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 Subject: RE: more on Fractions, concept and calculations Author: PWR Date: Jan 23 2005
I'm familiar with the fraction darts program and with the Shodor resources, but
not with the Utah State site.  Could you please supply a web address?
Thanks--

On Jan 23 2005, ihor wrote:
> More thoughts on fractions, etc. I'm still thinking about what
> Cynthia wrote last september.

Cynthia wrote on Sept. 30:

"...I
> was teaching a test-prep class to seniors who needed only to pass
> the math test in order to graduate, having failed it several times.
> I wrote the problem of ordering fractions on the board. The students
> had some ideas of getting common denominators, etc. to work the
> problem, but I asked them to talk about the problem a bit to see
> what they understood about fractional parts. To try to get at what
> they understood, I wrote 6/7 and 7/6 on the board and asked them to
> put those in order. And the students couldn't.

So what does that
> mean? I felt like they had no clue about what these numbers meant.
> So I thought why spend time teaching students to
> add/subtract/multiply/divide fractions (which also was tested) when
> the numbers held no meaning for them. How could this happen? These
> students were plenty bright. I'm sure they'd seen lots of pies cut
> up all through math classes. Why didn't they get it? Where was the
> dis-connect in the understanding?.."

Maybe its because they never
> got it connected in the first place. At some point the light has to
> go on and if it doesn't its all a hodge podge: with lots of
> misconceptions thrown in. All in all - very fragile knowledge.
> One approach could be to chip away at their misconceptions (or lack
> of conceptions) by going after some of the "powerful ideas"
> surrounding fractions. One that seems to be obvious, but not well
> understood is that if you increase the numerator and leave the
> denominator the same the fraction gets larger. Increasing the
> denominator and freezing the numerator has the opposite effect.
> What I like about the fraction darts program is that kids can pop
> the balloon using that strategy alone. See
> http://www.ciese.org/ciesemath/fdarts_s.html to try out the applet.
> You need to download a plug-in to make it work.)

I've also start
> to use the fraction applets from Utah State site (which my teachers
> have nicknamed "matti"). There are 10 altogether:

Fraction Pieces
> – Working with various pieces and wholes to learn about fractions.
> Fractions - Adding – Illustrates what it means to find a common
> denominator and combine.
Fractions - Comparing – Judge the
> size of fractions and plot them on a number line.
Fractions -
> Equivalent – Illustrates relationships between equivalent
> fractions.
Fractions - Naming – Write the fraction
> corresponding to the highlighted portion of a shape.
Fractions -
> Parts of a Whole – Relates parts of a whole unit to written
> description and fraction.
Fractions - Rectangle Multiplication
> – Visualize and practice multiplying fractions using an area
> representation.
Fractions - Visualizing – Illustrate a
> fraction by dividing a shape and highlighting the appropriate parts.
> Fractions (Improper) - Rectangle Multiplication – Visualize and
> practice multiplying improper fractions using an area
> representation.

Shodor has these 8:

Fraction Pointer
> Graphically determine the value of 2 given fractions represented as
> points on a number line then graphically find a fraction whose value
> is inbetween the value of the 2 given fractions and determine its
> value.

Bounded Fraction Pointer
Similar to "Fraction Pointer"
> but the user gives the values for the fractional points on the
> number line  rather than having the computer randomly generate them.
> Fraction Finder
Similar to "Fraction Pointer" but there is no
> arrow to help the user determine the value of a fraction  between
> the two endpoints.

Bounded Fraction Finder
The same as "Bounded
> Fraction Pointer" but there is no arrow to help  the user determine
> the value of a fraction between the two endpoints.

Fraction
> Sorter
Students represents fractions by coloring in the appropriate
> portions of either a circle or a square, then order those fractions
> from least to greatest.

Equivalent Fractions Pointer NEW!!
> Visually represent equivalent fractions by dividing squares or
> circles and shading portions equivalent to a given fraction. Also
> shows the fractional value on a number line as you color in the
> fraction.

Equivalent Fractions Finder NEW!
Visually represent
> equivalent fractions by dividing squares or circles and shading
> portions equivalent to a given fraction. Also shows the fractional
> value on a number line after you check to see if your fraction is
> correct.

Fraction Four
Students play a generalized version of
> connect four, gaining the chance  to place a piece on the board by
> simplifying a fraction. Parameters:  Level of difficulty of
> fractions to simplify.

NCTM has the their fraction track game
> which I'll comment on at later time.

I'm in the process of
> reviewing them and seeing how they work with middle grade students.
> I'll be reporting on this from time to time. In the meantime I'd
> love to hear from teachers who have used them with kids who are
> “at-risk” with learning fractions and see if these tools have
> helped.

-Ihor

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