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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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    $\begingroup$ I completely agree that learning math is akin to learning a language (and also akin to learning a "virtual" reality like when one gets immersed into some game (not necessarily a computer one)). However I strongly disagree that it is a foreign one. For me it is a "native tongue" and the game is of the same type as "hide and seek", only with more diverse environment than a typical house or playground can provide. Children (up to the age of 15) are very good at learning both. The only reason that they don't learn math (IMHO) is that nobody talks and plays it with them on a regular basis. $\endgroup$
    – fedja
    Jan 15 at 13:42
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    $\begingroup$ The first (wikipedia) link does not seem strongly related to the question. $\endgroup$
    – Tommi
    Jan 15 at 14:40
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    $\begingroup$ @AmyB When I learned the programming in Russia (ALGOL68, if you are old enough to remember punch cards), all commands were in English (do, break, goto, while, etc.). That actually didn't make it any harder if one understood the underlying logic well and since I did, it was still like native tongue for me despite the Latin alphabet and fancy words whose exact meaning I didn't even know (I only knew what the operator would do if one writes them). But when, say, our administrators try to speak English, I know every word but the meaning escapes me and translating into Russian does not help. $\endgroup$
    – fedja
    Jan 17 at 21:06
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    $\begingroup$ "Currently, most universities consider computer and statistics (a form of math) courses as foreign language courses". Sorry, that seems absurd: most? Can anyone point to, say, 3 universities that considers computer and statistics as foreign language courses? $\endgroup$
    – KCd
    Jan 18 at 18:36
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    $\begingroup$ @KCd Cleveland State seriously considered allowing a programming language to count for the foreign language requirement. I actually don't even know which way this decision went. Completely absurd. $\endgroup$
    – Steven Gubkin
    Jan 18 at 19:13

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That not regularly practicing a language or math makes you forget them is a pretty weak reason for suggesting learning math is like learning a foreign language. The same feature (namely no practice leads to forgetting) is true for learning how to play music well, making good basketball shots, solving a Rubik's cube very fast, and so on.

I like what Feynman once said about the comparison between math and speaking a language ("The Character of Physical Law", pp. 34--35):

You might say, "All right, then if there is no explanation of the law, at least tell me what the law is. Why not tell me in words instead of symbols? Mathematics is just a language, and I want to be able to translate the language." [...] But I do not think it is possible, because mathematics is not just another language. Mathematics is a language plus reasoning; it is like a language plus logic. [...] The apparent enormous complexities of nature, with all its funny laws and rules, each of which has been carefully explained to you, are really very closely interwoven. However, if you do not appreciate the mathematics, you cannot see, among the great variety of facts, that logic permits you to go from one to another."

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  • $\begingroup$ "Mathematics is a language plus reasoning" Yep, that is what I meant when saying that it is like learning virtual reality or the rules of a new game. Feynman could express it in a clearer and more concise fashion, of course, but the meaning is pretty much the same. On the other hand, to be completely fair, a foreign language is also more than a language: it is a language plus the underlying culture and they are often taught together when they train translators, diplomats and such (for idle sightseeing or shopping all you need is ou se truve... and pouvez-vous me donner...). $\endgroup$
    – fedja
    Jan 18 at 21:21

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