Mathematics? I Speak it Fluently

by

David Pimm

In Mathematics? I Speak It Fluently, David Pimm emphasises the distinct nature of mathematical language compared to everyday English and the importance of communication in mathematics education, focusing on how mathematical meaning is conveyed between teachers and students. This communication should be verbal, with pictures and symbols. Mathematical symbols are concise ways to represent relationships, and students need to understand this system to use symbols effectively and express their mathematical thoughts. He says that the main role of a math teacher is enhancing fluency,both oral and written in mathematical language. He presents three perspectives on math as a language: it's part of English, a universal shorthand, and a unique language.

Mathematics English and Ordinary English

In most of the mathematical classes, we use a mixture of ordinary English words and mathematical English words. This sometimes results in errors or confusion. As an example,he takes "What is the difference between 30 and 7?

the possible answers are:

• 30 is greater than 7
• 30 is even and 7 is odd
• and some students say 23

We write 8-4 but sometimes say 4 from 8 where the written left to right order is different from the spoken order.

In mathematics, language is precise, and there are few synonyms, meaning each term has a specific meaning. The same mathematical operation can be expressed in different ways, but the order in which operations are performed is crucial. For example, addition (e.g., 2 + 3 = 5) and multiplication (e.g., 2 × 3 = 6) can be done in any order without changing the result. However, subtraction (e.g., 5 - 2 = 3) and division (e.g., 6 ÷ 2 = 3) must be performed in a specific order; reversing the order changes the outcome. Some students mistakenly believe that you should always subtract or divide the smaller number from the larger one, but this isn't always true. In everyday language, numbers often describe nouns, acting like adjectives. For example, in "three apples," "three" describes how many apples there are. In mathematics, numbers function as nouns themselves. The position of numbers and symbols is also important. For instance, in the number 23, the "2" represents twenty, but in 32, the "2" represents two. The size and position of numbers can show different relationships, so understanding the context is essential.

Metaphor

In mathematics education, metaphors serve as cognitive tools, mapping familiar experiences onto abstract concepts to aid understanding. However, relying on metaphors can sometimes lead to misconceptions if students interpret them too literally or apply them inappropriately across different contexts.Metaphors in mathematics can lead to confusion when taken too literally. He suggests that children's difficulties with math concepts may arise not only from their abstract nature but also from how these ideas are presented and communicated.

Stop 1

"Mathematics is notorious for attaching specialised meanings to everyday words, words which already have meanings."(p.140)

When I read the article, this sentence resonated with me and made me think about the picture shown below which I have seen before.

www.reddit.com(pic credits)

Root in everyday life means part of the plant underground whereas in Mathematics, it represents square root. This duality creates barriers for students, as they may assume the meaning of mathematical operations based on their everyday life experiences. As we said before in class, some words give a related meaning to that mathematical concept like in Malayalam, even "iratta" which means twins and odd (otta) means alone. But there are other words which have no connection to the exact mathematical meaning of that words.

This makes me reflect on how deeply language shapes mathematical understanding. It raises some questions like how do we ensure that mathematical terminology is introduced in a way that minimizes the misconceptions?

Stop 2

"Many kids difficulties with mathematics may be due more to the complexity of wording or written material rather than the mathematical task being requested."(p.149)

I completely agree with this. In academic resources. many students' difficulties in math is due to the complex wording, technical vocabulary and abstract phasing.

As an example,"A farmer has 3 times as many apples as oranges. If he has 12 oranges, how many apples does he have?"A student struggling with the wording might not immediately recognize that "3 times as many" means multiplying 12 by 3. The difficulty is not in performing the multiplication but in interpreting the language of the question.

This issue is especially challenging for students who are multilingual learners or have weaker reading comprehension skills. Even students proficient in the language may struggle when everyday words are used in specialized ways in math.

Reference

Language in the mathematics classroom - Scientific Figure on ResearchGate. Available from: https://www.researchgate.net/figure/Mathematical-words-and-their-everyday-usage_tbl1_44296272 [accessed 17 Feb 2025]