Good Questions


Maria Terrell, PI, mst1@cornell.edu

Robert Connelly Co-PI


Project website http://www.math.cornell.edu/~GoodQuestions/


Can you raise the visibility of key calculus concepts, promote a more active learning environment, support young instructors in their professional development in their early formative teaching experiences, and improve student learning? We think the answer is yes, if you ask students Good Questions and encourage them to refine their thinking with their peers. What makes a question good? A Good Question


We tested Good Questions Fall 2003 in traditional first semseter calculus at Cornell –350 students, 17 small sections, 14 different instructors with the freedom to choose teaching method (ie to use or not use GQ.) We used electronic polling devices and surveys to collect data.


What did we learn about how instructors used GQ?

Instructors used the questions 3-4 days per week, 1-2 days per week, or rarely/ never.

Good Questions were tagged with three labels (Quick Check, Probing, and Deep) that reflected that questions were designed to assess and to engage students in progressively deeper levels of mathematical thinking and reasoning. Most instructors most frequently used Quick Checks in their teaching, but some instructors primarily used Probing and Deep questions. Some instructors regularly followed each Good Question with peer discussion, some instructors only occasionally used peer discussion, and others explained the answers to the class themselves with no peer discussion. We classified these types of instructor use as:

Deep, many Deep and Probing questions, peer discussion, GQ used 1-4 times per week;

Heavy Plus Peer, GQ used 3-4 days per week with regular use of peer discussion;

Heavy Low Peer, GQ used 3-4 times per week but minimal/no use of peer discussion;

Light to Nil, GQ used 1-2 times per week or not at all with no significant use of peer discussion.


What kind of data on student performance did we gather?

Regular course-wide common exams--- 3 preliminary and one comprehensive final, were graded consistently across all classes. Each exam had questions identified as conceptual.

SAT and demographic data --were provided to us by university administration.


What do the data suggest?

The data suggest different ways of using GQ appear to effect student learning:




















Differences in student learning increase through the term and are most pronounced on the comprehensive final


Ranksum Tests Difference in Medians Between “Deep and Heavy Peer” (High Peer) and “ Heavy Low Peer and Light to Nil” ( Low Peer) Groups

Variable

No/Low Peer

Medians

N

High Peer

Medians

N

Null: Mds Equal?

(a=0.05)

Level of Signif

Verbal SAT

660

148

660

95

Accept

0.71291

Math SAT

680

148

700

95

Accept

0.060299

Prelim1

84

136

87

97

Reject

0.0055365

Conceptual

Sub score

21

135

22.5

97

Accept

0.085491

Prelim2

76

153

81

96

Reject

0.0070296

Conceptual Sub score

19

153

21

96

Reject

0.001862

Prelim3

73

152

78.5

96

Reject

0.0093109

Conceptual Sub score

34

148

35

96

Reject

0.041864

Final Exam

119

153

128.5

96

Reject

0.0008038

 

Support for the Good Questions project is provided by the National Science Foundation’s Course, Curriculum, and Laboratory Improvement Program under grant DUE-0231154.