Week 3: Response to "The 'Verbification' of Mathematics: Using the Grammatical Structures of Mi'kmaq to Support Student Learning" by Borden (2009)

Brief Summary:

Lisa Lunney Borden is a mathematics educator and researcher working in a Mi’kmaw Kinamatnewey (MK) school for ten years. She argues that teachers and students are supposed to acknowledge their identity and culture in order to stop the further disengagement of many students from marginalized groups. In addition, she worked on developing her teaching philosophy based on the concept of “verbification” of mathematics. Borden gave an example of conducting a mathematics lesson on prisms and pyramids in a grade three class by adopting the unique grammatical structures in a verb/action-based language to support student mathematics understanding. She believes that mathematics is not just about objects and facts, things that can only be described as nouns, but verbification is also an efficient way to describe mathematics. 

Three Stops: 

            a. “Everyone has something that they can learn.” (p. 9)

I love the attitude that Borden sought the advice of many community elders. The community leader suggested she use the word mawikinutimatimk which means “coming together to learn together”. How powerful a word is! As a teacher, we must acknowledge that each participant that joins in the class has something unique to contribute. This piece of discussion reminds me of the First People Principle of Learning and how they really benefit all learners in a classroom. It is worth trying to find an entry point for us to reach out to students of (Indigenous) culture.

b. When Borden articulates the model for examining the complexities of mathematics learning for Mi’kmaw students, she mentions the significance of making ethnomathematical connections for students.

I totally agree with Borden’s idea, we should not ignore the influence of one’s culture. Although ethnomathematics is widely known, as well as the frame of the curriculum approaches of employing ethnomathematics in classrooms gradually diverse, however, ethnomathematics in the Chinese mathematics classroom seems superficial and only is used for the introduction part in the mathematics concept. From a math teacher’s perspective, I think it might be time for our Chinese mathematics teachers to take our cultures into account and bring them to our mathematics classroom. It is believed that mathematics education can be more effective if examples are taken from culturally specific contexts (Barton, 1996). Teachers should look over and analyze the proper activities from different cultural backgrounds, then find the activities that are appropriate to be integrated into the class, and create a really rich and inspiring environment to help students develop their potentials” (Gerdes, 2001). All students, all people, have the capacity to do and study mathematics, to study and make sense of the patterns that are part of the land/place we experience.

c. I love the part that Borden had a communication with a Mi’kmaw speaker around the word “flat”. In Mi'kmaq, verbification can be seen everywhere, they would say the tire was losing air instead of a flat tire, they would say the prism could “sit still” instead of the prism was flat. I am wondering, if we more often use verbification in our math class, mathematics would be visible and vivid. Even the students’ descriptions of the prisms as “going like this” along with gestures indicated the motion embedded in their conceptual understandings (p. 12)

My Questions: 

Have you ever thought about how traditional/regular mathematics classes discourage students from constructing a personal understanding of mathematics? Do you have any ideas or resources to develop an intercultural class for mathematical education?

Reference: 

Barton, B. (1996). Making Sense of Ethnomathematics: Ethnomathematics is Making Sense.

Gerdes, P. (2001). Exploring the Game of Julirde: A Mathematical-Educational Game Played by Fulbe Children in Cameroon.

Week 2: Response to Discourse analysis and mathematics education: An anniversary of sorts by David John Pimm (2004)

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?

1. 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.

2. 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!

3. 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?

Week 1: Response to M.A.K. Halliday's (1978) "The Social Interpretation of Language and Meaning"

There are a few moments I stopped while I was reading Halliday's article. They were the moments that made me stop to do some search, take some notes, have conversations with my colleagues and reflect on myself.

Professor M.A.K Halliday

(i) A language that is 'developed', being used in all the functions that languages serves in the society, tends to have a higher status... (p. 194)

Because I am not an expert in language, I can't tell the characters or evidence of a 'developed' language. If this quote's opposite is true as well, do I have the conclusion that if a language tends to have a higher status, that can be said that language is 'developed'? On the basis of my living and studying experience, I have the sense that there is a class system when it comes to languages. Some languages are given higher social status, than others, deliberately or otherwise. Montaner (2018) argues that "No language in history has dominated the world quite like English does today". And English is by far the world's most studied language in the world. Some of my parents' friends moved from China to Canada in the past ten to twenty years, and their children were born in Canada. They all reflected a fact that their kids were reluctant to speak Chinese (Mandarin or Cantonese) at home because they thought they would feel marginalized when they said Chinese but not English at school. However, the 2016 Census in Canada provides data on more than 140 immigrant languages and 21.1% of the Canadian population in Canada spoke an immigrant language at home, which is an increase of 14.7% from 2011 to 2016. Is the situation getting better when more and more people admit and speak their immigrant languages? Is sustainable if a language is given a higher social status that has dominated the world for a while?

(ii) We should not think of a mathematical register as consisting solely of terminology... (p. 195) AND  ...whereas in earlier days, mathematics tended to remain quite separate from the rest of a child's experience (p. 202).

I had a lecture on Art, Education and Cultural Diversity by Dr. Berard the last term. We had a lot of discussions about my final paper "Art Infusion in Elementary Mathematics Teaching". When I talked about the phrase "mathematical beauty" people misunderstand it as an oxymoron. Where is the beauty in a subject that makes so many people feel disconnected, un-human, and incapable? Dr. Berard can't help nodding her head and agreeing that students today have a belief that mathematics is a collection of isolated rules and facts unrelated to the real world, it is difficult for them to make sense of mathematics. I think one of the reasons why mathematics was treated as the product of pure logic without recourse to the world of things and other people is that tons of arcane mathematical terminologies exist in this discipline. For instance, in Chinese, we have never used a character like "幂" (mì) in daily life which means "power" in English mathematical terminology. The unusual and irrelevant terms make it students hard to understand the meanings.

 (iii) Some notes:

I appreciate that Prof. Halliday gave so many examples when delivering his ideas and notions. For example, when he introduced the development of a register of mathematics and various ways in which a new register of mathematics can be done (p.195), he would immediately give examples of different rules of "making" new words, it made me have a better understanding of what he would like to express. 

Prof. Halliday mentioned that "Developments that took centuries in English and French are expected to happen in ten years, or one year, or sometimes one month" (p.197). I am wondering why the developments of languages speed up in this era,  because of the development of the Internet and technology?

References:

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.

Montaner, M. (2018, July 27). Behemoth, bully, thief: How the English language is taking over the planet. Retrieved January 17, 2022, from https://www.theguardian.com/news/2018/jul/27/english-language-global-dominance

Introduction

Hello everyone, welcome to Jianying's Mathematics Space. It's so nice to meet you all.

I am Jianying (and you can call me Erica) from Guangdong, a southern province in China, and have been in Vancouver for four months. I have done my Bachelor of Economics and Bachelor of Mathematics in China. It is my second year in the MEd program in math education. This semester is my last semester at UBC, and I will graduate in May this year if everything goes well!!

I have three years of teaching experience in an elementary school in my hometown, focusing on Grade 2 and Grade 3 mathematics and sometimes science. Before I went to UBC to pursue my master's program, I was interested in Flipped classrooms applying in elementary schools and have done some research on it.

I love travelling so much. I hope I can visit more places in Canada when the Covid situation is better!

I had my birthday yesterday!