MAA Calculus Study: Progressive Teaching

Last month (MAA Calculus Study: Good Teaching) I discussed the student-described attributes of instructors that were highly correlated with improvements in student confidence, enjoyment of mathematics, and desire to continue to study mathematics. This month I will discuss a second set of instructor attributes that we are labeling "Progressive Teaching" because they are generally associated with approaches to teaching and learning that focus on active engagement of the students.

Here the evidence for improved results is less clear. In particular, Sadler and Sonnert discovered a strong interaction with the attributes we are calling "Good Teaching": teachers who rated high on Good Teaching improved student outcomes if they also rated high on Progressive Teaching. But if they rated low on Good Teaching, then a high rating on Progressive Teaching had a strongly negative effect on student confidence. This might have been expected. Good Teaching describes student-teacher interactions, including the degree to which students feel encouraged to participate in class and supported by the instructor. It is not surprising that students who are encountering unfamiliar approaches to classroom learning react negatively if they believe that that the instructor is not encouraging or supportive.

We also have evidence of some consistently positive effects from Progressive Teaching. Even with a low score on Good Teaching, Progressive Teaching was seen to be helpful in convincing students to continue the study of mathematics. Our conclusions are that:

a.       Good Teaching and Progressive Teaching are independent clusters of student perceptions of instructor behaviors,

b.      Good Teaching is more important to student persistence than Progressive Teaching,

c.       both can serve to improve student outcomes, and

d.      teaching is most effective when instructors rate high on both measures.

There were 12 student responses that clustered into what we are calling Progressive Teaching:

My calculus instructor frequently
1.      Assigned sections of the textbook to read before coming to class.

2.      Had students work with one another.
3.      Had students give presentations.
4.      Asked students to explain their thinking in class.
5.      Required students to explain their thinking on homework assignments.
6.      Required students to explain their thinking on exams.
7.      Held whole class discussions.

My calculus instructor did not frequently
8.      Lecture.

Assignments completed outside of class
9.      Required that I solve word problems.
10.  Were problems unlike those done in class or in the book.
11.  Were often submitted as a group project.
12.  Were returned with helpful feedback and comments.

With one exception, the following graphs show the percentage of students who reported that their instructors employed each of these practices often or very often (a 5 or 6 on a Likert scale from 1 = not at all to 6 = very often). The exception is practice #8. Here we record the percentage of students who responded 1, 2, or 3 on the same scale to the question, "During class time, how frequently did your instructor lecture?".

We see that for most of the instructor behaviors (practices 1 through 8), the undergraduate colleges and two-year colleges are where these are most likely to be employed. The relatively large percentage of instructors at masters universities who had students give presentations in class (13% as opposed to 6% at all other types of institutions) is still small and may be an artifact of the relatively small number of responses from students at masters universities (305 students at 18 institutions).  The research universities are where we find the most challenging problems being posed on assignments, either word problems or those unlike those done in class or in the book. Instructors at two-year colleges provide the most helpful feedback on assignments, instructors at research universities the least helpful feedback.

Figure 1: Instructor practices 1 through 3 and 8

Figure 2: Instructor practices 4 through 7

Figure 3: Instructor practices 9 through 12

The MAA national study of calculus, Characteristics of Successful Programs in College Calculus, is funded by NSF grant no. 0910240. The opinions expressed in this column do not necessarily reflect those of the National Science Foundation.