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Topic: Simplifying Algebraic Expressions with Subtracted Expressions
Replies: 67   Last Post: Nov 25, 2013 12:57 PM

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Bishop, Wayne

Posts: 2,171
Registered: 12/6/04
Re: Simplifying Algebraic Expressions with Subtracted
Expressions

Posted: Nov 16, 2013 11:49 AM
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The 5th grade Singapore Primary Series book is about right;
challenging problems that are not too far down that road. By 6th,
however, some of them are so complicated that you sort of want to
pull your hair out and scream, "Dammit, use algebra!". The
underlying algebra is evident to anyone who knows algebra and they
are certainly done algebraically except for the abstraction to bars
representing concrete things but what's the point? Lots of schools
here in the US and in Singapore just go directly to real algebra and
the kids are ready.

Wayne

At 04:17 PM 11/14/2013, Robert Hansen wrote:
>I looked at the article again. The problem is from a 5th grade textbook ...
>
>"A few years ago the field of U.S. mathematics education experienced
>a small shock from a word problem in a fifth-grade Singapore textbook..."
>
>And it is prior to the students learning algebra ...
>
>"The time at which students are asked this question, just after
>learning division by fractions, is very important. Prior to that,
>students have not learned the entire definition system. Later,
>students will learn to solve such problems using algebra."
>
>I realize she is trying to describe the state of mind of a complete
>arithmetic student. Where you expect a student to be after a very
>solid arithmetic experience. I also recognize the importance of
>definitions and layering them through those years. However, I am not
>so keen on her notion that this "defines" solid arithmetic, it is
>just but one of the defining elements. I also no longer believe that
>a solid sequence of arithmetic is best defined by elements, strands
>or standards. After studying so many such descriptions of solid
>arithmetic, I still find the very best description to be a good
>textbook on the subject, complete with problems and exercises, from
>start to finish.
>
>I realize that education went the other direction the last 20 years,
>trying to define arithmetic (and algebra etc.) with standards and
>strands, and the curriculums have suffered and are weak compared to
>those previously. I don't know if that will change anytime soon, but
>I collected all the classics in case it doesn't.:)
>
>Bob Hansen
>
>On Nov 14, 2013, at 6:20 PM, Robert Hansen <bob@rsccore.com> wrote:
>

> > But you do agree that for word problems less complicated than
> this there is no {x}? I mean that the the student identifies and
> controls, even subconsciously. That would be algebra. I was under
> the impression that this problem was given to elementary students
> without the benefit of algebra. I need to read the article again
> once my plane gets off the ground.

> >
> > Bob Hansen
> >

> >> On Nov 14, 2013, at 4:34 PM, Joe Niederberger
> <niederberger@comcast.net> wrote:
> >>
> >> Yes, I think so for a word problem of this type there would have

> to be something in the mind that stands for "total #tarts produced


Date Subject Author
11/11/13
Read Simplifying Algebraic Expressions with Subtracted Expressions
MVTutor
11/11/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Robert Hansen
11/12/13
Read Re: Simplifying Algebraic Expressions with Subtracted
Expressions
Bishop, Wayne
11/12/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
MVTutor
11/13/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Jonathan Crabtree
11/13/13
Read Re: Simplifying Algebraic Expressions with Subtracted
Expressions
Bishop, Wayne
11/14/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Joe Niederberger
11/14/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Robert Hansen
11/14/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Joe Niederberger
11/14/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Robert Hansen
11/14/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Joe Niederberger
11/14/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Robert Hansen
11/14/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Louis Talman
11/14/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Joe Niederberger
11/14/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Robert Hansen
11/14/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Robert Hansen
11/16/13
Read Re: Simplifying Algebraic Expressions with Subtracted
Expressions
Bishop, Wayne
11/16/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Robert Hansen
11/14/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Joe Niederberger
11/14/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Robert Hansen
11/16/13
Read Re: Simplifying Algebraic Expressions with Subtracted
Expressions
Bishop, Wayne
11/14/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Pam
11/15/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Robert Hansen
11/15/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Joe Niederberger
11/15/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Robert Hansen
11/15/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Joe Niederberger
11/15/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Joe Niederberger
11/15/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Joe Niederberger
11/15/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Robert Hansen
11/16/13
Read Re: Simplifying Algebraic Expressions with Subtracted
Expressions
Bishop, Wayne
11/16/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Robert Hansen
11/17/13
Read Re: Simplifying Algebraic Expressions with Subtracted
Expressions
Bishop, Wayne
11/17/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Robert Hansen
11/17/13
Read Re: Simplifying Algebraic Expressions with Subtracted
Expressions
Bishop, Wayne
11/15/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Joe Niederberger
11/15/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Robert Hansen
11/15/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Pam
11/15/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Robert Hansen
11/15/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Pam
11/16/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Robert Hansen
11/16/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Robert Hansen
11/16/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Joe Niederberger
11/16/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Robert Hansen
11/18/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Louis Talman
11/21/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Robert Hansen
11/21/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Louis Talman
11/16/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Pam
11/16/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Robert Hansen
11/16/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Pam
11/16/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Robert Hansen
11/18/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
GS Chandy
11/17/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
GS Chandy
11/17/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Pam
11/17/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Robert Hansen
11/17/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Pam
11/17/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Robert Hansen
11/17/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Pam
11/18/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Robert Hansen
11/18/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Robert Hansen
11/18/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Pam
11/18/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Robert Hansen
11/25/13
Read Re: Simplifying Algebraic Expressions with Subtracted
Expressions
Bishop, Wayne
11/25/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Robert Hansen
11/22/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Joe Niederberger
11/25/13
Read Re: Simplifying Algebraic Expressions with Subtracted
Expressions
Bishop, Wayne
11/23/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
GS Chandy
11/24/13
Read Re: Simplifying Algebraic Expressions with Subtracted Expressions
Robert Hansen
11/25/13
Read Re: Simplifying Algebraic Expressions with Subtracted
Expressions
Bishop, Wayne

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