Summary    

 Chapter 3 : Quantity: Trapping Numbers in Grammatical Nets

Chapter 6:A Never Ending Braid: The Development of Mathematics

By Bill Barton

In Chapter 3, the author describes the grammatical handling of numbers in languages and their effects on math communication. It takes into consideration Maori, Kankana-ey, Dhivehi, and English. It observes that Maori prefer using numbers as verbs, Kankana-ey as descriptive adjectives, and Dhivehi as nouns predominantly. In contrast, English possesses a flexible grammar wherein numbers easily shift functions (as adjectives, as nouns, or independently) and is therefore effective for math communication. This chapter argues that this similarity between mathematics and English can influence the way mathematical ideas naturally occur in this language as opposed to others.

In Chapter 6, the author discusses how mathematics has been developed through its interaction with society, culture, and the human imagination. The chapter compared mathematics to a braid with strands woven together, each symbolizing various mathematical ideas from various cultures and traditions. The author critiques the view of mathematics as one universal stream and, instead, presents a more inclusive and enriched vision that embraces cultural contribution and alternative number systems. Through examples of Pacific navigation and the Indian tradition of art(kolam), the chapter illustrates how mathematics has borrowed and reinterpreted ideas from elsewhere, in most instances excluding or marginalizing their originators. This dynamic exchange, as guided by linguistic and social environments, underscores the value of more flexible and comprehensive perspectives of mathematical development.

Stop1:

“Watching women making kolam patterns he realised that another method for developing a language could be to create an array of symbols, as the women built an array first, before drawing their patterns. This was a new mathematical idea generated by the traditional craft.”(p.g.100)

This quote caught my attention because it recognizes how a very cultural and artistic activity, like kolam, shapes mathematical understanding in a way that is not necessarily obvious. I paused here because it captures the intersection of visual, symbolic, and mathematical "languages" and reminded me of how similar traditions, such as Onam pookkalam (flower carpets celebrated during Kerala’s Onam festival), may be interpreted as symbolic, non-verbal languages.

Being a math teacher, I can reflect on this quote to consider how such traditional practices have supported mathematical ideas through innovative and entertaining methods. This brought me to the consideration of how such an activity can aid in bridging mathematics with real-life and cultural importance to students.

Are there any traditional practices or art forms in your country that reflect mathematical ideas or use symbolic 'languages'? How could such practices be used to make mathematics more engaging and culturally relevant in classrooms?"

Stop 2:

Mathematics absorbs good ideas, techniques, even symbol systems, and makes them part of the mainstream of the subject. The worth of the ideas are judged on mathematical grounds. But this is not a braid with independent strands woven together but retaining their individuality, this is a river with tributaries flowing in"(p.g.103)

I stopped at this quote because it shows that mathematics borrows ideas from everywhere but sometimes reduces their uniqueness. It made me recall my experience of teaching symmetry using patterns from nature. My students were willing to discover the mathematics of the patterns; however, I made sure that we also discussed their cultural importance so that we would keep their distinctness. The reading concerns Pacific navigation, where navigators employed ocean swells in a manner that was like mathematical ideas, but different from the conventional conception of mathematics. This reminds me that, as a teacher, I need to expose my students to the multiple origins of mathematics, originating from various cultures and ideas, thus acquiring a sense of appreciation for its variety rather than as a single entity.

Have you ever used cultural examples in your math lessons to highlight mathematical concepts and their cultural significance?

Reference

Barton, B. (2008). The language of mathematics: Telling mathematical tales. Springer.

Reflection on Discourse analysis and mathematics education: An anniversary of sorts

 

Reflection on Discourse analysis and mathematics education: An anniversary of sorts

By David John Pimm

Discourse analysis and mathematics education: An anniversary of sorts by David Pimm (2014) explores the concepts and method of discourse analysis (a study of how language is structured and used in real-world contexts) in mathematics education.

In this article, the author discusses the four categories of discourse analysis:

1) Voice: It refers to how authors of mathematic texts present themselves and readers using pronouns.

2) Meta discourse: Use of hedging tools (e.g. probably, approximately, almost) to show the varying level of certainty in mathematical reasoning

For example: If P is some proposition, say the Poincaré conjecture or the Riemann hypothesis, then I can say ‘I think P is probably true’, which softens the more dogmatic assertion ‘P is true’ in two ways – first by saying I only ‘think’ it true rather than asserting it to be so, and secondly by deploying the additional hedge ‘probably’.(Pg. 4).

