The Calculus I Instructor

*David M.
Bressoud, *June 2011

Last month [1] I reported on student data from the MAA’s survey [2] of mainstream Calculus I classes. We also surveyed the instructors, both at the start and at the end of the Fall term in 2010, gathering basic demographic information as well as information about how the class was taught and attitudes toward student learning. We are hoping to learn whether there are any correlations between instructional practice or instructor attitudes and student performance, both in terms of learning the material and in terms of intention to persist in a field that requires at least a full year of college calculus.

Right now, this is just a report of some of the cumulative data, collected from 700 instructors at 212 colleges and universities, both 2- and 4-year programs. All instructors in this survey, including the graduate students, were the instructor of record for their class. The results reported here are drawn from a survey completed by the course coordinator before the term began, an instructor survey completed at the start of the term, and an instructor survey completed at the end of the term.

I did not find any of the results particularly surprising. Graphing calculators are still very common, regularly used and required by 61% of the instructors. Only 37% use computer demonstrations in class, and only 21% expect their students to use computer software such as

MathematicaorMatlabin conjunction with the class. Online homework systems such asWeBWorKare now being used by 45% of instructors (often complemented by other ways of collecting homework).Most instructors use classroom quizzes at least occasionally, and most instructors give three or four exams before the final exam. The emphasis in exams is on computational technique, but almost all instructors have some points devoted to graphical interpretation of central ideas, and most include some complex or unfamiliar problems as well as proofs or justifications.

Most instructors see themselves as fairly traditional. They view lecture as the best way to teach students and believe that procedural fluency precedes conceptual understanding.

Perhaps the most intriguing insight from this study was how accurately instructors at the start of the term were able to predict the percentage of D’s, F’s, and W’s in their classes. Most of the instructors have taught Calculus I many times. Their collective accuracy may simply reflect the consistency of their experience combined with the fact that the average of the estimates made by a group tends to be much closer to the true number than one would expect from any individual. But it does raise the question whether the final grade distribution was in some sense shaped by instructor expectations of what it would be.

Demographics of Instructors

- 48% are tenured or tenure-track faculty, 28% are other full-time faculty, 9% are part-time faculty, 15% are graduate students.
- 70% are male.
- 79% are White, 13% are Asian, 3% are Black; 4% are Hispanic.
- The mean age is 43 with a standard deviation of 14; the median age is 41 with an interquartile range of [31,56].
- PhD is the highest degree for 59%, Master’s for 34%, Bachelor’s for 7%.
- 76% earned their undergraduate degree in the United States, 90% earned their highest degree in the United States.
- 17.5% were teaching calculus either for the first time or for the first time within the past five years.

Characteristics of the course

- Class size distribution at the end of the term was

- 20 or fewer, 19.5%
- 21–30, 35.7%
- 31–40, 24.5%
- 41–50, 7.3%
- 51–75, 3.5%
- 76–100, 3.2%
- 101–150, 3.2%
- 151–250, 2.4%
- more than 250, 0.8%
- From the point of view of the student (percentage of students who are in classes of each size), the distribution at the end of the term was

- 20 or fewer, 7.8%
- 21–30, 23.4%
- 31–40, 20.9%
- 41–50, 8.2%
- 51–75, 5.4%
- 76–100, 6.8%
- 101–150, 10.0%
- 151–250, 11.6%
- more than 250, 5.9%
- Asked what percentage of student attended each class session in a typical week, instructor responses had a mean of 81% and standard deviation of 14%; median of 85% with an interquartile range of [75%, 90%].
- 23% of the classes were taught with recitation sections led by TA’s.
- 95% used a textbook selected by the department:

- 43% used one of the editions of Stewart.
- 19% used Hughes-Hallett
et al.- 9% used Thomas/Weir/Hass/Giordano or Hass/Weir/Thomas.
- 6% used Rogawski.
- each of the other textbook authors was cited by less than 4%.
- 3% of classes were taught either entirely or partially via online distance learning.
- 4.6% of classes were classified as honors.

