The author’s demonstration starts with the language
used in a US mathematics textbook.
Voice:
operationalize the
notion of voice by focusing on the construction of relationships and roles for
the author and reader (teacher and students) by examining particular linguistic
features of the textbook.
Language choices can
construct the reader as a thinker and in other cases as a scribbler.
Interpersonal
function (the speaker’s meaning potential as an intruder
into the context of the situation) is central as it focuses on personal
relationships established in a text, and focuses attention on power and
authority.
Inclusive imperative (“consider”,
“define”, “prove”) demands that the speaker and hearer institute and inhabit a
common world or that they share some specific argued conviction about an item
in such a world, and so they construct the reader as a thinker.
Exclusive imperatives (“build”,
“bring”, “create”) requires a reader to carry out a specific activity, which
construct the reader as a scribbler who performs actions.
In order to do
mathematics, people need to both scribble and think.
Ideational
function includes (a) who is involved in doing what kinds of
processes; and (b) the depiction or suppression of agency.
Textual
function can be examined through investigating the ways in
which the text maintains consistency.
The material researched
here is a 64-page student edition of Thinking with Mathematical Models (TMM,
not CMP). It is the only one that both the teacher and the student read (implying
students do not read textbooks?).
Findings:
Sometimes
when the authors said they were going to ask questions, they actually used
imperatives, i.e., “These questions will help you …”, and more than half the
reflections were actually imperatives, which were instructions to direct
actions. This confusing of imperative sentences with questions is a common
feature of all mathematics textbooks.
Within the imperatives,
more than 2/3 are exclusives, emphasizing the reader’s role as a scribbler. In turn,
these exclusive imperatives highlight the authors’ authoritative voice as they
were in a position of telling the students what to do and how to do.
Meanwhile, first-person
pronouns were entirely absent from the student edition, which obscure the
presence of human beings in the text and affects “not only the picture of the
nature of mathematical activity but also distances the author from the reader,
setting up a formal relationship between them”. On the contrary, “you” was
widely used in the textbook. Statistics show that the “You + verb” form is the
most common form (165 times our of 263 times) in the textbook, normally appears
when the authors defined what they thought the reader was doing. Also, the
authors used “you may find …” to control the sense that a reader made of
something and were defining what s/he should have taken away from an activity.
This means that the authors were attempting to define and control the common
knowledge in the classroom.
It is true that math
textbook in this style keeps students away. I do not want to read a book like
this until I really realize that I need to read it. This may explain why
students refuse to read textbooks, lol. But what should we do?
I wish I could say I find the distinction of scribbler versus thinker surprising. Most of the textbooks I have encountered involve the repetition of the same style of calculation over and over (perhaps solving for the half-life in a radioactive decay problem or finding the period of a sinusoidal function). But very few questions are questions which demand critical thought (e.g. "show in at least three ways that the function y=x^2-7 is symmetric about the y-axis"). This explains for me, at least somewhat, why my first few years of post-secondary were so challenging; I certainly had mastered "the art of the A", but hadn't mastered the art of critical thought. While I think that there is certainly some level of scaffolding required for students to excel, it is undeniable that many textbooks do not move forward beyond simple modifications of even simpler problems. It is no wonder that students lose interest in mathematics; twelve of the same problem is less than engaging.
回复删除We, as educators, frequently revoice our students' ideas to motivate a particular concept in question and to maintain their interest in the topic. The authors clearly point out that whether we revoice aptly through repeating, rephrasing and expanding students' ideas, we may sometimes be faced with unintended results of our revoicing.
回复删除I remember that last year I met a teacher in one of my courses at UBC. He is an experienced non-native English speaker who teaches ESL English in an education centre. When he first learned about revoicing, he used it to teach his ESL students in his English lessons. Unfortunately, his revoicing led his students to think that his English skills were not up to standard. They filed complaints about him to the principal which eventually cost his job. This story may suggest that we need to be very careful in using revoicing as a teaching technique.
(Kevin, you seem to be responding to a different article -- the one on revoicing, rather than the one on textbooks and their voice!)
回复删除I am sorry about misplacing my response. I found out my mistake after I posted it.
回复删除I am really impressed by the ways the author analyzes the inner voice of a math textbook. I would have never thought of how the different forms of the second person carried hidden messages concerning the roles and relationships between the audience and the textbook writer.
As a student, I treated a math textbook like a bible. It was simply a perfect reference for me to develop all the important knowledge that I needed to build on later. I have to admit that I trusted the information in math textbooks more than I trusted what my math teachers said in their lessons. However, as a tutor now, I realize that there are limitations to math textbooks due to their authoritative nature. When I tutor students in math, I use the first person plural and avoid imperatives as a way of inviting them to learn math with me. So, they will not feel distanced from their learning.
Interesting to hear about your implicit trust in the textbook, Kevin. Perhaps because it speaks with a voice of such authority, students take it to be an authority!
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