I cringe at those basic math question posted on the web.

3 hours ago, Proton2 wrote

Question to C9ers: Is calculus mentioned in high school today?

Yup. Though, our sequence was geometry, algebra II, precalc, calc. Math during senior year was optional, so the majority of students opted out of calc.

On a separate topic, I really don't like the typical high school math sequence. Focuses on the wrong areas imo, which could put people off who would have otherwise enjoyed a college math major. Too much equation solving and not enough mathematical/computational thinking.

@Blue Ink: Mathematics were more "discovered" than "made" so there are a lot of things that are arbitrary because that's just the way it is.

@MasterPie: I actually think a lot of high schoolers would benefit from a slightly dumbed-down course in discrete mathematics.  Sure, it can cover some really eye-glazing areas that are only of minute interest to an average high schooler, but a lot of other principles can be useful in general logical thinking it seems to me.  The pigeonhole principle for example.  Also permutations and combinations.

20 minutes ago, kettch wrote

@Blue Ink: Mathematics were more "discovered" than "made" so there are a lot of things that are arbitrary because that's just the way it is.

That discussion is an entire area of philosophy. And there are certainly big names and good arguments on both sides of that discussion

48 minutes ago, brian.​shapiro wrote

*snip*

Sure there's a reason. If the operators applied based on order in the equation, then the operations couldn't be freely associated with each other and always would have to be put in place in a certain order. For example, lets say you had an equation x × 2 = y × 3. You want to be able to rewrite the equation as x × 2 - y × 3 = 0 and still have it mean the same thing without putting in parentheses. If it was based on the order in the equation you couldn't do that very well. Stacking operations isn't very intuitive for people, only useful for calculators that can only enter one operation at a time. And if you had addition/subtraction taking precedence before multiplication/division you would have something that was intuitively strange, too.

Its not absolutely necessary, of course, but there's a reason behind it; its not arbitrary that standard order of operations works like that.

nope. You have to box the object since you are moving the entire box, not individual items. Telling someone to move box of toys, or take toys out and move them, are completely different things, as the box is gone and the toys do not have the same relative displacement anymore. It is the same as you pass in a student object pointer or pass in individual student attributes in the parameters. They are very different and is no brainer to programmers.

31 minutes ago, brian.​shapiro wrote

Its not absolutely necessary, of course, but there's a reason behind it; its not arbitrary that standard order of operations works like that.

But it's only reasonable in the context of the standard interpretation of math in which we have mathematical phrases that try to map to our spoken expressions ("He is twice as tall as she, but she is three times as tall as someone else"). The interpretation tells us all the possible valid phrases there are out there, which places constraints on the syntax construction. Take another interpretation (possibly less complete), and the rules for writing syntax changes. You could very well start at the syntax with no knowledge of the interpretation you're using (or that there even exists a standard interpretation) and then become confused why you must do things a certain way.

But this is just true in general when told to memorize facts and processes - without context, you have nothing to really attach to and you just become a slave to prescribed facts, incapable of generating your own extensions to ideas.

@Kental2: Permutations/combinations are taught in some high schools - it's also a staple of the SATs.

I think they should teach basic proof technique (direct/contradiction) and use that as a backdrop to many of the major topics. Then, it becomes obvious where all these facts students typically take for granted come from.

19 minutes ago, MasterPie wrote

I think they should teach basic proof technique (direct/contradiction) and use that as a backdrop to many of the major topics. Then, it becomes obvious where all these facts students typically take for granted come from.

Like how the biggest prime is 2,147,483,647

 

Proof by contradiction:

Suppose X is a prime larger than 2,147,483,647

Contradiction: there are no numbers larger than 2,147,483,647

QED.

Here is a simple explanation. 1 apple + 3 apples = 4 apples. Obviously you cannot say that as, (1apple + 3 ) * apple because 3 is NOT an apple.

36 minutes ago, magicalclick wrote

*snip*nope. You have to box the object since you are moving the entire box, not individual items. Telling someone to move box of toys, or take toys out and move them, are completely different things, as the box is gone and the toys do not have the same relative displacement anymore. It is the same as you pass in a student object pointer or pass in individual student attributes in the parameters. They are very different and is no brainer to programmers.

Yea, but the alternative is an order of operations which is difficult to use in practice. So some type of "boxing" order of operations is preserved, higher order mathematical functions are given first priority, and the "boxing" is in your head. I never said it was necessary, just that it wasn't arbitrary, and its not arbitrary.

The standard order of operations also prevents a left-to-right "stacking" of the operations and allows you to do it from either direction.

So lets say someone knows nothing of math and sees an equation and doesn't get what to do. I understand the problem. But if you take one or two math courses, the choice for the standard order of operations should seem intuitive, and not something easy to forget.

@brian.shapiro: I agree. It is very basic for people who have being taught with elementary math. Hence, I cringe at people who failed this.