Use of Technology

- 93 of the 212 colleges or universities that responded to the survey (44%) have clickers available for their faculty. Two of these 93 recommend their use, and two more require their use. 36 of the institutions (17%) provide training for their faculty on the use of clickers in the classroom.
- 34% of instructors frequently or always look for ways to use technology to illustrate an idea in class.
- 35% occasionally demonstrate an idea in class using a graphing calculator, an additional 9% do so in at least half of their class meetings; 30% occasionally demonstrate an idea in class using a computer algebra system (such as
Mathematica), an additional 7% do so in at least half their class meetings.- 33% occasionally have students use their graphing calculators during class, an additional 28% do so in at least half of their class meetings; 15% occasionally have students do work with a computer algebra system during class, an additional 6% do so in at least half their class meetings.
- 61% require students to use graphing calculators on out-of-class assignments; 45% require students to use online websites; 23% require students to work with a computer package such as
MathematicaorMatlab.- 53% allow graphing calculators on exams; 27% require graphing calculators for exams.
- 45% use an online homework system (such as
WeBWorK) for students to submit at least some of their homework; 63% have students submit at least some of their homework on paper; 5% have students submit homework electronically but not via an online homework system (e.g. using email or a course management system).- 39% grade at least some of the homework themselves by hand; 28% use a grader to grade at least some of the homework by hand (3% do both).

Other Instructor Practices

- 69% frequently or always look for application problems to motivate an idea.
- 57% frequently or always follow how the textbook develops the ideas; 56% frequently or always look to alternate sources for different ways to teach the idea.
- 50% give occasional quizzes, an additional 20% give quizzes in at least half of their class meetings.
- 25% give two or fewer exams before the final exam, 37% give three such exams, 26% give four such exams, and the remainder give five or more such exams.
- 14% assign one or two projects (group or individual) during the term; an additional 12% assign more than two projects.
- 56% supply supplemental curriculum materials for their students, 29% supply lecture notes for their students, 26% supply computer animations or interactive software for their students.
- Instructors were asked what percentage of the points in their exams focused on each of the following five types of questions. They were given the choices of 0% through 100% in increments of 10%. They were told that the percentages did not need to add to 100%.

“Skills and methods for carrying out computations (e.g. methods of determining derivatives and antiderivatives).”

- 20% or less of the points, 11% of instructors.
- 30–40% of points, 30% of instructors.
- 50–60% of points, 34% of instructors.
- 70–80% of points, 21% of instructors.
- 90–100% of points, 4% of instructors.
“Graphical interpretation of central ideas.”

- None of the points, 2.5% of instructors.
- 10% of points, 30% of instructors.
- 20% of points, 36% of instructors.
- 30% of points, 20% of instructors.
- 50% or more of points, 6% of instructors.
“Solving standard word problems.”

- None of the points, 1.2% of instructors.
- 10% of points, 26% of instructors.
- 20% of points, 40% of instructors.
- 30% of points, 19% of instructors.
- 50% or more of points, 7% of instructors.
“Solving complex or unfamiliar word problems.”

- None of the points, 30% of instructors.
- 10% of points, 47% of instructors.
- 20% of points, 14% of instructors.
- 30% of points, 4% of instructors.
- 40% or more of points, 5% of instructors.
“Proofs or justifications.”

- None of the points, 33% of instructors.
- 10% of points, 50% of instructors.
- 20% of points, 10% of instructors.
- 30% of points, 4% of instructors.
- 40% or more of points, 3% of instructors.

Instructor Attitudes

- 53% have a very strong interest in teaching Calculus I, and an additional 34% have a moderately strong interest; 2% are not at all interested in teaching Calculus I.
- 93% have a very or moderately strong interest in improving their own teaching.
- 39% describe their teaching as very or somewhat innovative; 61% as very or somewhat traditional.
- 64% agree with the statement “All students in beginning calculus are capable of understanding the ideas of calculus.” 23% disagree or strongly disagree with this statement.
- 64% agree with the statement “Calculus students learn best from lectures, provided they are clear and well-prepared.” 16% disagree or strongly disagree.
- 64% agree with the statement “Understanding ideas in calculus typically comes after achieving procedural fluency.” 16% disagree or strongly disagree.
- 82% agree with the statement, “It is the student’s responsibility to address his or her deficiencies with prerequisites.”
- 92% agree with the statement “If I had a choice, I would continue to teach calculus.”
- On average, instructors at the start of the term expected 26% of their students would receive D, F, or W; 74% would receive C or higher. (Grades reported at end of term were 27% D, F, or W; 73% C or higher.)

[1] David Bressoud, The Calculus I Student,

Launchings, May, 2011, www.maa.org/columns/launchings/launchings_05_11.html[2]

Characteristics of Successful Programs in College Calculus, NSF DRL REESE grant no. 0910240.

Access pdf files of theCUPM Curriculum Guide 2004and theCurriculum Foundations Project: Voices of the Partner Disciplines.Find links to course-specific software resources in the

CUPM Illustrative Resources.Find other

Launchingscolumns.

David Bressoud is DeWitt Wallace Professor of Mathematics at Macalester College in St. Paul, Minnesota, and Past-President of the MAA. You can reach him at bressoud@macalester.edu. This column does not reflect an official position of the MAA.