Student Course Evaluations
Instrument 23: Combinatorics Interview
Project: Teaching Introductory Combinatorics by Guided Group Discovery
Dartmouth College
Funding Source: NSF: Course and Curriculum Development (DUE)
Purpose: To gauge the "depth and completeness of students' understanding of the material" in intervention and comparison group versions of a combinatorics course
Administered To: Post-secondary students
Topics Covered:
- Attitudes & Beliefs (Student): content, understanding
- Academic Habits: study habits
Format/Length: 11 open-ended questions
COMBINATORICS INTERVIEW
WINTER 2001 [TRADITIONAL]
WINTER 2002 [EXPERIMENTAL]
1. Tell me a little bit about your math background.
- What is your intended major?
2. Why did you decide to take this course?
- What did you hope to get out of it?
3. How was this course different from other math courses you've taken?
- Did those differences change what you learned?
- . . . the way you learned it?
4. How regularly did you attend class? If you frequently skipped class, why did you do
so? What consequence did you perceive for doing so? Would you feel the same about
class attendance in other math courses?
5. Can you tell me something you learned in the course?
- Why did you pick that to tell me?
6. Can you give me an example of how you might use something you learned in this
course in real life, perhaps in a job, or in another math course?
7. Now I'm going to ask you to engage in what psychologists call "metacognition,"
which is thinking about how you think and learn! I want you to try to describe your own
mental processes as you learned things in the course.
- What was the easiest concept for you to master? Why do you think that concept
was the easiest for you?
Probe: the way it was presented? knowing similar things already? spending more
time on it?
- What was the hardest concept to understand? Why was that the most
challenging for you? If you did finally understand it, what was the process that
moved you from not understanding to understanding?
- Were there any teaching strategies that you found particularly useful—or not
useful—for learning this material? Why were they particularly helpful?
Probes: lecture? class discussion? office hours? the homework problems? the
way homework was structured? (I.e., where did learning happen for you?)
- Compared to how you feel after taking other math classes, how solid do you feel
about the material in this class?
EXPERIMENTAL GROUP: Your course involved a lot of in-class group work. I'd like to find out how that process worked for you.
- First, how was the rationale for collaborative group work explained to you in the
class? Were you given guidelines about how to work as a group?
- How did you feel about the way the in-class groups were structured (e.g.,
same/different from day to day, self-selected/assigned). Did you find this
structure helpful? How did you feel about having a fast group break off toward
the end of class?
- Please describe the dynamics of your group. What factors facilitated
conversation? Which inhibited it? (Probe: nature of problem, characteristics of
group members)
- Did working in groups help you understand the mathematics? Why? Was it
more or less useful than spending that time on other common classroom
activities, such as lecture and whole-class discussion? How was the work related
to the homework, and class discussions?
- How would you describe the instructor's role?
- How did you feel about reading and commenting on others' work, and having
other students read and comment on yours? Did it help your learning?
- What did you think of the grading system? Did it fairly represent your learning
in the course?? Did it help you learn the math (i.e., did it motivate you)?
- One of the goals of this course is that students will learn to work "like
mathematicians." What do you think working like a mathematician entails? (i.e.,
how is it different from working like a math student?)
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8. Did taking this course change the way you think about mathematics? How?
- How would you define what math is, as a discipline?
- Has your understanding of what math is—your definition of math—changed as
a result of this course?
8a. (not used with experimental group.) People who study how mathematics is learned
often talk about "working like a mathematician." What do you think it means to work
like a mathematician? How is the way a mathematician works different from the way
other people—math students, everyday citizens—approach mathematics?
9.Did you find this course worthwhile?
a. If so, what factors made it worthwhile? Were there also weaknesses in this
course, things that could be improved?
b. If you did not find it worthwhile, what accounts for that? Were there strong
points, nonetheless?
10. How would you advise another student thinking about taking this course?
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