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Textbook mediation of teaching: an example from tertiary mathematics instructors

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Abstract

Drawing on data from interviews with mathematics faculty in three different types of undergraduate institutions and using Rabardel’s model of instrument use (Vérillon & Rabardel 1995), we describe three ways textbooks mediate college faculty work regarding instruction. The model anticipates epistemic and pragmatic mediations between the instructor and teaching, others, and self, with the textbook playing a significant role. We provide illustrations of each of these mediations as described by the participants. Pragmatic rather than epistemic mediations were more common. In addition, we found that the mediations seem largely dependent on instructors’ categorical perceptions of their students, either as “math students” or as “undergraduate students”. These alternate perceptions resulted in different descriptions of schemas for using the textbook with each type of student. The analysis generates further questions for research regarding either a developmental component or a curricular component that could explain this categorization of students.

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Notes

  1. Source: Integrated Postsecondary Education Data System (http://nces.ed.gov/ipeds/).

  2. The students we surveyed described their own uses of textbooks in different ways than their instructors imagined: in general more students read beyond the examples in the textbook than what their teachers anticipated. However, as it was not part of our research question to compare student and instructor uses, we do not explore these distinctions here. We suggest that such an analysis merits follow-up research.

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Acknowledgment

Portions of this study have been presented at the Research in Undergraduate Mathematics Education Conference, in San Diego, February, 2007, and in the Annual Meeting of the American Educational Research Association, Chicago, April 9–13, 2007. This work has been supported by the Office of the Vice-Provost for Research (#5466) and the Rackham Graduate School at the University of Michigan.

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Authors and Affiliations

  1. University of Michigan, 3111 SEB, 610 East University, Ann Arbor, MI, 48109-1259, USA

    Vilma Mesa

  2. University of Michigan, 2016 SEB, 610 East University, Ann Arbor, MI, 48109-1259, USA

    Brett Griffiths

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  1. Vilma Mesa
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Correspondence to Vilma Mesa.

Appendices

Appendix 1. Interview protocol

The purpose of this interview is to gather information about how instructors of undergraduate mathematics use their textbooks. First I would like to ask you a few background questions and then general and specific questions about your uses of textbooks.

Background questions

  1. 1.

    What is your academic background (e.g., bachelors when and where; master’s, PhD)?

  2. 2.

    How many years have you been teaching and what types of courses?

  3. 3.

    Describe the courses you teach currently in terms of audience, class size, textbook used, content, pre-requisites, etc.

  4. 4.

    How did you use your mathematics textbooks when you were studying mathematics as an undergraduate? As a graduate student?

    1. (a)

      Follow-up if there are differences: to what do you attribute the different uses you gave to the textbook?

    Uses of textbooks

  5. 5.

    Let’s look at one of your current courses.

    1. (a)

      How did you select the textbook that you are currently using?

    2. (b)

      What would you say is the main goal of this textbook?

    3. (c)

      In which ways do you use the textbook for preparing your class (e.g., for designing the syllabus, for assigning homework, for assigning projects, for preparing class, etc.)?

    4. (d)

      What features of the textbook that you are using for this class do you find the most and least useful and why?

    5. (e)

      In which ways and how frequently do you use the textbook during class (e.g., for checking reading, for assigning in-class work, for checking answers, etc.)?

    6. (f)

      Imagine you were to design a book that would assist you in teaching mathematics for this particular group of students. Besides the mathematical content, what features would you include and why?

    7. (g)

      How is your use of this textbook different from the use of the textbook for your upper division courses?

    8. (h)

      How do you think your students in this particular course use the textbook?

  6. 6.

    Any other thoughts or comments?

Appendix 2. Main coding categories and sample of codes

Processes (included 27 codes): What instructors do with the textbooks, prior and during class

  • Classroom interaction—text used in class to go over difficult problems or demonstrate graphics/theorems/equations

  • Classroom interaction—class time allows students to try out questions for homework

  • Instructor prep—creates lecture to loosely follow content of text

  • Instructor prep—writes lecture from text chapters/pace

  • Students required to explain how their problems worked

  • Text assignments are mainly problems from chapter

Textbooks (included 14 codes): What instructors indicate texts are, ought to be, should be or not

  • Text should serve as a reference/recipe book for students

  • Math texts are formal and require different reading skills

  • Text should not be too long

Students (included 11 codes): What instructors indicate students are, should do, ought to do, or not

  • Students today—do not read the text

  • Students today—do problems and only read the text strategically

  • Students today—come unprepared to do college-level work

Environment (included 10 codes): What instructors indicate are the institutional influences on instruction

  • Classes need to be uniform with other sections of the same course

  • The course objectives do not match the time allowed or sequenced

  • Text selection process—by department

Instructors (included 8 codes): What instructors indicate instructors ought or should do or not in classrooms

  • Good instructors add more to the class by deviating from the textbook

  • Instructor should not overly criticize the textbook

  • Teaching draws on existing skills and strengths

Mathematics (included 3 codes): What instructors say about mathematics

  • Mathematics is

  • Mathematics should be

Two more categories (including 39 codes) were useful for contextualizing the data: “Instructor demographics” (years taught, private versus public institution) and “Instructor as student” (instructors’ own descriptions of how they used their textbook when they were students).

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Mesa, V., Griffiths, B. Textbook mediation of teaching: an example from tertiary mathematics instructors. Educ Stud Math 79, 85–107 (2012). https://doi.org/10.1007/s10649-011-9339-9

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