<div dir="ltr">In secondary math classes we often say "Math is a language", but we really don't teach it that way.<br><br>The closest we get to that is calling the comparison operators 'verbs' and the various kinds of values that can be combined into expressions 'nouns'.<br>
<br>So, as far as contemporary secondary math thinking is concerned, the only 'verbs' in 'math' are '=', '<', and '>', forms of 'to be'.<br><br>However, I'd bet that a lot of students, and even teachers, would categorize '+', '-', '*', and '/' as 'verbs'.<br>
<br>After all, they seem to suggest 'action'.<br><br>But is '2 + 3' a sentence or a complete thought?<br><br>No, it is an expression which is equivalent in value to another expression, namely, '5'.<br>
<br>I keep thinking that, mathematically, it makes more sense to say that '2 + 3' is one of the already-existing partitions of '5'.<br><br>Interestingly, if '2 + 3' were to be taken as a sentence, it would be imperative:<br>
"Hey you! Yeah, you! Find the value of 2 + 3, now!"<br><br>Mathematically speaking, it would be more accurate to read '2 + 3' as 'the sum of 2 and 3'.<br><br>Mathematically speaking, '2 + 3' is a value that does not need to emerge in time. It already exists.<br>
<br>But, computationally speaking, it actually does make sense to think of '2 + 3' as a process.<br><br>We start with a '2', then we do something with some registers or whatever, and we increment '2' by '3', and we end up with '5'.<br>
<br>And then this leads into the question of functions - are they 'nouns' or 'verbs'?<br><br>In OO terms, functions are how objects relate to other objects.<br><br>Mathematically speaking, at least according to contemporary secondary textbooks, a function is a set of ordered pairs.<br>
The expression 'f(x)' is a VALUE. So, 'f(x)' is a 'noun'.<br><br>But again, computationally speaking, a function is a process. It takes in some information, does something to it, and then yields some new information.<br>
<br>In computational terms, a function is something we 'do' to a value to produce a new value.<br><br>I do apologize if this is not the correct venue for raising such questions, as it is not language specific, but I find this really interesting. I think it might have a lot to do with contemporary students, and teachers!, not 'getting' what math really is, and it might shed a lot of useful light on the disconnect between the current secondary math curriculum and the current state of computational understanding.<br>
<br>This semester, at a high school level, I do intend to teach math as a 'language', and I'd like to get really clear about these kinds of things.<br><br>Thanks very much for any feedback,<br><br>Michel Paul<br>
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