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