- --- In mathforfun@yahoogroups.com, "brianejensen" <brianejensen@p...>

wrote:> Most of the math I see including these absolute values has no

Brian,

> purpose. But understanding graphs is very important.

>

> [snip]

>

> So much math is worthless, yet when students get out of school,

> they don't know how to calculate the important things.

>

So far in this group you've called factoring and the quadratic formula

worthless and/or uninteresting, and declined (aside from one sentence

about graphs above) to say what mathematics you yourself use regularly

or find important. Judging from your posts, much of mathematics *is*

useless or uninteresting *to you*; that's your business. However, when

you make these comments as if they were factual, it seems an attempt

(perhaps unconscious) to instill students with mistrust or contempt of

theoretical considerations. (Perhaps you're aiming at plodding and/or

ignorant school teachers, but if so you're shooting wide of the mark.)

You've mentioned software on multiple occasions, but seem to ignore

that fact that someone had to write the software, and therefore had to

understand how mathematics works theoretically and be able to verify

that the software does what it claims to do. I'd be sorry to see

students oblivious to the fact that computers are tools (not thinking

machines), and taught to treat all computer answers as definitive.

Training students to use a particular piece of software instead of

teaching them to think with logic, clarity, and organization would be

an educational disaster, in my opinion.

vcamt1510's absolute value questions may not have direct mathematical

relevance, but they serve at least two obvious pedagogical purposes:

* Applying a definition recursively.

* Organizing cases.

In my experience, students are often surprised that W-shaped graphs

can be described by a single formula, so a third result might be

"breaking down conceptual misperceptions".

Regards,

adh - Well said, adh. As for myself, I was wondering why someone who

thinks "so much math is worthless" would even be a member of this

group.

As I think I've mentioned before, I'll be teaching a class called

Introduction to Brownian Motion and Stochastic Calculus next

semester. It will be the most advanced and theoretical class I have

so far taught in my short career. And yet, I've been told by fellow

faculty that most of my students will not be math majors. They will

be finance majors, biologists, and other applied scientists.

For whatever reason, these "real world" folks find this kind of math

useful. And you can rest assured that they all will know how to

factor, apply the quadratic equation, and deal with absolute values.

The idea that these tools are worthless is just so incredibly naive.

I want to write more, but I feel I'm probably wasting my "breath".

Also, comments like this probably deserve less attention than

they've gotten. So enough said. But hopefully younger members of the

group will come to their own, independent conclusions about the

value and interrelationship of all parts mathematics.

--- In mathforfun@yahoogroups.com, adh_math <no_reply@y...> wrote:

>

> --- In mathforfun@yahoogroups.com, "brianejensen"

<brianejensen@p...>

> wrote:

> > Most of the math I see including these absolute values has no

> > purpose. But understanding graphs is very important.

> >

> > [snip]

> >

> > So much math is worthless, yet when students get out of school,

> > they don't know how to calculate the important things.

> >

> Brian,

>

> So far in this group you've called factoring and the quadratic

formula

> worthless and/or uninteresting, and declined (aside from one

sentence

> about graphs above) to say what mathematics you yourself use

regularly

> or find important. Judging from your posts, much of mathematics

*is*

> useless or uninteresting *to you*; that's your business. However,

when

> you make these comments as if they were factual, it seems an

attempt

> (perhaps unconscious) to instill students with mistrust or

contempt of

> theoretical considerations. (Perhaps you're aiming at plodding

and/or

> ignorant school teachers, but if so you're shooting wide of the

mark.)

>

> You've mentioned software on multiple occasions, but seem to ignore

> that fact that someone had to write the software, and therefore

had to

> understand how mathematics works theoretically and be able to

verify

> that the software does what it claims to do. I'd be sorry to see

> students oblivious to the fact that computers are tools (not

thinking

> machines), and taught to treat all computer answers as definitive.

> Training students to use a particular piece of software instead of

> teaching them to think with logic, clarity, and organization would

be

> an educational disaster, in my opinion.

>

> vcamt1510's absolute value questions may not have direct

mathematical

> relevance, but they serve at least two obvious pedagogical

purposes:

>

> * Applying a definition recursively.

> * Organizing cases.

>

> In my experience, students are often surprised that W-shaped graphs

> can be described by a single formula, so a third result might be

> "breaking down conceptual misperceptions".

>

> Regards,

>

> adh - --- In mathforfun@yahoogroups.com, "brianejensen"

<brianejensen@p...> wrote:> Most of the math I see including these absolute values has no

purpose.

Sorry you feel that way Brian. They do have a purpose though:

Look outside of your window. It's a non-linear world out there.

And Mathematics is a refelction of that non-linearity. Know about

the "butterfly effect" huh? The smallest of inconsequential,

seemingly unimportant concepts in math can lead to profound effects,

a bifurcation if fact. Now they want to control hurricanes by . . .

but I digress. "The Mandelbrot set broods in silence at the center

of the complex plane". Thus began a revolution.

I recently found another use for the quadratic formula . . . and RSA

(I'm doin' that now). You know, if you know phi(n) then you can

find p and q by the . . .

Dragon - For many of these problems, the case-by-case method works well. See

also other post re: the importance of organizing cases. However,

one should also recall that there is an algebraic (non-piecewise)

definition for the absolute value. abs(x)=sqrt(x^2). So we could

write sqrt[(1-abs(5x)^2]=sqrt[x^2] then square both sides to get (1-

abs(5x))^2=x^2, and et cetera. Like I said, for this particular

problem, I think the case by case method is going to be easier.

Note also that some of these problems are identities, e.g., #3, abs

(x)>=0 always, so abs(x)+2>=2 and so abs(abs(x)+2)>=2 and is always>1. #2 is similar except abs(2-abs(x)) might equal 0, when abs(x)

=2, when x=+/-2.

Good luck!

Adam

--- In mathforfun@yahoogroups.com, "vcamt1510" <destinygurl15@h...>

wrote:>

> how would I start off these problems?

>

> 1) |1 - |5x|| = |x|

>

> 2) | 2 - |x| | > equal 0

>

> 3) ||x| + 2 | > and equal to 1

>

> 4) |5 - |x| | > and equal to 1