Brief Summary:
Pimm represented some of the sorts of linguistic phenomena at work and at play within mathematics education and within mathematics itself. He proposed to discuss and exemplify how the concepts and methods of discourse analysis apply in mathematics education (and into mathematics itself). In the paper, he talked about three categories of discourse analysis: aspects of voice, instances of meta-discourse and components of temporal structure.
(a) Voice is about the relationship between the delivers and the recipients (eg. the author and the reader, the teacher and the student).
(b) Meta-discourse is presented as a hedging phenomenon in mathematics, using specific expressions to soften the assertion in order to make the words in a “safe” range.
(c) The components of temporal structure mention the sense of timelessness of mathematics and the role it plays in expressing mathematical facts, concepts and problems.
What are the three stops?
The pronouns in mathematical discourse
It is well worth considering noticing the pronoun changes in mathematical discourse. Pimm gave three examples about the pronoun changing, switching from “we” to “I” and sometimes ‘you’, given the teacher-student relationships change. From my point of view, using different pronouns carries out different relationships in terms of attitude, emotions, power, and status. I noticed that I usually use “we” and “I” in our conversations during math class. I think it encourages students to engage in group work and acknowledge each other’s ideas.
The sense of timelessness in mathematics
I agree that mathematics is frequently described as “timeless” (p. 4). We can sense and see that phenomenon when we describe mathematical ideas (such as facts, concepts, theories, etc) by using the present tense in most cases. When talking about time sense, I think it is an interesting topic to discuss. Because differ from western languages such as English have several ways to express tense, Mandarin Chinese does not have any verb conjugations. We express the sense by stating the date, modal particles, specific characters, or completed actions. So I am wondering how we express the sense of timelessness in mathematics, that is a question I have never dived into!
The ways we present the problem
Here are two instances are shown in Pimm’s article:
In these two problems, the author used the true names of real girls from the class and created a scene to give mathematical problems, which may have some interaction between the real and fictional worlds. Dr. Gerofsky holds the fact that word problems have no truth value: the people and the events could be fictional (p. 9). Sometimes the textbook doesn’t consider the world problem. Take the out-of-date price as an example, the students in my classroom are born after 2020, but the price of a pencil box is 5 RMB which may be the price 10 years ago. In addition, there are many problems set in the context of the 2008 Beijing Olympic Games and they have no idea of why the textbook always mentions the Olympic Games. To prevent students from keeping away from the real world, I think the ubiquitous word problem is a worthy item to study.
One question:
Based on the stop (c) above, what is your opinion about the "word" problem? Do you think the real name, real scene, real story or real background work better in comparison with the fictional ones?
Hi Erica
回复删除Thank you so much for sharing relevant information regarding this article. I agree with your viewpoint that sometimes its totally depend upon the context to use different pronouns in math classroom. To use 'we' might be confusing in some context but it would be required in other context to show sense of belongingness and unity in our classes.
Related to your question, I found it interesting to think that sometimes word problems are so unrealistic that their meaning could not fit in real life; which impacts on the critical thinking of the child. unrealistic word problems are the matter of imagination which could not be translated into concrete or real form of experience, which came as a difficulty in front of the math students. In addition to it, sometimes the language of the word problems are confusing which make a separate path to think for the students which sounds problematic in a way to solve them. For example, under point c, as stated in the last line of the first question, "How much more does jane weigh than lucy?" much, more have the same kind of meaning which could make the students think twice about solving the problem.
Many interesting topics are addressed here! Remind me to mention RME (Realistic Mathematics Education) from the Netherlands this evening, as well as something about the inclusive and exclusive 'we' -- and we'll talk a lot about word problems in an upcoming class!
回复删除Hi Jianying!
回复删除My article also discussed the use of "we" in the mathematics classroom. Barwell saw it as an ambiguous term that mathematics teachers use to say "we in this classroom" and "we who do mathematics" when working through a problem. I agree with your article that the pronoun "we" needs to be well defined in it's context. When you are working through a question with the class or giving directions, you have to be clear about who you are referring to.
I definitely believe that word problems have to have context. Whenever I give a random, fictional question, I always try to make it a story and have some background to the question. One my favorite things to do in math 10 & 11 is make questions about canoeing. I canoe regularly, so I have a lot of stories about when I contemplated the topic. For example, you can use trigonometry or solve for speed. This helps the algebraic concepts connect to real world applications and I find it illuminates what we are learning in class a lot more.