matlinb
Trad climber
Albuquerque


Feb 24, 2014  11:06pm PT

Some people are good at math. Others not so much. Kinda like climbing.


rgold
Trad climber
Poughkeepsie, NY


Feb 25, 2014  09:29am PT

if you try to teach a 1st grader how to think mathematically without procedure, most will be lost (and perhaps even intimidated by the subject for a life time.)
Sure, but this is a false dichotomy. Moreover the situation of uppergrade highschool students is different.


whitemeat
Big Wall climber
San Luis Obispo, CA


Topic Author's Reply  Feb 25, 2014  09:51am PT

its due tommarow, I am making headway!!!
thanks for the replies!!!!


Darwin
Trad climber
Seattle, WA


Feb 25, 2014  10:11am PT

Guangzhou/Eman,
You are a hero. I think there are a constellation of factors that make learning math possible: an engaged teacher and making math relevant seem the most obvious to me. I go back and forth about dialing back the difficulty and making the problems easier. Sorry if I've missed or restated previous posts. I tuned out of this thread when Clint actually started helping OP with the concepts. Clint you too get a hero badge.
Hey, I have a question. Why bother with factoring? Why not just start with the quadratic equation? Way back in the day, the guessing involved in factoring made me very suspicious and confused about the whole field. Then the teacher might, after the fact, reverse engineer the factored equation. I guess for precalculator times, the factored equation is much more informative.


wbw
Trad climber
'cross the great divide


Feb 25, 2014  01:30pm PT

Rgold, you suggested the dichotomy with the following statement upthread:
One of the many problems in math education is the tendency to treat the subject as procedural.
What I am saying is the thinking in math begins for most with the procedure. After the procedure, then questions such as "why doesn't this work in all cases" might be asked and addressed. Yes, it is different for upper high school aged kids than first graders. But when teaching trigonometry to talented math students, the first thing I do is show where all trig values can be found (the unit circle), and then we start discussing other ways of thinking about the trig functions, and why different ways are helpful in different situations. First the moreprocedural stuff, then the thinking can take place, in my opinion. . although I understand that many folks get turned off by the procedure.
Which is why we do a disservice by selling it as "fun". (No offense Guangzhou. If you're turning kids onto math by taking a week to introduce slope by walking up and down stairs and measuring, and they love it, you are engaging in some worthy teaching. I don't have a week in the curriculum that I am required to teach to do so.)I don't disagree that an interested student is easier to teach than a disinterested student. It's just that by saying it should be "fun", that detracts from the longterm goal of math which is to develop a way of thinking. That long term process is often anything but "fun", and I find it to be insincere to say otherwise.


wbw
Trad climber
'cross the great divide


Feb 25, 2014  01:52pm PT

Hey, I have a question. Why bother with factoring? Why not just start with the quadratic equation? Way back in the day, the guessing involved in factoring made me very suspicious and confused about the whole field.
The quadratic equation is supercalculation intensive, and when I see students bust it out on a quadratic that can be reasonably factored, they often make mistakes.
Plugging numbers into the quadratic formula is procedure. Getting a quadratic to factor is more along the lines of thinking. Also, some other kinds of polynomials can be solved by formula, but those formulas are not practical because they are very complicated. Solving many 3rd degree polynomials by factoring is far easier than using a cubic formula for doing so.


T Hocking
Trad climber
Redding, Ca


Feb 25, 2014  02:00pm PT

its due tommarow, I am making headway!!!
thanks for the replies!!!!
Hope it goes well Meat, let us know how it turns out.
We can work on spelling and capitalization tomorrow.


Big Mike
Trad climber
BC


Feb 25, 2014  02:12pm PT

Rgold wizzards .....
Lol!!


JLP
Social climber
The internet


Feb 25, 2014  02:27pm PT

The quadratic equation is supercalculation intensive, and when I see students bust it out on a quadratic that can be reasonably factored, they often make mistakes. In the real world, nothing is factorable, nothing of matter is even calculated by hand.
The calculation and modeling tools NASA (for example) uses to fly sh#t to the moon are tested and verified to no end by highly specialized and small PhDbeendoingthisandonlythisforever kinds of teams.
They then sell a computational product (Ansys, Matlab, Ansoft, etc) to engineers who will iterate, optimize and match to laboratory test results to no end until a working model of the system of concern is verified. ONLY THEN, the magic calculation is made.
Quadratic Formula = kindergarteners learning to wipe their butt.


jgill
Boulder climber
Colorado


Feb 25, 2014  03:26pm PT

One of the many problems in math education is the tendency to treat the subject as procedural (rgold)
Well, yes and no, Rich. One can easily go too far in the other direction. In the mid 1960s I taught at Murray State in Kentucky and we adopted a college algebra text that began with axiomatic set theory and field theory and required students prove some of the basic properties of algebra. This was the New Math and it didn't fly well there, to say the least. Perhaps with a class of Alevel students it might have.
I agree there should be a balance between procedural and theoretical, but the former will get most students further than the latter.
On the other hand you may be talking about challenging word problems, which do foster the ability to think, sometimes well outside the traditional box.


wbw
Trad climber
'cross the great divide


Feb 25, 2014  03:49pm PT

Quadratic Formula = kindergarteners learning to wipe their butt.
Nice platitude JLP, but, uh, we were speaking in the context of math class; not rocket science.


