Student Perceptions of the Use of Writing in a Differential Equations Course

Abstract

The use of writing to learn mathematics at the university-level is a pedagogical tool that has been gaining momentum. The setting of this study is a second-year differential equations class where written assignments have been incorporated into the course. By analyzing survey results and students' written work, we examine the extent to which students view writing as an effective learning strategy, as well as their beliefs about the relationship between mathematical writing and communication. We also discuss what students' narratives reveal about their past mathematical experiences.

Keywords:

• Mathematical writing
• tertiary education
• differential equations
• psychological determinants
• student beliefs

Notes

1 We speak from personal experience. The second-year differential equations course at the university where this study took place has been taught in this way by several instructors. By looking at syllabi and speaking with instructors of introductory differential equations courses at several universities in Canada, we learned that their teaching approaches were very similar to what we had witnessed at the aforementioned institution.

2 McMaster University has an online monitoring system, accessible to all instructors, which shows the number of students who completed teaching evaluations for each course.

3 Copied here verbatim, without any changes in style, grammar or spelling.

4 We label the 12 survey questions as Q1, Q2, … , Q12.

5 Assignment 4.

6 Again, in addition to statistical concerns due to a small sample size.

7 We refer to the 12 students who gave us permission to use their written assignments by the code names S1, S2,…, S12 in order to protect their privacy. If a quote does not have a code name, then it was taken from the survey data.

8 Examination of the Grades 11 and 12 Mathematics curriculum document [17] reveals that the pillars of mathematics theory (definitions and theorems) are not at all discussed. For instance, the word “definition” does not appear in the document; no expectation (each topic in the curriculum comes with a list of overall expectations) states that students should be able to quote and/or create definitions of mathematical objects they are using. Not a single theorem is quoted as such. Neither the logical structure of a theorem (assumption implies conclusion), nor the way it is supposed to be used, nor the common misconceptions about the use of a theorem are discussed.

9 We could not find any students whose quotes suggest that they exhibited a helpless behavior pattern.

10 The instructor includes her responses on the back of the assignment page, but we omit that here.

11 Assignments 2, 3, and 5 included the instructions: Answer each question fully, explaining all reasons. If you use a theorem, explain why you are allowed to use it (i.e., why are the assumptions of the theorem satisfied?).

Additional information

Notes on contributors

Lauren DeDieu

Lauren DeDieu completed her Ph.D. at McMaster University, and is currently a MathCEP Assistant Professor at the University of Minnesota. Her research lies in the intersection of algebraic geometry and combinatorics. Additionally, she has a strong interest in tertiary mathematics education: in particular, psychological determinants of student success in mathematics and the role of programming in the mathematics curriculum. Lauren is a wildlife enthusiast and enjoys taking pictures of squirrels and birds.

Miroslav Lovric

Miroslav Lovric completed his Ph.D. at Ohio State University, and is currently a professor at McMaster University. His research has been focused on modeling in mathematical biology and medicine, and he has supervised a large number of students. He is interested in mathematics education, and has studied the transition from secondary to tertiary mathematics, quality of narratives in math textbooks, as well as teaching mathematics in interdisciplinary contexts. He has authored several mathematics textbooks. Miroslav loves reading books, spending time in nature and traveling.