Seminal Text on Math Textbook: Love and Pimm (1996)

Posted on July 5, 2012 by

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Love and Pimm.  1996.  “This is so: a text on texts”  Bishop, Alan J. 1996. International Handbook of Mathematics
Education. Springer.

Methods:

A literature review:

  1.   Examines visible features of texts, pedagogic functions.
  2.   Discusses use of text materials in class and future developments.
  3.   Discusses commercial and governmental constraints.

Problems of the text are revealed. (p.371)

Findings:  

  • Text has already been written.  “This is so” (p.372)
  • Texts are what remain as records of past classrooms. (p.373)
  • Range of text materials:  books, booklets, workcards, disposable worksheets, re-usable masters. (p.373)
  • Textbook is a book designed to provide an authoratative pedagogic version of an area of knowledge.  (Stray 1994)
  • “I’ve come to the conclusion hat the essential difference between book-writing and script-writing isn’t that the latter is mostly dialogue— it’s a question of tense.  A script is all in the present tense.  Not literally, but ontologically.  Whereas, when you write something in a book, it all belongs to the past;  even if you write, “I am writing, I am writing,” over and over again, the act of writing is finished with, out of sight, by the time someone reads the result.  (Lodge 1995, p.285) p.379
  • The presence of a text produces a potential splitting of student focus:  between the teacher and the text (p.380).
  • Rene Thom’s observation.  “As soon as one uses a textbook, one establishes a didactism, an academicism, even if the book be so written as to promote individual research’ (Thom 1973, p.202)
  • Susan Gerofsky draws attention to [the complexity of deixis in mathematics] of current verbal textbook problems, and observes that such problem writers ‘seem to be taking pains to say, “Here is a story, ignore this story” (p.380)
  •  The deictic relation of mathematics text questions to the material world is a highly problematic one.  The questions in texts seem to be referential, yet they actually call the world of which they seem to speak into being.  Mathematics texts can be viewed not as speaking of an external world, but instead as offering substitute experience that is largely self-contained.  (p.381)
  • There are a few devices that break the presumed linear textual flow of reading:
    1. Answers at the back of the book
    2. Cross-references, appendices, footnotes
    3. Use of margins (p.381)
  • With diversity of images comes a variety of intentions and both tacit and explicit ways of working on such images for mathematical ends (p.382)
  • Mathematical texts increasingly adopting visual conventions from popular forms:  hands, speech bubbles, cartoons, magazine-style layout;  symbolizes change away from exposition towards narrative as the dominant rhetorical mode.
  • Observes more photographic material in school texts
  • A fundamental issue of the pedagogy of mathematics is concerned with the question of how to make written communication ideographic or how to make mathematical thinking visual and active (Otte 1983: p.25) (p.384)
  • Textbook authors usually regard the student as the main reader.  They want teachers to encourage students to read the book.  Because they cannot intervene directly in the communication between teacher and students, the authors usually write the textbook from the teacher’s position.  (Kang & Kilpatric 1992: p.5) (p.385)
  • Devices to organize the reader’s work:  exposition, explanation, questioning, exercises, examples, and tests.  The most widespread type of text organisation is the ‘exposition-examples-exercises’ model (p.385)
  • Exposition:  student arrival at destination of knowledge will be clearly signalled;  students become impatient with exposition and skip to the ‘essential’ results (p.387)
  • Examples:  intended to be paradigmatic or generic offering students a model to be emulated in the exercises…Assumes that student forms generalization from examples which can then be applied to exercises.  However many texts do not state what generalizations students are assumed to have made. (p.387)
  • Exercises:  Principal means by which student is encouraged to be active reader of the text (p.387).
  • Exposition-examples-exercises – can be used flexibly (p.388)
  • The texts aim at a precise fixation of every single step of the student, developing fro that purpose an enormous apparatus of unnecessary terminology which hides the fundamental ideas and causes confusion about the character of theoretical generalisations and about matehmatics in particular (Otte 1983:  p.25) (pp.388-389)
  • Those texts that obsessively aim at arousing a precise response on the part of more or less precise empirical readers […] are in fact open to any possible aberrant decoding (Eco 1979: p.8) (p.389)
  • Since the intention of the text is basically to produce a model reader able to make conjectures about it, the initiative of the model reader consists in figuring out a model author that is not the empirical one and that, in th end, coincides with the intention of the text (Eco 1992:  p.64) (p.392)
  • One intent of providing a diagram is to stabilise thought, a role shared by other symbols, as well as to offer a focus for attention.  Yet, because diagrams seem so iconic, so transparent, it is easy to forget that they too need to be ‘read’ rather than merely beheld (p.393)
  • Teachers in the USA depend heavily on textbooks.  This dependence has roots that go back to the introduction of free public education into a frontier society:  the textbook was used to compensate for a shortage of well-educated teachers.  As a result, textbooks are marketed much like automobiles:  publishers’ representatives find out what the consumer wants and then the publishers compete to offer it to him in the most attractive package possible.  Novelty is at a premium;  yet the changes offered are frequently cosmetic and rarely radical.  The greatest changes in US textbooks in the last three decades have come from outside the commercial arena — many of them in response to the stimulus provided by federally-funded projects — but in each case the forces of the marketplace acted quickly to dampen the change (Howson et al. 1981, p.62) (p.395)
  • States and school districts will not adopt a book unless it has extensive accompanying material:  teachers manuals, software, photocopiable masters, assessment materials, enrichment booklets, foreign language assistance, videodiscs…)…These forces result in a relatively oligopolistic system….independence of each state in the US (and province in Canada) with regard to education results in state/province-wide or curricular guidelines needing to be met.  Textbooks are usually created by intersection rather than union, which often results in anodyne, lowest common denominator text materials, rendering serious innovation (whether curricular or pedagogic) unlikely (p.396)
  • What research data could there be?  There is often no discussion to record, no actions by the teacher worth noting.  Students sit at their tables, each with their copy of the same textbook, each reading the text and writing in their exercise books.  The teacher may have interacted with the whole group before this happens — explicating the text — or may talk to individual students about their work while the rest are working.  But frequently students are silent, working separately from anyone else.  The use of texts by a student outside of class, working alone, perhaps as part of their homework, following up a lecture, or perhaps because the course is taught ‘at a distance’ is even more opaque to enquiry (p.397).  Some studies have been undertaken of discussions by groups of students arising from consideration of textual materials (p.397)
  • Students working on their own through a text, because they are not being assisted by a teacher, are likely to create a model author who is dramatically limited.  There is evidence that students tend to stick rigidly to the tasks as they see them defined.  They can be described as working throught the text rather than working on it.  (p.398)
  • Because students have to be able to work through the texts unaided, the mathematical ideas, the types of task and the language need to be such that they will not give difficulty to an isolated student (p.399)
  • Must see objects as text to be read.