Quantitative Results

The primary question of interest was whether the quality of participation in the Calculus Conversation activity was related to performance on a conceptually related but contextually varied exam question.  Examination of those two variables becomes important to understand the overall analysis. Calculus Conversation responses were coded as high quality (response is clear and well thought out, moves the conversation forward -- 4), average quality (response is understandable, keeps the conversation even -- 3), low quality (response is vague, confuses the conversation -- 2) or did not participate (1). Table 1 shows the overall average performance for students on each of the Calculus Conversation problems. The high averages are more indicative of instructor reluctance to discourage participation than to actual contributions by students to the conversation. It is important to mention that there was a noticeable difference in the distribution of grades for the Calculus Conversation activity by section (Appendix III, Tables 10 a,b,c)  that certainly clouds any conjectures drawn from the quantitative analysis.
TABLE 1

Problem 1

Problem 2

Problem 3

3.65

3.53

3.45

           

     Table 2 shows the average performance of all students on each exam question conceptually related to but contextually varied from the Calculus Conversation problems.

TABLE 2

Exam 1 Question Average

Exam 2 Question Average

 Exam 3 Question Average

64.48 %

86.97 %

60.03 %

     Table 3 shows the average exam question performance for students in each of the Calculus Conversation scoring categories.  For example, on problem 1 the related exam question average was 43.40 % for students who received a grade of 3 on the Calculus Conversation problem.  Recall that students could score from 1 to 4 (where 4 was highest) on each Calculus Conversation problem.  In general one does see a pattern of lower Calculus Conversation scores associated with lower grades on the related exam question. 

TABLE 3

Problem 1

Exam  1 Question

Problem 2

Exam 2 Question

Problem 3

Exam 3 Question

1

25.00 %

1

83.00 %

1

52.80 %

2

--

2

79.00 %

2

--

3

43.40 %

3

79.80 %

3

53.42 %

4

76.04 %

4

90.56 %

4

64.29 %

    A statistical examination of the relationship between the Calculus Conversation problem score and the related exam question is significant (p < .01).  Table 4 shows the results of a Pearson’s Product Moment Correlation for each set of relationships.

TABLE 4

Calculus Conversation

Exam 1 Question

Exam 2 Question

Exam 3 Question

Problem 1

      .420

Problem 2

      .354

Problem 3

      .503

     The results do show that a statistical relationship exists between a student’s performance on the Calculus Conversation activity and performance on a conceptually related but contextually varied exam question.  While we were pleased to see that participation in Calculus Conversation correlated with performance on the related exam questions, we do not necessarily conclude that this relationship is causal.  Not surprisingly, we also found a statistically significant relationship between  students' ACT math scores and their performance on the related exam questions.  However, we do note that prior to the insertion of the Calculus Conversation activity, average exam scores on questions that were conceptually related to the material being studied, but contextually varied from practiced problems had ranged from 25% to 50 %.  This at least leads us to conjecture that the Calculus Conversation activity may enhance students’ abilities to transfer information learned in one context to a new setting.

     We also asked if the relationship between the activity and performance was stronger or weaker in certain populations.  Analysis of the data did not allow us to draw many generalizations for performances subdivided by course section, by gender, by high school versus college students, or for first-time calculus students versus those who were repeating it after having already taken the course in high school.  For a complete discussion of findings for these populations see Appendix III.