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It seems to me that the mathematical equivalent of the intensional vs. extensional distinction in philosophy would be the distinction between "formal" vs. "functional" objects: formal power series vs. convergent power series, formal integration by parts (with no regard for checking the validity of the operation in a real analysis sense) vs. rigorous integration by parts, formal polynomials vs. functions which happen to be represented by a polynomial, etc. If so, I would say that the formal vs. functional distinction is usually dealt with in more advanced classes, though usually not at the first-year undergraduate level.

For instance, in algebra, the concept of an indeterminate variable in algebra (and its distinction from the set-theoretic notion of a variable in a fixed domain) tends to be sufficient for keeping the two concepts distinct in most situations involving set-theoretic functions and the formal expressions giving rise to those functions. In particular, polynomials can be formal by living in some polynomial ring $R[x]$ generated by an indeterminate $x$, rather than having to be set-theoretic functions on some domain. Algebraic geometry also takes particular care in distinguishing an ideal of polynomials from the set-theoretic locus that that ideal cuts out over a given field, or more generally by distinguishing a scheme from a variety.

Similarly, real analysis, with all its cautionary counterexamples as to how various formal iterations operations (e.g. exchanging limits or sums) can lead to disaster if the appropriate functional hypotheses are not verified, also tends to be pretty good about distinguishing a formal computation from a functional one; often the former is used as an initial heuristic motivation only, with the latter then being brought in for the rigorous proof. Although certainly mistakes have been made by treating a formal computation as if it were functionally valid...

Related to this is the ubiquitous "abuse of notation" in which a package of objects, structures, and forms is referred to via its most prominent component (i.e. by synecdoche). Thus, for instance, one often sees a polynomial function $P: {\bf R} \to {\bf R}$ being used to simultaneously represent both the polynomial function and the formal polynomial that represents it, or vice versa (e.g. "the polynomial $x^2$" to refer to the function $x \mapsto x^2$). Another common instance of this is when dealing with spaces (sets with additional structure); one often abuses notation by using the set itself to denote the space, e.g. a group might be denoted by its set $G$ of elements, rather than by the tuple $(G, e, \cdot, ()^{-1})$ of group structures, or a set-theoretic function by just the mapping $f$, rather than than the triplet $(f,X,Y)$ that includes the domain and codomain of that mapping. Such abuses are technically illegal using the strictest interpretations of mathematical notation, but they save a lot of space and, when used correctly, allow readers to focus on the actual content of an argument rather than on its formalism. Still, it is useful and important to point these abuses out explicitly from time to time...

For instance, in algebra, the concept of an indeterminate variable in algebra (and its distinction from the set-theoretic notion of a variable in a fixed domain) tends to be sufficient for keeping the two concepts distinct in most situations involving set-theoretic functions and the formal expressions giving rise to those functions. In particular, polynomials can be formal by living in some polynomial ring $R[x]$ generated by an indeterminate $x$, rather than having to be set-theoretic functions on some domain. Algebraic geometry also takes particular care in distinguishing an ideal of polynomials from the set-theoretic locus that that ideal cuts out over a given field, or more generally by distinguishing a scheme from a variety.
Related to this is the ubiquitous "abuse of notation" in which a package of objects, structures, and forms is referred to via its most prominent component (i.e. by metonymy)synecdoche). Thus, for instance, one often sees a polynomial function $P: {\bf R} \to {\bf R}$ being used to simultaneously represent both the polynomial function and the formal polynomial that represents it, or vice versa (e.g. "the polynomial $x^2$"). x^2$" to refer to the function$x \mapsto x^2$). Another common instance of this is when dealing with spaces (sets with additional structure); one often abuses notation by using the set itself to denote the space, e.g. a group might be denoted by its set$G$of elements, rather than by the tuple$(G, e, \cdot, ()^{-1})$of group structures, or a set-theoretic function by just the mapping$f$, rather than than the triplet$(f,X,Y)$that includes the domain and codomain of that mapping. Such abuses are technically illegal using the strictest interpretations of mathematical notation, but they save a lot of space and, when used correctly, allow readers to focus on the actual content of an argument rather than on its formalism. Still, it is useful and important to point these abuses out explicitly from time to time... 1 It seems that the mathematical equivalent of the intensional vs. extensional distinction in philosophy would be the distinction between "formal" vs. "functional" objects: formal power series vs. convergent power series, formal integration by parts (with no regard for checking the validity of the operation in a real analysis sense) vs. rigorous integration by parts, formal polynomials vs. functions which happen to be represented by a polynomial, etc. If so, I would say that the formal vs. functional distinction is usually dealt with in more advanced classes, though usually not at the first-year undergraduate level. For instance, in algebra, the concept of an indeterminate variable in algebra (and its distinction from the set-theoretic notion of a variable in a fixed domain) tends to be sufficient for keeping the two concepts distinct in most situations involving set-theoretic functions and the formal expressions giving rise to those functions. In particular, polynomials can be formal by living in some polynomial ring$R[x]$generated by an indeterminate$x$, rather than having to be set-theoretic functions on some domain. Algebraic geometry also takes particular care in distinguishing an ideal of polynomials from the set-theoretic locus that that ideal cuts out over a given field, or more generally by distinguishing a scheme from a variety. Similarly, real analysis, with all its cautionary counterexamples as to how various formal iterations (e.g. exchanging limits or sums) can lead to disaster if the appropriate functional hypotheses are not verified, also tends to be pretty good about distinguishing a formal computation from a functional one; often the former is used as an initial heuristic motivation only, with the latter then being brought in for the rigorous proof. Although certainly mistakes have been made by treating a formal computation as if it were functionally valid... Related to this is the ubiquitous "abuse of notation" in which a package of objects, structures, and forms is referred to via its most prominent component (i.e. by metonymy). Thus, for instance, one often sees a polynomial function$P: {\bf R} \to {\bf R}$being used to simultaneously represent both the polynomial function and the formal polynomial that represents it, or vice versa (e.g. "the polynomial$x^2$"). Another common instance of this is when dealing with spaces (sets with additional structure); one often abuses notation by using the set itself to denote the space, e.g. a group might be denoted by its set$G$of elements, rather than by the tuple$(G, e, \cdot, ()^{-1})$of group structures, or a set-theoretic function by just the mapping$f$, rather than than the triplet$(f,X,Y)\$ that includes the domain and codomain of that mapping. Such abuses are technically illegal using the strictest interpretations of mathematical notation, but they save a lot of space and, when used correctly, allow readers to focus on the actual content of an argument rather than on its formalism. Still, it is useful and important to point these abuses out explicitly from time to time...