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Topic: RE: Reply to a Post of 2/06/09 Why Robert Atkin method offactoring trinomials works
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Fred Siegeltuch

Posts: 19
Registered: 10/7/05
RE: Reply to a Post of 2/06/09 Why Robert Atkin method offactoring trinomials works
Posted: Apr 21, 2009 12:52 PM
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Laura , of course you are correct.

One part of the problem is the high cost of appropriate calculators or computers. TI has some very nice products but they are expensive. But the age of affordable smart phones such as the iPhone, or affordable smart music players such the iPod Touch is fast approaching. While these devices are currently more expensive than a graphing calculator, they or similar items will not be for long. Moreover, many students will already have them and they will also be less resistent to buying them because they are multi purpose devices. A quick Google search showed me that there are many (often free) apps that can graph and/or do symbolic algebra. If the SAT and the ACT allowed the use of these devices as long as the app was not more powerful than the equivalent calculator then high schools would start to make the move to these devices because ultimately they would save money. Once this happens it will be even easier for community colleges to design courses where
devices like these are required.

Fred

--- On Tue, 4/21/09, Laura Bracken <bracken@lcsc.edu> wrote:

From: Laura Bracken <bracken@lcsc.edu>
Subject: RE: Reply to a Post of 2/06/09 Why Robert Atkin method offactoring trinomials works
To: mathedcc@mathforum.org
Date: Tuesday, April 21, 2009, 11:12 AM

Of course you are assuming that the students have either access to Excel or a graphing calculator.  Most developmental elementary algebra students in the U.S. are not allowed to use a graphing calculator.

I am concerned that the divide between those of us that support reforms in the traditional curriculum, including many who belong to AMATYC, and what the rest of the country just keeps on doing, especially those that rely heavily on adjuncts, is getting wider. The technology question is only one part of it. 

Laura



-----Original Message-----
From: owner-mathedcc@mathforum.org [mailto:owner-mathedcc@mathforum.org] On Behalf Of Robert Kimball
Sent: Tuesday, April 21, 2009 8:53 AM
To: mathedcc@mathforum.org
Subject: Re: Reply to a Post of 2/06/09 Why Robert Atkin method offactoring trinomials works

to get an idea of how Excel can be used to support what Fred has said,
go to:  http://www.therightstuff.amatyc.org/materials.htm
and clck on:   

Using Excel to Create Immediate Formative Assessment (XLS)

Rob


Robert L Kimball
rob.kimball@yahoo.com
Consultant
919-449-4439



>>> Fred Siegeltuch <notesforfred@yahoo.com> 4/21/09 10:22 am >>>
If I were a secondary school teacher, I would have to teach factoring
quadratics because my students would need to do it on standardized
tests. Do community college teachers have similar restrictions? If not,
why teach it with so much emphasis on being able to do it quickly by
hand? Factoring itself is important, but factoring quadratics can be
done via completing the square just as one might to derive the quadratic
formula. Students put the quadratic formula on their calculators. It
wouldn't be much different to put on a small program to factor. In order
to build conceptual understanding, I would prefer a course that
reinforced these aspects including teaching the students to do the
programming themselves,either on their calculator or on a spreadsheet.

Fred Siegeltuch

- --- On Tue, 4/21/09, Annette Hawkins <hawkins@waynecc.edu> wrote:

From: Annette Hawkins <hawkins@waynecc.edu>
Subject: Re: Reply to a Post of 2/06/09 Why Robert Atkin method of
factoring trinomials works
To: mathedcc@mathforum.org, jritchey5072@yahoo.com
Date: Tuesday, April 21, 2009, 7:57 AM

Please don't use this method because:
1.  When the students enter College Algebra, they can't keep up with
the instructor when he/she has to factor a problem.  These students
are
left in the dust in a College Algebra class.
2.  They have no clue how to factor trig equations and exponential
equations.
3.  The idea is to think about where the terms come from in the
trinomial and undo the process.  Some thinking is required.
 
Just my two cents.

Annette D. Hawkins, Ed. D.
Math Department Head
Wayne Community College
3000 Wayne Memorial Drive
Goldsboro, NC 27534
919-735-5151 x 709
hawkins@waynecc.edu



>>> <jritchey5072@yahoo.com> 4/20/2009 4:03 PM >>>

I have the same text book (Sullivan Algebra Trigonometry, 4 ed.) and
came across the same method for factoring trinomials. I LOVE IT!  I am
the tutor at a community college, and, after discussing the method
with
an instructor and understanding its mathematical process, I regularly
show it to my students.

The reason this method works is due to the factoring out of the common
factors.

Given the trinomial:  6x^2 - x - 12
Multiply coefficient a with constant c   6(-12) = -72
Factors of -72 whose difference (or sum) is 1 are 8 and -9

The coefficient of the leading term and the square root of the
variable
are then written as the first term of each factor:

(6x     )(6x    )

Then the 8 and -9 are inserted into their positions as the second:

(6x +  8)(6x - 9)

What is NOT shown in the text book (page 47), is that the factors must
be understood to be written over a common factor of the EXTRA number
used in the second factor, in this case 6.

(6x + 8)(6x - 9)
- ----------------------
          6

When the GCF's are removed from each factor, the real factors are
obtained, and the common factors are cancelled by the common
denominator.

2(3x + 4)(2x - 3)3
- ----------------------
          6

(3x + 4)(2x - 3)

NOTE: Just as with any other method of factoring trinonials, make sure
ALL GCF's are removed as the first step.


     

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