartments of Mathematics by type of instructor and type ofschool: Fall 1995.

Graduate TAs

Part-time

Other full-time

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First-Year Courses: Calculus and Statistics 75

Univ (PhD) Univ (MA) Coll (BA)

Reform text

Graphingcalculator

Writingassignments

Computer

assignments

Group

assignments

FIGURE Percentage of enrollment in Mainstream Calculus I taught

using various reform methods in Departments of Mathematics by type ofschool: Fall 1995.

Reform text

Graphingcalculator

Writingassignments

Computer

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Tables FY.3 and FY.4 MA and BA mathematics departments part-time faculty teach about theThese tables are an elaboration of Tables SFY.20 and in chap- same percentage of students enrolled in these same courses.

ter 1, Summary. There seems to be some use of "reform" material in small sections ofIn PhD mathematics departments, graduate teaching assistants teach non-mainstream Calculus I taught at PhD universities, but little use of such

of the students enrolled in the non-mainstream calculus, while at the material elsewhere in the non-mainstream calculus courses.

TABLE FY.3 Percentage of enrollment in Non-mainstream Calculus I and Non-mainstream Calculus II taught by other full-time, part-time, and graduate teaching assistants in Departments of Mathematics by size of sections and type of school: Fall Also totalenrollments (in thousands) and average section sizes.

Course

Non-mainstream calculus

Large lecture with recitation

Regular section

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Enrollment (thousands)

Percentage of enrollment taught using

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Tables and FY.6

These tables are an elaboration of Tables SFY.22 and SFY.23 in chap-ter 1, Summary.

While there are some differences in the way these two courses are offeredbetween PhD statistics departments and the three types of mathematicsdepartments, the one large difference is the percentage of students whohave required computer assignments. In PhD statistics departments, 60%

of the students in these two courses have required computer assign-

ments, compared to 39% of students enrolled in these courses in PhD math-ematics departments. Perhaps this disparity has to do with the type offaculty offering the courses. In PhD mathematics departments, per-cent of students enrolled in these two courses are taught by tenured ortenure-eligible faculty, while the comparable figure for statistics PhDdepartments is 41%. On the other hand, it could be the result of differentapproaches to the course by the two departments.

TABLE FY.5 Percentage of enrollment in Elementary Statistics (no calculus) and Probability and Statistics (no calculus) taught by tenured/tenure-eligible, other full-time, part-time, and graduate teaching assistants in Departments of Mathematics by size of sections and type of school: Fall Alsopercentage of students in classes requiring computer assignments, total enrollments (in thousands) and average section sizes.

Course

Elementary

Statistics (no

calculus)Lecture with recitation

Regular section

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TABLE FY.6 Percentage of enrollment in Elementary Statistics (no calculus) and Probability and Statistics (no calculus) taught bytenured/tenure-eligible, other full-time, part-time, and graduate teaching assistants in Departments of Statistics by size of sections and typeof school: Fall Also percentage of students in classes requiring computer assignments, total enrollments (in thousands) and averagesection sizes.

Course

Elementary

Statistics (no

calculus)

Lecture with recitation

Regular section

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Graduate TAs

Part-time

Other full-time

tenure-eligible

(PhD)

FIGURE FY.6 Enrollment in ElementaryStatistics (no calculus) in Departments of Statisticswith PhD programs by type of instructor: Fall

Graduate TAs

Part-time

Other full-time

tenure-eligible

Univ (PhD) Univ (MA) Coll (BA)

FIGURE FY.5 Enrollment in Elementary Statistics (no calculus)in Departments of Mathematics by type of instructor and type ofschool: Fall 1995.