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Complex concepts made easy with visual models in an equitable way!

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 meta-analysis of sixty studies (kinder- garten through post-secondary) that compared the effects of using concrete materials with the effects of more abstract instruction, Sowell concluded that the long-term use of concrete 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 concrete-to-representational-to-abstract (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 follow-up 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 problem-solving tests.

  Notes on Common Core.