I am not teaching in a classroom, as yet. I tutor on occasion, but I'm still preservice in an ed graduate program (as a career changer). Our superb instructor, Susan Schneider, gave us a treasure trove of different kinds of home-made manipulatives in the curriculum course "Teaching Mathematics in the Elementary Schools." The math topics and degree of introduction depended upon the specific grade level. Our childhood-education curriculum covers K-6. We made our own tangrams for geometry, and cut shapes from construction paper to make flags for a manipulative lesson combining geometry with fractions, as two examples. All of the hand-made manipulatives and games we crafted were from inexpensive materials. These work as well as the costly wood and plastic manufactured manipulatives (which I enjoy using).
Curriculum guides that include lesson plans and "Blackline Masters" or separate activity books from regimented series such as Everyday Math include patterns and instructions for constructing your own manipulatives. These are all going to vary according to what one is trying to teach and illustrate or demonstrate, specifically. Anything manufactured can also be improvised from cheaper materials.
There are dozens of activity books available. Try visiting the Web site of Educators Publishing Service <A HREF="http://www.epsbooks.com/index.asp">Educators Publishing Service and Stern Structural Arithmetic <A HREF="http://www.sternmath.com/">Stern Structural Arithmetic Materials to get an idea of manufactured manipulatives. Catherine Stern was the "godmother" of hands-on math teaching and the rods, etc., that Unifix and Cuisenaire, et al., all copied. The books provide games for materials.
The interactive math Web sites use manipulative exercises in a two-dimensional perspective, with programs for animated, immediate responses to children. Some of the kids I've tutored can get something out of them (the ones who are stronger in math than in reading) and others (the reverse type) can't, at all. Here's a site that lists many other workable math Web sites: <A HREF="http://aolsearch.aol.com/aol/redir?src=websearch&requestId=ebf90ab645e14c16&clickedItemRank=10&userQuery=interactive+math+sites&clickedItemURN=http%3A%2F%2Fwww.teach-nology.com%2Fteachers%2Feducational_technology%2Finternet_in_class%2Fstudents%2Fmath%2F">Math Sites To Use With Students
To sum it up, there is nothing better for learning math than direct, hands-on "experiencing" of concrete demonstrations and illustrations of these abstract concepts. (I even adapted childhood-ed manipulative techniques to help with a university-level statistics class I'm taking at the moment. Sampling can be illustrated with a "population" of jellybeans or m&m's and bell curves can be cut out from paper.)
The textbook we used in the above-mentioned math-teaching course, which I just completed this past July, was also excellent; I see it referenced frequently. It's by John Van de Walle and it's titled Elementary and Middle School Mathematics. We used the 5th edition (2001), but even the older versions are still quite applicable.
Hope this helps. I'm looking forward to putting the wonderful portfolio of things I got from this summer course to work for me in a children's class some day soon.
(Posted and e-mailed)
In a message dated 08/19/03 2:17:05 PM Eastern Daylight Time, firstname.lastname@example.org writes:
> When you suggest manipulatives, what specifically do YOU suggest and use? > > Thanks. > >