Reilly
Mountain climber
The Other Monrovia CA


Feb 25, 2014  03:52pm PT

The US educational system is an abject failure, face it. Most people don't
even understand compound interest, let alone quadratic equations.


wbw
Trad climber
'cross the great divide


Feb 25, 2014  04:09pm PT

Actually Reilly, I am constantly amazed that our education system works at all in a society in which more than 50% of married people get divorced, where poor people get marginalized in every conceivable way, and where success is defined as the ability to get more and more materialistic stuff than any single person could need. I think you're wrong.
The expectations we have of our schools to babysit, feed, socialize, moralize, inspire, remediate and yes, even educate our children far exceeds the total amount of resources we put into the endeavor. A free public education is the best bargain a person could ever get.
We tend to measure math education using standardized tests taken by the top students in the world. I would put money on some of the kids in my school competing against the world's best, although admittedly I don't teach at an "average" public high school.


rgold
Trad climber
Poughkeepsie, NY


Feb 25, 2014  04:58pm PT

Hey, I have a question. Why bother with factoring? Why not just start with the quadratic equation? Way back in the day, the guessing involved in factoring made me very suspicious and confused about the whole field. Then the teacher might, after the fact, reverse engineer the factored equation. I guess for precalculator times, the factored equation is much more informative.
Well, factoring applies to far more than quadratic equations. Moreover, for quadratic equations, factoring is equivalent to finding roots, but for higherdegree polynomials, factorizations do not necessarily involve linear factors and so is not about finding roots in the same sense.
The process you learned isn't guessing, properly understood. The point is that if a polynomial with integer coefficients can be factored, then there are a finite number of possibilities, and by trying all of them you either discover a factorization or you determine that the equation is irreducible. Of course, in order to make a valid conclusion of irreducibility, you have to have a factoring method that really does look at all possibilities, and the subject may or may not be taught in a way that provides students with the tools to have that assurance.
One can prove in general that any polynomial with integer coefficients (this includes polynomials in several variables!) is either irreducible or else can be factored in a finite number of steps. Contrast this with the fact that general formulas for roots analogous to the quadratic formula are only available for polynomials of degree less than or equal to four.
Factoring integers and polynomials has a vast array of applications in mathematics. The concepts and techniques can't even remotely be replaced by the quadratic formula, useful though it is.


Guck
Trad climber
Santa Barbara, CA


Feb 25, 2014  05:48pm PT

By the time you have read all these posts, you could have learned to do the stuff!


whitemeat
Big Wall climber
San Luis Obispo, CA


Topic Author's Reply  Feb 25, 2014  06:31pm PT

ok all you naysayers!!!!!!!!
I have finished the packet and have all correct answers!!!!!!!
think I am lying? ask me the hardest question on there and I will give you the answer, I also understand the stuff!!!!
PS: I did it on my own rather copy :)


moosedrool
climber
Stair climber, lost, far away from Poland


Feb 25, 2014  06:55pm PT

Excellent, Whitemeat!
Now, about your writing skills...
;)
Moose


whitemeat
Big Wall climber
San Luis Obispo, CA


Topic Author's Reply  Feb 25, 2014  07:02pm PT

well moose,
that final is on thursday...


moosedrool
climber
Stair climber, lost, far away from Poland


Feb 25, 2014  07:19pm PT

May the Force be with you!


JLP
Social climber
The internet


Feb 25, 2014  07:58pm PT

Nice platitude JLP, but, uh, we were speaking in the context of math class; not rocket science. No, the context here is academia vs the real world  go learn to factor polynomials so you can be successful  go learn to think by solving math problems  or else you'll be boiling fries  it's a farce, a huge cultural myth  and for most people it's just plain wrong.
What makes it even funnier, as I mention, is that nobody actually uses this crap in the real world.
Reality is that most complex theories and equations came from trying to explain why some weird sh#t blew up in a lab somewhere. So they blew some more up and eventually fitted a few equations to it. Galileo, Newton, Bell, the stories are classics  reduced to mere numbers crammed down the throats of today's youth with near zero context.
Math teachers like you  frankly  are perpetuating a reality that does not exist in the real world  and for people like whitemeat, it all just may not sit well for this reason  a lie never does  and maybe he just doesn't know why yet.
The best engineers took their toys apart. The worst ones didn't. Etc.



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