Colleagues,

I have also used rulers (both inches and centimeters) and  measuring 
tapes extensively for work with fractions. I have even had learners 
create measuring "ribbons" with inches marked off.  As we measure 
windows for shades, it becomes apparent soon that there is a need to 
have more exact measurements, and we get into fractions, starting with 
adding halves to the ribbons, and then later, fourths, etc. These also 
function as a number line and give meaning to adding and subtracting 
fractions as well as estimating. Centimeters work for understanding 
decimals. These tools can be used for area and perimeter as well. Using 
these tools does not seem "babyish" to learners, has real-life practical 
applications, and you would be amazed at how many people don't know how 
to measure.

Lynda

-- 
Lynda Ginsburg
Senior Research Associate, MetroMath
Rutgers University
118 Frelinghuysen Road
Piscataway, NJ 08854
Tel: 732-445-1409       Fax:  732-445-2894



Judy Ward wrote:


>The research supporting use of manipulatives is the concrete to semi

>concrete (or representation) to abstract sequence. All of that research was

>done with children and, to my knowledge none has been done using adults in

>ABE/GED/Literacy programs. There were a couple of studies completed during

>the late 1990's with community college algebra students. 

>

>The CSA sequence begins with the concrete (blocks, fraction rods, etc) so

>the concept can be seen and handled. Using beans or chips for counting is an

>example. The semi concrete or representation is the use of a drawing of the

>concept or problem to find an answer (drawing sticks for counting). The

>abstract is the step taken when the student can perform the operation or

>solve the problem with out the first two steps. Adult students tend to go

>back and forth between the first and second step and then "leap" to the

>third. 

>

>Adult students have gaps in their knowledge of mathematics. Those gaps can

>be concepts like place value, multiplication, fractions, etc. The use of

>manipulatives can help the adult student "see the why" and fill in those

>gap(s). There are many success stories told by instructors who took the

>knowledge of how to use manipulatives back to their students. Those students

>became more confident in their math ability by "seeing the why". 

>

>Mev and Susan pointed out that manipulatives can be made out of construction

>paper and other items found around the home and school. The cutting and

>tearing of construction paper, paper plates, rulers, etc are wonderful

>activities from which the student learns many things and can be used as an

>assessment technique. But, if you think differently and look closely there

>are things all around you that can be used.  

>

>I looked in many $1 stores in small Arkansas towns as well as Wal Mart for

>geometry "things". Guess what? Look in the cosmetic section of Wal Mart,

>Walgreens, Kmart, Target and most grocery stores and you will find cosmetic

>sponges that are very inexpensive and are great for teaching geometry

>concepts. They come in circles, rectangles and wedges (some of them are very

>nice prisms) of different sizes that can be cut, stacked and colored. 

>

>The manipulatives that are "store bought" are not expensive because only one

>set is usually all that's required. The Cuisenaire Rods come in sets for 1

>to 4 people and cost around $10. There several reasons why I like using the

>CR. 1. the student learns that "1" can be anything. When using fraction

>circles one is always 360 degrees. 2. the student can see immediately what

>an equivalent fraction is and it makes sense. 3. that "reducing" a fraction,

>which doesn't make sense, is actually "exchanging for fewer parts". 

>

>I use a great paper back book with the CR titled "Everything's Coming Up

>Fractions". The adult instructors and students that I have worked with love

>manipulatives. They work and they make sense! 

>

>Judy 

>

>

>

>Judy Ward, Ed.D.

>6886 Young Farm Avenue

>Springdale, AR 72762

>Phone: 479.361.2223

>Fax: 479.361.2223

>Email: j.e.ward at cox.net

>

>Arkansas Adult Numeracy Campaign

>Teaching Mathematics Effectively to Adult Learners

> 

>

>

>

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