Observations and Interviews of Students Using their Math Textbooks

Posted on August 6, 2012 by

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Rezat, Sebastian. 2012. “Interactions of Teachers’ and Students’ Use of Mathematics Textbooks.” In From Text to “Lived” Resources, ed. Ghislaine Gueudet, Birgit Pepin, Luc Trouche, Andrea Peter-Koop, and Patricia Wilson, 7:231–245. Mathematics Teacher Education. Springer Netherlands. http://www.springerlink.com/content/kg0q6474u8630353/abstract/
Methods:
  • The main aims of the study were to identify activities in which the mathematics textbook is incorporated in as an instrument for learning, and to analyse the ways students utilise their mathematics textbooks to learn mathematics (p. 233)
  • The data collection method is characterised by a triangulation of questioning,
    observation and interviews. Firstly, data on teacher mediation of textbook use in the
    classroom were collected by classroom observation. Field notes captured every use
    of the textbook in class. Both, the uses of the textbook by students and by the teacher
    were taken into account. (p.233)
  • Additionally, they were asked to explain the reason why they used the part
    they highlighted in a small booklet by completing the sentence “I used the part
    I highlighted in the book, because . . .”. This method was developed to get the
    most precise information about what the students actually use and why they use
    it. Furthermore, this method facilitated data collection at different locations, for
    example at school and at home. (p.233)
  • Thirdly, stimulated recall interviews were conducted with selected students. The
    method was used in the way that students were confronted with their own markings
    and comments in the book and were asked to explain their way of proceeding. These
    data on students’ use of textbooks gathered in the booklets and in the interviews has
    proven particularly illuminating in revealing information about teacher-mediation
    of textbook use (p.233)
  • Data were collected for a period of 3 weeks from 4 teachers and 74 students
    in 6th and 12th grade from two German secondary schools (Gymnasium). Within
    the German tri-partite school system, these schools are considered to be for highachieving
    students. (p.234)
Findings:

  • In planning activities teachers rely heavily on textbooks (Bromme & Hömberg, 1981; Chávez, 2003; Hopf, 1980) and the mathematical content of the classroom is heavily influenced by the text (Johansson, 2006; Schmidt, Porter, Floden, Freeman, & Schwille, 1987) (p.231)
  • Mathematics textbooks are used by teachers in two dominant ways, namely as a source for tasks and problems (Pepin & Haggarty, 2001, p. 168), and as a guide for instruction. The latter relates to decisions about
    what to teach, which instructional approach to follow, and how to present content
    (Valverde et al., 2002, p. 53). (p.231)
  • In the analysis of three Swedish teachers organization of their mathematics lessons, Johansson (2006) found that the mathematical content in the classroom is influenced by the textbook to a large extend even when the
    textbook is not apparent for two of the three teachers. Stodolsky (1989) concludes
    from her investigation of six fifth grade teachers’ use of mathematics textbooks that
    “math textbook content tends to place something like a cap on content coverage in
    classrooms” (p. 176). (p.232)
  • Teacher 1 (6th grade) uses tasks from the book only once in a while but he draws
    attention to the book in a general way almost every lesson. Whenever he asks the
    student to do a task or problem he points to the book as a helpful means, for example
    “If you don’t know how it is done you can look it up in your textbook”1 or “in order
    to do the following task there is a resource you might use: your book”. In addition, he
    arranges teaching scenarios where students have to use their books to find assistance. (p.235)
  • Teacher 2 (12th grade) uses tasks and problems from the book mostly for assigning
    homework, for example “Homework, due Monday: Page 184, number 5 b, e, h”.
    After introducing the integration by parts rule as a new subject she points to the
    book in a general manner: “What we have done today you can find on page 182”. (p.235)
  • Teacher 3 (6th grade) and teacher 4 (12th grade) use the mathematics textbook
    predominantly in a way that is regarded as typical in the relevant literature, namely
    as a collection of tasks and problems. The structure of the lessons of teacher 4 can
    be best described as a sequence of tasks and problems from the book with short
    instructional interludes. Typically, he refers to the book in the following way: “And
    now we want to look inside our books on page 22, number 7, please”; “Let’s look
    inside the book on page 33, number 2, please”; “For Wednesday, please work on
    numbers 3, 4, and 5 on page 33”. (p.235)
  • The first dimension relates to the way in which the students’ use of the textbook is affected by the teacher. Students’ use of textbooks might be influenced directly or indirectly by the teacher. All references to the
    textbook quoted above are explicit: The teacher is talking about the book in some way. Thus, the students’ attention is drawn directly to the book. However, it will be shown later that students’ utilisations of mathematics textbooks are also influenced indirectly by the mere use of the textbook by the teacher in the classroom.
  • The second dimension of mediation of textbook use relates to the specificity
    in which the teacher refers to the book. Teacher 4 typically refers to a specific section in the book, for example page 22, task number 7. On the contrary, teacher 1’s
    references to the book are general. He does not refer to specific sections, but draws
    attention to the book in a general way. In the case of teacher 1, the students have to
    decide themselves which section on which page they are using. Specific and general
    mediation of textbook use can only appear in combination with direct mediation,
    because the characteristic of indirect mediation is that the teacher does not refer to
    the book at all, but the students are influenced by its use in class.
  • The third dimension relates to the binding character of the mediation. Teachers’
    mediation of textbook use might be voluntary or obligatory. Teacher 1 mediates the
    use of the textbook as a voluntary task. He reminds the students that they can use
    the book in order to get assistance. But, the students do not have to use the book if
    they do not need assistance. In contrast to teacher 1, the mediation of textbook use
    of teacher 4 is obligatory. The students do not have a choice to use the book or not.
    They are supposed to work on the assigned tasks and problems (p.236)
  • Emma (6th grade) uses tasks from her mathematics textbook voluntarily for consolidation.
    First of all, she repeats tasks that were done in the mathematics class.
    Additionally, she picks tasks that are adjacent to these tasks from the mathematics
    class in the book. She explains her way of proceeding as follows: “If we did no. 4
    in the mathematics class then I will do no. 5, because it is similar.” (p.237)
  • One of Merle’s (6th grade) utilisation schemes of the textbook is her use of kernels
    and excerpts from the expository section of the textbook lesson that follows
    the textbook lesson corresponding to the latest topic of her mathematics class. She
    infers the relevance of the section from its position in the book. Underlying this
    inference is the assumption that the order of the textbook lessons corresponds to the
    succession of the topics in the mathematics class. (p.238)
  • If the teacher does not use tasks from the
    book, Emma will not utilise her textbook. In contrast to Emma the teacher’s use of
    the textbook is not a prerequisite for Merle’s utilisation. She can find out the lesson
    in the textbook that corresponds with the latest topic in the mathematics class herself.
    However, if the teacher does not follow the sequence of the book her scheme is
    not useful (p.238)
  • Merle’s case sheds a different light on teachers’ close adherence to the book.
    Whereas an instruction that closely follows the book is sometimes connoted negatively
    (Ewing, 2004), it provides the foundation for an effective utilisation of the
    book by Merle…Whereas in the first case the teacher’s use of textbooks in class is
    a prerequisite for Emmas’ self-directed selection from the book, the second case
    shows that a close adherence of teacher’s instruction to topics and sequencing in the
    textbook might afford students’ self-regulated learning (p.238)