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Peer-reviewed publications analogize learning math to learning a L2. But what are the DisAnalogies and CounterArguments? How can you distinguish learning math from learning L2?

Luciana Oliveira, Marta Civil. Teaching Mathematics to English Language Learners (2020), p. 75

Algebra, first and foremost, is another foreign language and, as such, has to be understood, transcoded, and treated as one.

Linda Pound, Trisha Lee. Teaching Mathematics Creatively (2021). No page number listed.

• Learning to talk mathematically has been likened to learning a foreign language (Worthington and Carruthers 2006): Lee (2006:2) confirms this analogy:

For many pupils learning to use language to express mathematical ideas will be similar to learning a foreign language. Unless the pupils know about the way that language is used in mathematics they may think that they do not understand a certain concept when what they cannot do is express the idea in language.

Paul D. Nolting, Winning at Math, p. 24 includes a cartoon referring to Spanish, French, Latin, Chinese! Nolting holds a Ph.D. degree in Education in Curriculum Instruction from the University of South Florida. His Ph.D. dissertation was "The Effects of Counseling and Study Skills Training on Mathematics Academic Achievement."

Math as a Foreign Language

      Another way to understand studying math is to consider it as a foreign language. Looking at math as a foreign language can improve your study procedures. Learning how to speak math as a language is the key to math success. Currently, most universities consider computer and statistics (a form of math) courses as foreign language courses. Some universities have now gone so far as to actually classify math as foreign language. In the case of a foreign language, if you do not practice the language, what happens? You forget it. If you do not practice math, what happens? You are likely to forget it, too. Students who excel in a foreign language must practice it every day. The same study skills apply to math, because it is considered a foreign language.       Like a foreign language, math has unfamiliar vocabulary words or terms, which must be put in sentences called expressions or equations. Understanding and solving a math equation is similar to speaking and understanding a sentence in a foreign language. Listen to yourself or others as they explain a math equation. They are taking mathematical symbols and translating them into words and sentences.

In 1987, Joseph Newmark and Frances Lake published Mathematics as a Second Language (4th ed). Newmark received his BS and MS degrees in mathematics from Brooklyn College, and his PhD in Operations Research from New York University.

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  • Math is a kind of language, though more like a code, but it is not what is called a natural language. The main point is the verb likened and the adverb like. These are analogies.
    – Lambie
    Commented Jan 22, 2023 at 19:09
  • "How can you distinguish learning math from learning L2?" - In my L2s that I know, I can now read books that are written completely in that language, and it is quite enjoyable to do that. Where are the mathematics books that are written completely in mathematical notation and that don't contain any other language (such as explanations in English, in German, in French, etc.) on its pages?
    – Brandin
    Commented Jan 24, 2023 at 13:53

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Oversimplifying maths and thinking of it as a bunch of equations (which a lot of lay people do) leads to the analogy that it's like a foreign language, in that there is new notation, vocabulary, and "grammar" rules (mathematical operations). This is probably because maths is encountered at a young age, and may be the first time the student is aware they're learning domain-specific vocabulary, so it feels foreign.

Students are often unaware that they should be expressing mathematics in sentences using words, leading them to exclusively use mathematics terminology and notation in their assignments, etc. In reality, good mathematics communication requires constructing sentences and thus language skills, but usually in one's native language. Also, mathematical vocabulary is added to one's native vocabulary, unlike for a foreign language where it replaces your native vocabulary.

In any case, here's my feedback on this analogy (I have a PhD in maths, and I've been actively studying Chinese for years):

Learning X and learning Y will have "learning" in common for any X and Y.

After a certain level, the learning process will always involve learning domain-specific vocabulary and notation, learning how to correctly communicate domain-specific ideas, and learning the key domain-specific concepts and how to apply them. Thus, you could replace "foreign language" and "math" in the analogy with anything, say "Minecraft" and "ancient Roman history", and come up with comparable analogies. The question is: are these analogies useful?

Learning mathematical vocabulary is different to learning foreign vocabulary.

Like a foreign language, math has unfamiliar vocabulary words or terms, which must be put in sentences called expressions or equations.

Learning maths as e.g. a native-English speaker requires learning maths-specific vocabulary ("exponent", "Pythagoras", "cosine"), which is used within English sentences. However, learning e.g. Chinese as a native-English speaker is not merely a matter of introducing a selection of Chinese words into English sentences, you need to produce wholly new sentences, and you learn words which you already know in English (三 "three", 姐妹 "sister", and 蓝色 "blue").

Mathematics is not just equations.

Thinking of maths as a bunch of equations is an oversimplification (you can't just ignore theorem proving; mathematical modelling; etc.). Mathematics is expressed using natural language; writing sentences purely using mathematical notation is advised against in mathematical-writing style guides:

One of the misconceptions students have about writing mathematics (which probably arises from their writing habits in secondary school) is that the writing should be composed mostly of equations and mathematical symbols. This is not true at all. By contrast, a piece of mathematical writing should contain mostly words, supplemented by equations and mathematical symbols. Take any mathematics textbook to verify this. Even in their worked examples, the solutions contain mostly words.
Guide to Writing Mathematics (pdf)

If anything is to be learned here, it's that expressing mathematics requires strong language communication skills, which is often overlooked by mathematics students who often just list out equations. Students (most likely) need to improve their mathematics communication skills in their native language and/or English, not necessarily a foreign language.

Is maths taught in foreign-language courses?

Currently, most universities consider computer and statistics (a form of math) courses as foreign language courses. Some universities have now gone so far as to actually classify math as foreign language.

When I read this, I was perplexed why someone with a PhD would write this? It's just not true. I've been to many universities---I'm not aware of a single example of this. It's illogical: mathematics students and mathematicians will not think to apply to foreign-language departments, and foreign-language students will not want to take mathematics courses.

I looked up the universities listed on his webpage thinking maybe his experience was unusual, but the USF Department of World Languages and the FGCU Department of Language & Literature webpage show no sign of anything related to computers, statistics, or mathematics.

The only conceivable scenario in which I feel this is plausible, is for a small university which does not have enough manpower, and merges otherwise-unrelated disciplines to reduce bookkeeping.

Suppose you and your teacher magically become expert mathematicians, mathematics educators, and mathematics communicators: how does that help you learn Dutch?

Being good at maths tends to help you think logically and break down problems into their essential components and identify key details. Sometimes this confuses people into thinking that some random discipline and mathematics are directly related, whereas mathematics is just how the universe works and is intrinsically related to everything.

Moreover, people who are good at mathematics have the discipline to put in (or the habit of putting in) long hours of study, and so they tend to be people who enjoy spending large amounts of time learning things. Thus, being good at maths often implies having strong general-learning skills, which can be applied to learning a foreign language, as well as learning any other topic.

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