I can't speak to your K-12 math education, but I used mine all the time.
* There were always word problems. I had to take a few sentences or even a paragraph, and turn it into a representation that allowed me to get the answer. In later years this representation included variables that let me change some details and still get the right answer. Many of these had useless information included in the description, or were confusingly written, and I had to puzzle out the deeper model. This is not very different than taking a spec and making it into software. Particularly if you work directly with end users, who may include lots of unnecessary details. Sure the thing I build uses code rather than algebra equations, but that is not a huge leap - they are both mechanical rules that when applied to a problem give great, accurate answers.
* Speaking of variables - just learning variables and internalizing them is pretty damn useful for coding. This is not necessarily an easy thing to internalize - tutor some kids at basic algebra sometime. The idea that X holds a value seems pretty easy to grasp, but reasoning about X being any value[0] is pretty hard to grasp (until you do, then people say "i don't know why that was hard").
* Order of operations is another thing that was super important in k-12 math. Understanding that doing things in different orders gets different results is another big concept. It also leads to other operation ordering things - like doing things in a different order may be easier, and it's ok because they are equivalent (this is a huge chung of algorithms - do the steps in a different, equivalent order, and it's less work)
* Factoring in algebra and factoring in code are literally the same thing. Here is a list of variables and operations. Rearrange them into a different list of variables and operations using different functions.
* Substitution and systems of equations are pretty much the same thing. If y = x + 1, I can replace any Y with (x+1) and get correct answers. In coding we call this inlining and loop unrolling. Or even just replacing
$thing = func();
other_func($thing);
with
other_func(func())
And even more directly I was function composition (f(x), g(x), f(g(x)), f o g, etc) directly at least a couple times.
* Cartesian coordinates are very helpful when doing any kind of page layout - like say HTML/CSS.
* Simple set theory is useful all the time too. Heck I even use Venn diagrams (something I learned in 2nd grade) all the time. Set theory comes up obviously in databases (and other data stores) join is just a method of computing intersections. But it also comes up in other places when defining things. A huge problem when designing systems is what I call the "square/rectangle" problem - all squares are rectangles but not all rectangles are squares. This is fundamentally a set definition problem - figuring out what set we are talking about based on certain properties applies to (but is not limited to): database schema design, object hierarchy, program scope, filter creation, and so on.
Looking at your comment again makes me wonder if you are questioning the Parent's semantics of "useful functionality" and "simple" vs "trivial". I'm not going to dive into that, but I will say I used many of the above concepts daily in simple shell pipelines (opening the semantic argument of what a program is, but going as broad as possible, a shell pipeline is a one off program that can be turned into a stored program by putting it in a file).
I regularly want to find something in a logfile. Logs have a lot of data. Oh, I can find the subset with grep.
cat log | grep thing
Oh, thats a lot of data. I can need to filter more, I don't want all these lines about session validation. I guess I could make a regex. Or I could just factor that into a `grep thing|grep -v session`. Ill do that, its equivalent.
This is a trivial example of using composition, substitution and set thinking. I can extend it with "thats a useful search, maybe use a variable" and so on. Can this be learned, and done without having known the stuff taught in k-12 math? Maybe I don't know, but the place I first encountered and internalized those concepts is math class.
Even more controversial (from the is this a program point of view) is that these things are all useful in doing excel formulas and vba scripts.
[0] I know that's not strictly true, particularly with types in a computer language. But they taught me about domains, and things like "this is true when X is not 0" and so on. This translates well to code too - checking that values are acceptable in tests and input sanitization, or conversely, finding weird values by fuzzing are all applications of domains.
I think algebra actually hurts learning of programming, at least of the BASIC/FORTRAN/C style syntax. Programming variables don't work like algebra variables. I learned programming before algebra and had no problem with statements like "X=X+1". My brother on the other hand learned algebra before learning programming and a statement like that made no sense to him (what, 0 = 1?). Of course this was because in BASIC (as in many other languages) "=" is used both for assignment and comparison.
* There were always word problems. I had to take a few sentences or even a paragraph, and turn it into a representation that allowed me to get the answer. In later years this representation included variables that let me change some details and still get the right answer. Many of these had useless information included in the description, or were confusingly written, and I had to puzzle out the deeper model. This is not very different than taking a spec and making it into software. Particularly if you work directly with end users, who may include lots of unnecessary details. Sure the thing I build uses code rather than algebra equations, but that is not a huge leap - they are both mechanical rules that when applied to a problem give great, accurate answers.
* Speaking of variables - just learning variables and internalizing them is pretty damn useful for coding. This is not necessarily an easy thing to internalize - tutor some kids at basic algebra sometime. The idea that X holds a value seems pretty easy to grasp, but reasoning about X being any value[0] is pretty hard to grasp (until you do, then people say "i don't know why that was hard").
* Order of operations is another thing that was super important in k-12 math. Understanding that doing things in different orders gets different results is another big concept. It also leads to other operation ordering things - like doing things in a different order may be easier, and it's ok because they are equivalent (this is a huge chung of algorithms - do the steps in a different, equivalent order, and it's less work)
* Factoring in algebra and factoring in code are literally the same thing. Here is a list of variables and operations. Rearrange them into a different list of variables and operations using different functions.
* Substitution and systems of equations are pretty much the same thing. If y = x + 1, I can replace any Y with (x+1) and get correct answers. In coding we call this inlining and loop unrolling. Or even just replacing
with And even more directly I was function composition (f(x), g(x), f(g(x)), f o g, etc) directly at least a couple times.* Cartesian coordinates are very helpful when doing any kind of page layout - like say HTML/CSS.
* Simple set theory is useful all the time too. Heck I even use Venn diagrams (something I learned in 2nd grade) all the time. Set theory comes up obviously in databases (and other data stores) join is just a method of computing intersections. But it also comes up in other places when defining things. A huge problem when designing systems is what I call the "square/rectangle" problem - all squares are rectangles but not all rectangles are squares. This is fundamentally a set definition problem - figuring out what set we are talking about based on certain properties applies to (but is not limited to): database schema design, object hierarchy, program scope, filter creation, and so on.
Looking at your comment again makes me wonder if you are questioning the Parent's semantics of "useful functionality" and "simple" vs "trivial". I'm not going to dive into that, but I will say I used many of the above concepts daily in simple shell pipelines (opening the semantic argument of what a program is, but going as broad as possible, a shell pipeline is a one off program that can be turned into a stored program by putting it in a file).
I regularly want to find something in a logfile. Logs have a lot of data. Oh, I can find the subset with grep.
Oh, thats a lot of data. I can need to filter more, I don't want all these lines about session validation. I guess I could make a regex. Or I could just factor that into a `grep thing|grep -v session`. Ill do that, its equivalent.This is a trivial example of using composition, substitution and set thinking. I can extend it with "thats a useful search, maybe use a variable" and so on. Can this be learned, and done without having known the stuff taught in k-12 math? Maybe I don't know, but the place I first encountered and internalized those concepts is math class.
Even more controversial (from the is this a program point of view) is that these things are all useful in doing excel formulas and vba scripts.
[0] I know that's not strictly true, particularly with types in a computer language. But they taught me about domains, and things like "this is true when X is not 0" and so on. This translates well to code too - checking that values are acceptable in tests and input sanitization, or conversely, finding weird values by fuzzing are all applications of domains.