Date of Award


Degree Name

Doctor of Philosophy



First Advisor

Dr. Christine Browning

Second Advisor

Dr. Robert Laing

Third Advisor

Dr. Joseph Buckley

Fourth Advisor

Dr. Joshua D. Naranjo


The purpose of this study was to determine the impact of writing assignments on second-semester calculus students’ understanding of the limit concept, using both qualitative and quantitative techniques. The study involved two sections of second semester calculus (n = 37, 34) at Western Michigan University during the fall semester of 1997.

The treatment group completed six writing tasks focusing on the mathematical concept of limit. These conceptually-oriented writing assignments replaced some of the problem sets that the instructor would have normally assigned. The control group did not engage in writing tasks but handed in problem sets more frequently than the treatment group. Both sections used the same textbook and department syllabus. Prior to the course, the investigator met with the two instructors to confirm that both followed a traditional lecture/discussion format, and further, she monitored their classrooms intermittently during the semester.

The investigator used the writing assignments, as well as transcripts from a series of interviews of a subset (n =5) of the treatment group, to assess cognitive growth. This qualitative assessment was based on action-process-object-schema (APOS) theory. Quantitative analysis of student performance was based on a comparison of three computational problems common to the two sections’ final examination. These problems focused on the limit concept and provided for a two sample t-test to compare mean scores.

The students that performed the writing tasks increased measurably in their conceptual understanding of the limit concept. Some were able to achieve elements of object-level understanding, a level never before reported in the literature. The interviews showed that the subjects generally rose at least one APOS level. An exception was the one subject who did not engage in the assignments. Furthermore, all differences in the final examination problem scores favored the treatment students. These differences were significant in two of the three limit problems (p < .05). Finally, students reported they saw the benefits of writing, recommending its continued use.

Writing assignments focusing on the limit concept appear to provide the necessary cognitive conflict and resolution for students both to outgrow their misconceptions and to improve their mathematical performance.


Fifth Advisor: Dr. Dennis Pence

Sixth Advisor: Dr. Arnold Ostebee

Access Setting

Dissertation-Open Access