for all you math wizzards out there, I need help!!!!!!

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Guangzhou

Trad climber
Asia, Indonesia, East Java
Feb 24, 2014 - 07:35pm PT
Making math engaging, by (for example) having the kids take measurements to perform math on, is an education school myth. For one thing, most kids don't get too fired up about "real world" data because today they have so much at the touch of a keypad that it just doesn't impress them very much.


As math teacher, I couldn't disagree more. Currently, my eight graders are doing a "Bungie Baribie" project. (Algebra I) They are engaged and excited. Actually, we even added some technology components to it so students can use video cameras and their tablets.

Same is true when my seventh graders were learning about scale. We learned the basics, but they spent over a week mapping various parts of the school grounds to scale. We then took the various parts of the school and put them together into a large collage for a full layout of the school done to scale.

In my experience, students do enjoy technology added to the material whenever possible, but they also enjoy getting out of their seats, moving aorund and using hands on tools to do real math.

In two weeks, my seventh graders will explore slope. We'll use our stairs. Some of us might even meet at the local ski area with GPS and altimeter to figure the average slope of the ski area. (Extra credit)

Math procedure do need to be part of the instruction, but having students take those procedures one step further helps them enjoy math more. If I can get students excited about coming to class, they are easy to teach.

Cheers again,
Eman
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 upper-grade high-school 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 pre-calculator 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 more-procedural 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 long-term 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 super-calculation 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 super-calculation 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 PhD-been-doing-this-and-only-this-forever 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 A-level 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 pre-calculator 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 higher-degree 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!
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