Week 6 Reading

Introduction

In the article “Language, Paralinguistic Phenomena and the (Same-Old) Mathematics Register” by David Pimm, the author explores the intricate relationship between communication, language, and mathematics. Pimm examines how mathematical concepts are conveyed and understood through various modes of communication.

Pimm indicates that mathematics possesses a unique property in communication; it cannot be treated as a language, and mathematical symbols are not equivalent to words. The language used during mathematical communication is referred to as the mathematical register, which differs from everyday language. For instance, we do not say “+” in conversation; instead, we use terms like “plus” or “add.” Additionally, different languages express the same mathematical concepts in varied ways. Pimm argues that mathematical symbols cannot be directly transcribed into spoken languages, necessitating careful representation of mathematical communication and consideration of the nuances between spoken and written expressions.

Furthermore, Pimm highlights that while written mathematics often includes symbols and images, spoken mathematics is enriched by gestures and other paralinguistic features. This distinction is crucial as it influences how mathematical concepts are communicated and understood.

 

Stops

 

“Therefore, every single word (or character or …) in any transcription should be exactly that, namely written elements in the language(s) of the speaker (or a language of translation to match the language of the article or book). Which raises for me a reversing question: since written mathematical notation does not belong to any natural language, how can written mathematical notation be ‘read’ (aloud), and thereby incorporated into one (or more) language, considering that it does not belong to any natural language, although it is primarily alphabetic (which many natural languages are not). In order to be said aloud, with both grammatical and semantic elements, it needs to be invited (projected?) into a (specific) natural language. “ (P4)

 

“Mathematics is not a language, despite commonplace claims to the contrary, let alone a universal one. Later on in his report, Halliday adds, “However, it would be a mistake to suppose that the language of mathematics (by which is meant the mathematics register, that form of natural language used in mathematics, rather than mathematical symbolism) is entirely impersonal, formal and exact” (p. 71). So, mathematics itself is not solely part of any specific natural language, but the mathematics register is.” (P5)

 

Reflection

The article presents a fascinating discussion, challenging the common perception of mathematics as a language and equating the mathematical register with mathematics itself. It inspired me to reflect on the identity and differences between mathematics and the mathematical register used in teaching and learning.

I found the example of the symbol “+” particularly interesting. Many people equate the symbol “+” directly with the word “plus,” viewing them as two representations of the same concept. However, the article distinguishes between them, categorizing the symbol as separate from language and the word “plus” as part of the mathematical register developed to explain the symbol. While this distinction may seem negligible for a fundamental symbol like “+,” which carries minimal information, it becomes crucial for more complex symbols in advanced mathematics. These symbols often encapsulate more information, necessitating detailed explanations that a single word cannot convey. This insight prompted me to consider the importance of precision and accuracy, as discussed in our previous lesson. If the mathematical register fails to fully represent the mathematical concept, communication breaks down. Therefore, it is critical to choose words, registers, and paraphrases carefully to avoid confusion.

The article provides an excellent example of potential language use that could lead to misunderstandings:

“There is an obvious convenience in so doing, not least because one aspect of mathematical notation is compression (as well as easing manipulation) and, hence, it reflects a certain economy. But, there is also an unnecessary and unhelpful ignoring of what was actually said and so the transcript does not accurately reflect it. For instance, if r² was presented in the transcription, the speaker could actually have said, ‘r squared,’ ‘r to the power two,’ ‘r to the little two,’ or perhaps ‘the radius times itself’ or even ‘the area of a square whose side length is r’ (in relation to the quarter-circle). And on and on.” (p. 5)

       Moreover, this discussion prompts me to reflect on my experiences with translating between Mandarin and English. I believe similar challenges can arise when transcribing mathematics into English.

We need to understand that languages are developed to facilitate the convenient transmission of information. We assign meanings to syllables, allowing them to carry unique groups of information and become words. However, the way we assign these meanings varies. In one language, a word might be very specific and used for a single object, while in another language, the same word might be less specific and more vague.

A clear example we discussed last week is the word “cousin.” In Mandarin, this term can be broken down into several words, each specifying different types of cousins. This phenomenon can occur with every word, though it might be less obvious in some cases, perhaps differing by only 2%. This subtle difference can make bilingual speakers feel uncomfortable and that their expression is not fully accurate, but they cannot name it because it is the only translation for that word. As a result, it can lead them to code-switch for more precise communication.

 

Question

Do you have any experience that you find it challenging to explain a mathematical concept accurately using language?? Or what is your reflection based on my post?