A local teacher has been using Fraction Bars for about a year now, and The Principal said: "Informal surveys of the children in these classes show that about 20% say MATH is now their favorite subject!"
"A mastered algorithm in the hands of a student is an incomparable tool laying bare the conceptual structure of the mathematical problems that the algorithm solves. With such tools, and with the guidance of good teachers in their use, a student can grasp and integrate in twelve years a body of mathematics that it has taken hundreds of geniuses thousands of years to devise."
 David Ross, Ph.D., a mathematician at Kodak Research Labs
In a comprehensive review of activity
based learning in mathematics in kindergarten through grade
eight,Suydam and Higgins concluded that using manipulative
materials produces greater achievement gains than not using
them. In a more recent metaanalysis of sixty studies (kinder
garten through postsecondary) that compared the effects of
using concrete materials with the effects of more abstract
instruction, Sowell concluded that the longterm use of con
crete instructional materials by teachers knowledgeable in their
use improved student achievement and attitudes.
Witzel, Mercer, and Miller (2003) used 34 matched pairs of sixth and seventh graders in a comparison of an explicit concretetorepresentationaltoabstract (CRA) sequence of instruction. Students designated as learning disabled or at risk received instruction in mainstream classrooms. The students involved in the CRA instruction, which employed manipulatives as part of the instruction, outperformed those instructed with traditional abstract methods on both posttests and followup tests. An examination of error patterns indicated that the type of errors matched the type of instruction.
"I recommend you to question all your beliefs, except that two and two make four."
 Voltaire (L'homme aux quarante écus)
Students who use manipulatives in their mathematics classes usually outperform those who do not (Driscoll, 1983; Sowell, 1989; Suydam, 1986). This benefit holds across grade level, ability level, and topic, given that using a manipulative makes sense for the topic. Manipulative use also increases scores on retention and problemsolving tests.
"Belief is no substitute for arithmetic."
 Henry Spencer
Note: These materials preceed common core but still apply for everyone.
