The use of manipulatives provides memory cues for different kinds of learning. The movement of the arm in operations of addition or subtraction, multiplying or dividing, reinforces the meaning of the operations for kinesthetic learners. In the operation of addition, the arm sweeps two or more groups of blocks together. In subtraction, the arm moves to separate a part from the whole. In multiplication, the arm moves repeatedly to add a group a particular number of times. In division, the arm makes the sharing-out movement that card players or parents of small children recognize immediately. The shapes, colours and sizes of the manipulatives provide cues for visual learners, and they carry those images with them when they move to working mentally or on paper. Finally, since talking seems to go with using manipulatives, auditory learners get to tell themselves stories about what they are doing, and hear others talk about the processes they are demonstrating, and this verbal rehearsal of the process is committed to memory.
Most important, the students nearly always get the right answer when they use manipulatives. If you ask a student to add 1/3 + 1/6 using manipulatives, the answer will never come out to 2/9, which is a common error students make when adding fractions on paper. This means that the instructor deals with a student who has the correct answer. Rather than having to deal with an error, you can work on extending understanding, or helping the student articulate the concepts. The benefits in terms of student self-confidence are evident.
The advantage of commercial manipulatives is that they are accurate and available. Plastic pieces made in a factory are precise—they will stack as needed, and 2/10 are exactly equal to 1/5; 10 tens are exactly equal to 100. They cost money, not teacher time, and they are ready for use. If you live in an urban area, there may be a teachers' store that carries a variety of manipulatives and models. Outside of major centres, if you want to try before you buy, check with someone in the local K-12 system to see what they can show you. Anyone can look on-line for what is available; here are some places to start:
Artel Educational Resources, in Vancouver, sells many different types of manipulatives: http://www.arteleducational.ca/index.php
National Library of Virtual Manipulatives lets you try out, virtually, many different kinds of manipulatives that are available in real form for students: http://nlvm.usu.edu/en/nav/vlibrary.html
Center School District lets you cut strips into fractions, decimals, and percents. Fun for you to play with. Scroll down for instructions. http://arcytech.org/java/fractions/fractions.html