Discussion:  Roundtable 
Topic:  Fractions, concept and calculations 
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Subject:  RE: more on Fractions, concept and calculations 
Author:  ihor 
Date:  Jan 23 2005 
last september.
Cynthia wrote on Sept. 30:
"...I was teaching a testprep 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 disconnect 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 plugin 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 “atrisk” with
learning fractions and see if these tools have helped.
Ihor
 
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