3) Timelessness in Mathematics: Mathematics is frequently described as timeless, which implies that mathematical truths are unchanging regardless of specific moments or events.

The document highlights that understanding the role of language in mathematics can enhance teaching and learning. By evaluating voice, meta-discourse, and time, educators can better understand how mathematical ideas are communicated and how students interpret them. Moreover, this document emphasizes the importance of understanding how language shapes the way mathematics is taught, written, and learned. By doing so, educators can better support students in mastering both the content and the discourse of the subject.

Stop 1:

“As a subject where clarity about issues of truth, as well as the scope and validity of claims, are central, the phenomenon of hedging in mathematics might be of special interest.”(pg.4)

This statement highlights that in mathematics, precision and clarity are important when presenting ideas, claims, or proofs. However, hedging—using language to soften a statement or express uncertainty—sometimes appears in mathematical discourse to address situations where the claim might not be absolute, fully proven, or involve assumptions and approximations.

I can relate this quote to the situations where I used hedges in math class. At that time, I didn’t know that I was using hedges. For example, when teaching rounding numbers if we round off 54 nearest to ten, it is approximately 50. Another example that I used in class is: The total cost for 6 apples is probably around $12 if each costs about $2. Let’s calculate to see if that’s exactly right.

This quote reminds me of the math class where students asked ‘why do we need to study estimation and rounding ?” Even though I explained the importance of real-life situations, I now feel my explanation could have been more thorough. What do you think is the best way to explain the importance of these hedges in mathematics?

Stop 2:

Word problems have no truth value: the people and the events are fictional. Yet by using the names of real girls from the class in this problem, there may have been some interaction between the problem authors’ real and fictional worlds. (pg.9)

I found this quote very interesting and can relate it to my teaching experience. When I teach word problems in my class, especially for primary students it’s difficult to make them understand that the numbers and the situations are not real. However, I have noticed that when I include names or situations from my own class in a word problem, students are interested in solving those problems and it makes them solve it without much difficulty. This can bridge the gap between fictional problems and the real-life connection. For instance, if a problem says, “ Hannah and Sarah share 10 apples,” and there are actual students named Hannah and Sarah in the class, it might make the problem feel more connected to real life, although it is still a fictional scenario.

Do you think the way we use language in math class can change how students understand or feel about math? 

 Reading- Halliday math register

Stop 1:

What matters most to a child is how much talking goes on around him, and how much he is allowed and  encouraged to join in. There is a strong evidence that the more adults talk to a child and listen to him and answer his questions, the more quickly and effectively he is able to learn. (Halliday,1978, pg. 201)

I stopped at this quote because it resonated deeply with my professional and personal experiences. As a parent, I can relate this to my daughter’s journey of language development. When we were in Qatar, my daughter didn’t get many opportunities to interact with many people, which significantly impacted her language development. But when we moved to India, she started talking, and as she got the opportunity to be in touch with a lot of people daily. This change has affected her language skills, allowing her to communicate much more effectively and with much more confidence.



As a teacher, I have observed the same in my classroom When students participate in discussions, even if their responses are wrong, it fosters their ability to develop language skills. Giving children an open space to 

express their thoughts and ideas will encourage them to discover, learn, and develop their language skills. As this quote suggests, it is clear that the development of a child, be it at home or in an academic setting, happens through conversations.

Stop 2:

The more informal talk goes on between teacher and learner around the concept, relating to it obliquely through all the modes of learning that are available in the context, the more help the learner is getting in mastering it. (Halliday,1978, pg. 202)

I found this quote very interesting and can relate it to my teaching experience. The truth is informal conversations about a certain concept, whereby students come to understand it through shared experiences in the classroom. The more students engage with mathematical concepts using everyday, real-life situations instead of formal definitions, the greater interest they show. When teaching them fractions, I usually bring up sharing fairly with friends to introduce the topic. This simple, informal conversation allows students to visualize and understand the concept of fractions in a meaningful way. Moreover, when I teach word problems, some children are not able to understand the mathematical operations, I introduce this by framing the word problem as a real-life scenario which is more convenient for the students. This kind of informal discussion really creates a learning environment where students feel encouraged to connect mathematical concepts to their own lives, which subsequently makes the concepts more natural and interesting to them.

Hello World!

 Hi everyone.... I am Rosmy Mathew, an M.Ed student in mathematics education, and welcome to my blog where I explore the fascinating intersection of math and language.