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In Linguistics, recursion is the ability to amend one sentence to another, combining them in different ways. Example: "After I saw the movie, I went to a cafeteria and then I ate a pizza." Without recursion, we would have to use three phrases, something like: "I saw the movie. Then I went to the cafeteria. I ate a pizza.".

There is no consensus (the topic is controversial), but some linguists (Chomsky is one of them) argue that recursion is a particularity of human language. Only humans use recursion (the Pirahã language of an Amazonian tribe can be a counterexample). [Note: this phrase is very recursive!]

Well, on the one hand, recursion is an attribute of human language. On the other hand, recursion makes sentences longer and more complex.

Here's the dilemma: you're going to write a math textbook for Basic School. On the one hand, it seems that using simple sentences (without recursion) would be easier for the student to understand what is being addressed. On the other hand, shouldn't the student be familiar with recursive texts, including those dealing with Mathematics?

It would be possible to build a scale over the school years of the level of recursion that can be used to have a balance between understanding of the mathematical concept to be treated and, at the same time, doing this by practicing the linguistic attribute of recursion which is a linguistic characteristic of humanity?

Moreover, are there mathematical topics that can only be described via recursion? I think that every sentence of the form A => B is recursive: A is a sentence, B is a sentence and => combines the sentences, so A => B is (linguistic) recursive.

Does anyone know of any study that deals with what is expected, in terms of the development of linguistic resources (including recursion, verb tenses, ...), throughout the school years? What language resources could (should) be used in each school grade?

Here is a text that makes an introduction to recursion in linguistics and the comparison with the use of the term in Mathematics: https://onlinelibrary.wiley.com/doi/abs/10.1002/wcs.131

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    $\begingroup$ It's not all or nothing. But, my advice is that your style is too ornate. For instance, "It would be possible to build a scale over the school years of the level of recursion that can be used to have a balance between understanding of the mathematical concept to be treated and, at the same time, doing this by practicing the linguistic attribute of recursion which is a linguistic characteristic of humanity?" Even fixing the sentence by reversing the first two words, that is too flowery and long and distracting. Don't be scared of periods! P.s. But of course, kudos on the English. $\endgroup$ – guest Apr 25 '20 at 21:45
  • $\begingroup$ I cannot resist pointing out this clever recursion joke embedded into Google's Did-you-mean functionality: i.stack.imgur.com/Vnv4N.png After teaching recursion in an Intro Programming course, too few caught-on to this nerd-joke. PS. Please don't ruin the joke by over exposure! $\endgroup$ – Joseph O'Rourke Apr 26 '20 at 1:49

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