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Subject:   RE: Expressions vs Equations
Author: Gale75
Date: Jan 27 2011
Research would suggest that language is also important and is the downfall for
many who struggle with word problems and precise understanding of concepts.
There is a difference between posing a problem with an = sign given and students
putting one in to show their simplification.  My experience has been that
students who can multiply by a common denominator in an equation (because there
is something on the other side to keep balance) also want to do the same thing
with expressions - and they do not write something equivalent, they just ignore
the common denominator.

Sometimes quick algorithms (such as the one for converting between a mixed
number and an improper fraction) prevent students from understanding
equivalence.  Then we wonder why they don't understand equivalence.  I also have
students who use = as a "subtotal" as in the example below where things are NOT
equal until the end.

THE  PROBLEM:  Evaluate  3x - 4 when x = 5.

Student work:   3*5 = 15 - 4 = 11.
Obviously  3*5 does not equal 15 - 4, but that doesn't stop them from writing
On the other hand, if a teacher writes this, the student asks "where do you get
that ?"
These are the same students who don't understand why it is not enough to write
an answer without showing work.

Many times, it is when the students support their answers or explain their
thinking that we can see what small misunderstandings are keeping them from
being successful.

On Jan 27 2011, LFS wrote:
> I am wondering if we are putting too much emphasis on the
> "definitions" of expressions and equations for 2 reasons.
1. We say
> an expression has no "equals" sign and then we give the problem.
> Simplify: 3(x+2)-4x+5 To answer this question the student must then
> write "equals" signs, i.e. 3(x+2)-4x+5=3x+6-4x+5=-x+11. Isn't this
> confusing?
2. Our main concern is that the student understand the
> difference between what we do with expressions, equations and
> functions. This is why I really liked the youtube video Susan made -
> the emphasis was on where these mathematical objects come from and
> what we do and why with each of them.
I think the math is important
> and not so much the words. Just my thoughts :)

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