Timeline for Why don't we teach codomains of functions in high school?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 14 at 0:49 | comment | added | Taladris | @Lenny: by symmetry, you can always expand the codomain to whatever you want. And bijections are quite important. | |
| Oct 13 at 19:12 | comment | added | Lenny | The thing is, you can always limit the domain to whatever you want. The range comes from your domain. The codomain is kinda unnecessary unless you require conditions for bijections. | |
| Oct 5 at 1:11 | answer | added | user1815 | timeline score: 0 | |
| Oct 2 at 4:02 | history | edited | Taladris | CC BY-SA 4.0 | added 111 characters in body |
| Oct 2 at 4:00 | comment | added | Taladris | @Stef: I am French and I was also told the full notation in high school in the late 90s (middle school was only dealing about linear functions if I remember well). I am now teaching outside of Europe using US textbooks (Stewart's Precalculus now, Larson's Precalculus and Axler's Algebra and Geometry before). I do teach a bit about codomains and onto functions as extra-material in my precalculus course. | |
| Oct 1 at 9:27 | comment | added | Stef | You don't talk about codomains in high school?! That's news to me. What country are you in? Here the concept of function is introduced in middle school, with domain and codomain and the two-line notation you used yourself in your post (although 95% of the functions encountered in middle school happen to be real linear functions). | |
| Sep 30 at 0:16 | history | edited | Taladris | CC BY-SA 4.0 | added 5 characters in body |
| May 1, 2015 at 18:57 | comment | added | hunter | I think the bigger problem is the one you point out "the domain is ... seen as an inherent property of the formula" which compounds students' confusion between functions and formulas (a confusion which is roughly ok till precalculus and then sets one up for failure in calculus and beyond). In fact, even through calculus, the codomain can be taken as $\mathbb{R}$ without serious interesting real-world-oriented counterexamples. | |
| Apr 5, 2015 at 7:34 | answer | added | Scott Farrar | timeline score: 6 | |
| Apr 3, 2015 at 18:57 | answer | added | Joey Kramer | timeline score: 11 | |
| Apr 3, 2015 at 14:43 | comment | added | Karl | A great question. Perhaps at least part of the answer is that $\mathbb{R}\to\mathbb{R}$ is so common it is overlooked in favour of instilling algebraic manipulation. In my opinion it is important to investigate functions that have radically different domains and codomains (perhaps assigning a primary colour to a number or something like. ) But I agree it definitely should be taught earlier. | |
| Apr 3, 2015 at 13:31 | history | asked | Taladris | CC BY-SA 3.0 |