Week 3: Response to the “Verbification” of Mathematics

Summary:

The article is written by mathematics educator, Lisa Lunney Borden, who had worked in an aboriginal secondary school in Mikmaw community school in Cape Bretown, Nova Scotia for 10 years, where she has built ‘fictive kin’ with local community and developed her teaching philosophy based on the concept of ‘verbification’ of mathematics. By adopting the unique grammatical structures in Mi’Kmaq (a verb/action-based language) to support student mathematics learning, she identified it as alternative pathways to understanding mathematics concept from their cultural knowledge.

Stop 1: learning from their language and culture (verbification v.s nominalization)

Lisa realized the grammatical patterns in aboriginal language shape the way students conceived instruction, so she transitioned from asking noun-based questions to verb-based questions (verbification) by listening to the way students raised questions and modelling her instruction with similar grammar structures. Recalled from my own experience, relating to daily situation and rephrasing explanations are needed, to help students to make sense of the concept, especially for early learners, for example, when introducing vertices, edges, focuses etc. One of my early learners called a parallelogram as a rectangle which lies down (slanted) a bit, thus it is necessary to think about how to bridge what they already learnt and what they are coming to learn. 

Stop 2: how cultural identity influence students’ attitudes in learning math

I like how Lisa corporated mawikinutimatimk (“come together and learn together”) as the research methodology, which raised comprehensive and inclusive concerns emerged from aboriginal community in the conversation, identified specific knowledge and uncovered the cultural component of mathematics in indigenous environments, and later she reflected these cultural components of mathematics in her teaching.

Stop 3: ethno-mathematics as a foundation 

Lisa pointed out the disengagement in math learning has results conflict between aboriginal cultures (Mi'kmaw mathematical reasoning) and values embedded in school-based math curriculum. Students felt their cultures are denied which result deeper disengagement and resistance in learning. Thus, it is meaningful to encourage learning in identifying the presence of mathematic within ancestral knowledge, in such a reflective learning process, the application and appreciation of mathematics and culture would be promoted simultaneously.

Wonders:

•	What are the specific aspects do math teachers need to emphasize in their math class from an indigenous perspective? How do you overcome the indigenous cultural diversity in mathematics education?
•	How do math teaching practitioners develop an intercultural and contextualized design for mathematical education? Are there any resources or organizations that you are familiar to support math learning in indigenous environment? Are we (as mathematics educators) doing enough?

Reference:

Lunney Borden, L. (2009). The “Verbification” of Mathematics. Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics, Thessaloniki, Greece.

Week 2:  Reading Response on Discourse Analysis and Mathematics Education: An Anniversary of Sorts by David John Pimm

Summary:

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?

Week 1: Response to Social Interpretation of Language and Meaning by M.A.K Halliday

What it was that stopped you? 

1.     P195 The Notion of Register

As a second language learner, I agree that developing a language means gradually building and collecting new registers. For example, by expanding knowledge on a specific topic (describe someone), adding new vocabularies to word stock (i.e. adjectives in personalities, appearance, clothing etc.), using conventional grammatical structure (i.e. present tense and past tense etc.) to link all the information to make sense of the ideas.

2.     P196 Structural Aspects

I usually stuck by meaning making and translating in my first language, especially those blurry and compounded words, for example, ‘case analysis presentation slides’, where ‘presentation’ is a nuanced word to translate into a single word in Mandarin, ‘slides’ are usually presented as measure word, which is hard to link with the pages in PowerPoint without further hints. Thus, I guess demonstration in pictures, giving examples or synonyms would be helpful in explanation. 

3.     P199 The Uniqueness of Mother Tongue

There are many other words that are hard to find a matching translation in Mandarin due to the differences in culture, language and daily practices, such as ‘offer, pattern, available, and access etc.’, where in many casual occasions, young generation in China would generally keep the English word to avoid ambiguity. 

                                                                                                                    

4.     P 202 Mathematical Symbolism

     I came up with an example of reading fraction.

     12/15 was read from top to bottom as 12 over 15 in English.

     12/15 was read from bottom to top as 15 ‘分之’ 12 in Mandarin.

The position of two numbers are switched, I am not sure if there is a symbolism or philosophy in understanding fraction as a result of division?

Wonder:

If there is an extreme case, which aspect of language can be abandoned that people could still understand, vocabulary, grammar or others? So, can we say the dropped aspect is not that meaningful/useful for second language learners who just picked up the new language? 

Reference:

Halliday, M. (1978). Sociolinguistic aspects of mathematical education. In Language as social semiotic: The social interpretation of language and meaning (pp. 194-204). Edward Arnold.

Happy New Year 2020!

Happy New Year!🙋💕

This is the first blog made by Joy on 2020/01/09.