Author: Tim Rowland
Source: Educational Studies in Mathematics, 29(4), 327-353, 1995.
The author, Tim Rowland, conducted the interviews
with 10-12 years old children to linguistically analyze their uncertainty
(hedges) in their predictions, generalizations, and explanations within the mathematical
discourses. He utilizes the hedge model of Prince et al. (See the image below), and describes several
cases of the hedges by both the students and the teacher (the author) that were
extracted from the interviews.
(Rowland,1995, p.337)
- Ex)
- Plausibility Shield: I think…, maybe, probably
- Attribution Shield: According to N…
- Rounders: about, around, approximately
- Adaptor: a little bit, somewhat, fairly
In the interview, the participated children
often use Rounders and Plausibility Shields to express their proposition and to
move their understanding from uncertainty to certainty. He addresses many
children use the hedges to protect from being “wrong” since school-culture leads
students to believe mathematics is evaluated by only binary: right or wrong. However,
he suggests that using of the hedges in students’ conversations can inform their
anxiety, fear, or lack of confidence for their understanding. Therefore, it
makes teacher to be able to support their development from vagueness to conviction.
I agree with the idea that school-culture
forces students to provide high quality (accurate) opinions and instills fear in
them to be “wrong” in mathematics classes, and agree with that the words and
phrases of the hedges could help teachers to know their students’ understandings
toward to mathematics contents. It might be difficult for teachers to know
whether their students certainly understand what they have learned by tests
which only have very small spaces to fill students’ explanations, and to know
what they are exactly thinking. The interactions in the classroom, regardless of
among students or between teacher and student, hold a lot of information about
students’ attainments and idea, thus teachers need to be sensitive for their
conversations in addition to their answers.
In this article, Rowland mentions the zone
between students’ proposition and conviction. If I could talk to him, I would
ask him if there are any zones between nothing and proposition. After they confront
prediction, generalization, and explanation in mathematics class, I believe, students
might have something or nothing in their mind before they reach to uncertainly
phase. In this case, I wonder if they use the hedges as well or use other words
and phrases in their conversations.
Something that was not included in this paper
but actually I am interested, is about students who learn mathematics in
additional language. Because of their language limitation, their usage of the
hedges would be different from other students and other findings might be
observed.
Questions:
When you hear prediction/explanation/generalization/
from your students in mathematical discourse, what point do you watch? i.e.
facial expressions, voices, other student’s reactions etc.
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ReplyDeleteI usally pay a lot of attention to certain expressions such as "I think". It is in the category of plausibility shield. My reaction to the conversation goes as " how can we find out you are right". My intention is to help the student to learn to validate his/her conclusions using logic and proofs rather than to end of a conversation by subjective inclination. I appreciate that you concerned how ELL students would use hedges in math classroom. As the author suggested, that the noticeable usage of the hedges reveals anxiety, fear, and other psychological attributes of the speaker. It leads to questions of whether ELL students possess higher anxiety or tension? or whether they will use more or fewer hedges in conversations then? I am looking forward to more research to address these questions.
ReplyDeleteIn my class, I pay a lot of attention to tone and body language. Both are usually easy to watch and can give you a lot of information about the student: whether they understand the question, whether they are confident in their answer, even whether their neighbour gave them the answer! As I have mentioned before, in my class, my mistakes are not considered terrible events, but rather a show that even teachers can make errors. My mistakes are not frequent, and are sometimes on purpose, so my expertise is not undermined. I am finding the impact is that as the year progresses, students are becoming more comfortable taking risks in class and this is also leading to more confident students, who are less likely to use plausibility shields. I very rarely hear attribution shields unless the student hasn’t been listening! Similarly, approximators are not often used unless in context, such as when teaching estimation strategies.
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