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.

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

8. Lecture.

*not*frequently8. Lecture.

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.*

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