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.
Hi Rosmy, thank you for your insightful reflection. To answer your first question, I personally am not very connected to my Chinese heritage as a result of my parents assimilating into Canadian culture. As such, I would love to hear about yours! It is essential for teachers to create safe spaces for students to feel comfortable to share their cultural practices. If we are able to foster inclusive environments and highlight connections between practice and mathematics, students can build personal connections with the subject to foster deeper understanding and learning.
ReplyDeleteI have not used much cultural examples in mathematics, but I've occasionally used music and dance to make connections with the subject. For my Greek students, there is an evident connection with the Greek symbols in math and the Greek alphabet. Furthermore, music offers a natural bridge to math concepts -the rhythms, beats, syncopations of music, how many music notes can fit into a bar, all require some form of mathematical thinking.
While I was teaching math, I noticed many of my students carrying their band instruments and attempting to work on some music homework. I supported them throughout this and made direct connections to math. Since music and dance go hand in hand, many of my students who were in dance class would discuss routines and movements. Dance is quite angular, intricate, and positioning yourself in a group is almost permutational. Whenever students performed for me, I made sure to point out these connections, which helped them see the relevance of math in their daily lives and interests.
Of course my dear, Nigeria is rich in traditional art forms that reflect mathematical ideas particularly through the use of geometrical patterns and symmetry .Here are a but a few examples
ReplyDelete1)Beadwork designs which is used for adornment and ceremonial purposes often incorporate patterns and symmetry ,reflecting mathematical principles, we also used the beads to make abacus which is used for counting in our elementary schools.
2)Wood carving which is a traditional art work by arcticians often depicts geometrical shapes and symmetrical patterns.
3)Aso Oke weaving is a traditional attire made and worn by the Yoruba speaking people in the south west for clothing and ceremonial purposes. The weaving process involves creating geometrical patterns ,mathematical principles and repetition
4)Adire Textiles is a hand -dyed cloth made by the Yoruba people, the intricate patterns created feature geometric shapes and symmetrical designs showcasing mathematical concepts of symmetry and repetition.