Math manipulatives may include common objects used to assist in the illustration of mathematical concepts by using concrete or real, tangible objects. Many successful educators and parents rely on common household objects such as paperclips, pennies, measuring cups, buttons and money as manipulatives. The most important aspect of the manipulative is that it exists as a real object students can hold and manipulate in trying to work out a math concept or problem.
It has become understood in educational circles that students learn best through active experiences rather than lectures or passive listening. The abstract qualities of math concepts prove difficult for most students beginning to learn them. For example, figuring out the number of puppies possessed by a pretend boy who has 12 puppies then gives three to one friend and four to another may be difficult for a student. However, once the student holds 12 small objects in her hand that she can then pretend are puppies, she can act out the problem concretely and arrive at an understanding of the mathematical concept. Eventually, the manipulative no longer serves a purpose because the concept is internalized.
Manipulatives serve many purposes, all leading toward a better understanding of mathematical concepts and more success in figuring out correct answers. They provide a visual representation of math problems. Visual images stick with people longer and better than abstract or language based concepts. Manipulatives also help to hold the attention of inattentive learner. Often students become anxious when faced with a blank page of math problems and only a pencil to assist them in figuring out the answers. Even if they have a grasp of the concept, anxious learners benefit from the option of being able to first reassure themselves by visualizing the concept with manipulatives before writing it down.
Math manipulatives include tangible common objects such as dice, toothpicks or straws as well as educational materials such as geo-boards, pentominoes and pattern blocks. Math manipulatives may also be printed from paper and cut out. Math games, both commercial and modified traditional games like Math War, provide another type of manipulative. Some even consider artwork, such as drawing or painting a picture of the problem, as a manipulative.
Online virtual manipulatives and computer software use appear to be increasing. This form of manipulative math does not place the actual object into a student's hand. However, it does allow for the manipulation of on screen objects such as tangrams and pattern blocks as tools in figuring out mathematical concepts. Few would argue the fact that virtual manipulatives provide excellent sources of visual imagery for learners to associate with math concepts.