Week 2: Reading Response on Discourse Analysis and Mathematics Education: An Anniversary of Sorts by David John Pimm
Pimm discussed and demonstrated the the application of concepts and
methods of discourse analysis and enquiries into mathematics education
throughout four respects, including voice instances of meta-discourse,
components of temporal structure, and dimension of style, through motivating and concise examples in linguistics and mathematics.
Stop 1: Pronouns in Mathematical Discourse
What stops me is that, the pronouns that the lecturer adopted switched from ‘we’ to ‘I’ as the level of mathematical education increased.
From my point of view, it seems that the role and attitude the lecturer adopt, is changing from participant to mentor, from introducing content to signing blueprint, as his/her expectation changed from arousing interest in math in a lower leveled introductory class to demanding individual exploration in higher leveled mathematics?
In addition, is the lecturer deliberately changing his tone due to the content, or the presence as authority in class? Or is it possible that he/she is influenced by the textbooks used thus whose voices changed correspondingly in an unconscious way?
Stop 2: the Elements and its Style of Presentation
The Elements as a mathematical treatise and influential textbook covering from plane and solid Euclidean Geometry to elementary number theory etc. The style of presentation carries the assertion that “this is always the case”. It seems Euclid didn’t worry about the presence of potential readers and just pose these definitions, postulates, proposition in front of them. For example,
"To draw a straight line from any point to any point."
"To describe a circle with any center and distance."
Euclid, Elements, Book I, Postulates 1 & 3.
I was stopped by the logical and deductive Euclidean style as it sounds scientifically-impeccable. I was wondering is this a given stylized form or an invented one? How would that affect the later generations in reading and proving math?
Stop 3: the question of Time in Mathematics and Mathematics Education
As in the journal, “a mathematical text is embedded within a personal narrative.” (p.6)
When I was reading this, I was thinking that mathematics itself is time sensitive, so does the corresponding language used. For example, in theory of interest, when we calculate the compound interest, equations tell us about the time and duration. Thus, can we conclude that some mathematical equations are already time-based and time-dependent.
Another example is calculating the limit, ‘when time goes to infinity’, as we already indicating time in mathematical and linguistic way. Thus, can we say mathematic is a problem-solving tool when we present an event, and when we translate the event into equations, it already carries the feature of time with it?
Wonders:
1. As math educator, do you think students would notice a sudden change in the tone, voice and pronoun usage etc. in class?
2. What pronoun do students usually adopt in their conversation in mathematics classrooms, ‘we’, ‘you’ or ‘I’? Why do you think so?
From stop #1: I wonder if the change in tone is due to the content or presence of authority as well. When I walk around the class, I notice that students do behave differently when I am listening in or when I pretend to not pay attention to them.
回复删除2. I noticed that my class usually use "we" or "I" in their conversations during math. I encourage a lot of group work, and students acknowledge each other's efforts by using the "we" or "our group" when sharing their ideas.
1. I think students would notice a sudden change in the tone, voice and pronoun usage in class. I think using a tone and voice that encourage students to be curious and playful would help them explore the math concept. I find that using the pronoun ‘I’ to share how I use math with students can help them relate the concept to their own experiences.
回复删除2. My students usually use ‘I’ or ‘we’ during discussions. I think that they typically use the first-person pronouns because I encourage them to think about how they use math in their daily lives. For example, while discussing factors and multiples recently, I asked students to observe which numbers are used for things that come in a pack and what they notice about these numbers.