Hedges in mathematics talk: Linguistic pointers to uncertainty (Tim Rowland,1995)
After reading Rowland’s article, I found that it is pretty interesting reminding me of something that I have never paid attention to before. This article also let me recall the project that I did in Ann’s course last term. In the project, I had 4 interviews which aimed to examining the mathematical thinking in different grades of students. What impressed me the most among these interviews was that my students always replied me “oh, there are many” if they found the math problem has more than one answer/possibility. For example, “Three way of sharing” was one of the problems I posed to my students. It has 21 possible ways to share 8 cookies among 3 kids. I still remember that my interviewee presented her answer with “there are many ways” after she thought about the problem for a while. What’s the meaning of ‘many’? It’s a vague math word, which explicitly shows that my student is not sure about the answer. In looking back the word transcripts that I recorded for the conversations of the project between my students and me, I found that either my interviewees or I frequently used the words, such as about, around, maybe, probably, think, basically, normally, suppose, (not) sure, (not) really/exactly, all the words that are termed as hedges by Rowland. But I have never thought that these words can be advanced to such a theoretically linguistic view, I thought that they are very common words that can be heard quite often either in our daily speaking or the talking in subject learning. Honestly speaking, I use these hedges frequently and unconsciously sometimes when I talk about something that I’m not so sure or I feel less confident.
In my view, these mathematical hedges still reside in the mathematical register. They just convey the mathematical vagueness or uncertainty. Rowland has made two major contributions in this article concerning the investigation of vague language use in math education. The first one is that he has outlined and exemplified a classification (which he cited from Pince et al. 1992) of hedges into more detailed functional categories. The other one is that he offered us with an interpretive framework which can be applied to explain why children use some ambiguous and vague language when they are predicting and generalizing something in the math learning.
I don’t care about so much how to call these vague words in terms of the taxonomy of hedges, for instance, which type should the word ‘maybe’ go into?, but what I’m more concerned about is that what inferences about students’ math learning they can convey to us (teachers), therefore, we can know more clearly about what we should do next, for example, adjusting our teaching strategies or the ways of inquiry or providing further explanations, etc. I totally agree to the thoughts that Rowland either came up with individually (e.g. the effect of the announcement ‘I shall have to think about that’, pp345) or cited from other literatures as theoretical supports (e.g. he cited Channell’s thoughts about a number of goals of why people use vague expressions, pp350) regarding why students use the uncertainty and vague expressions in math learning.
Furthermore, as far as I’m concerned, hedges are important in students’ math learning, at least, providing students with an opportunity to conceptualize math knowledge through discussing with their peers or teachers. These conversations with peers or teachers should involve questioning, self-reflection and argumentation. What we should do is how to help students transform the initial uncertainty to the assurance step by step.
After reading Rowland’s article, I found that it is pretty interesting reminding me of something that I have never paid attention to before. This article also let me recall the project that I did in Ann’s course last term. In the project, I had 4 interviews which aimed to examining the mathematical thinking in different grades of students. What impressed me the most among these interviews was that my students always replied me “oh, there are many” if they found the math problem has more than one answer/possibility. For example, “Three way of sharing” was one of the problems I posed to my students. It has 21 possible ways to share 8 cookies among 3 kids. I still remember that my interviewee presented her answer with “there are many ways” after she thought about the problem for a while. What’s the meaning of ‘many’? It’s a vague math word, which explicitly shows that my student is not sure about the answer. In looking back the word transcripts that I recorded for the conversations of the project between my students and me, I found that either my interviewees or I frequently used the words, such as about, around, maybe, probably, think, basically, normally, suppose, (not) sure, (not) really/exactly, all the words that are termed as hedges by Rowland. But I have never thought that these words can be advanced to such a theoretically linguistic view, I thought that they are very common words that can be heard quite often either in our daily speaking or the talking in subject learning. Honestly speaking, I use these hedges frequently and unconsciously sometimes when I talk about something that I’m not so sure or I feel less confident.
In my view, these mathematical hedges still reside in the mathematical register. They just convey the mathematical vagueness or uncertainty. Rowland has made two major contributions in this article concerning the investigation of vague language use in math education. The first one is that he has outlined and exemplified a classification (which he cited from Pince et al. 1992) of hedges into more detailed functional categories. The other one is that he offered us with an interpretive framework which can be applied to explain why children use some ambiguous and vague language when they are predicting and generalizing something in the math learning.
I don’t care about so much how to call these vague words in terms of the taxonomy of hedges, for instance, which type should the word ‘maybe’ go into?, but what I’m more concerned about is that what inferences about students’ math learning they can convey to us (teachers), therefore, we can know more clearly about what we should do next, for example, adjusting our teaching strategies or the ways of inquiry or providing further explanations, etc. I totally agree to the thoughts that Rowland either came up with individually (e.g. the effect of the announcement ‘I shall have to think about that’, pp345) or cited from other literatures as theoretical supports (e.g. he cited Channell’s thoughts about a number of goals of why people use vague expressions, pp350) regarding why students use the uncertainty and vague expressions in math learning.
Furthermore, as far as I’m concerned, hedges are important in students’ math learning, at least, providing students with an opportunity to conceptualize math knowledge through discussing with their peers or teachers. These conversations with peers or teachers should involve questioning, self-reflection and argumentation. What we should do is how to help students transform the initial uncertainty to the assurance step by step.
1 comment:
Julia --
A very interesting blog entry! I like your examples and your self-reflection here -- I'm very glad that this topic relates closely to observations you have made of students and of yourself (and by extension, other teachers too).
I agree with you that, although the taxonomy of hedges is interesting, the most useful part of this study is the way it helps us interpret students' learning and conversation around math ideas.
Thanks!
Susan
Post a Comment