Research

Due to the popularity of manipulatives over the last twenty years, many researchers have conducted studies to test their true value in the classroom. This began in the 1960’s when Dienes and Bruner theoretically justified the use of manipulatives through their research (McCarty, 1998). Since these early studies “[m]any studies of the effectiveness of using concrete learning materials have been conducted since then, giving rise to agreement that effective mathematics instruction in the elementary grades incorporates the liberal use of concrete materials” (McCarty, 1998, p. 368). Many of the studies which have been conducted have focus on this idea of the value and importance of manipulatives.

A study completed by Resnick and Omanson investigated the difficulty children have when trying to form a connection between manipulatives and the mathematical concepts they represent (Uttal, Scudder & DeLoache, 1997). This research “addressed whether and how third graders established connections between different forms of mathematical expression” (Uttal, Scudder & DeLoache, 1997). Resnick and Omanson studied how children comprehended mathematical information in both written and manipulative form. Children were evaluated in both domains throughout the school year and most showed progress in using Dienes blocks and other manipulatives (Uttal, Scudder & DeLoache, 1997). According to this research “most children could interpret the Dienes blocks expressions for numbers involving hundreds, tens, and ones [and] moreover, they could solve multidigit addition and subtraction problems with the blocks” (Uttal, Scudder & DeLoache, 1997, p. 45).

However, when children were asked to interpret written expressions of problems which were similar to the block problems, they did not show an advantage (Uttal, Scudder & DeLoache, 1997). Students could not solve problems which were much simpler than those practiced (ex. students could solve 103 + 52 but had difficulty with 12+14) (Uttal, Scudder & DeLoache, 1997). This showed students did not understand the concept of addition but could work with their manipulative to solve the previous problem. Use of the Dienes blocks was almost separate from written solutions as seen in results in which children who performed best with Dienes blocks performed the lowest in written problems (Uttal, Scudder & DeLoache, 1997).

Students had learned how to use Dienes blocks but could not relate the manipulatives to other problems of a similar nature, showing how important it is for students to draw a connection between mathematical concepts and manipulatives. If children do not learn how to make this connection they will have to learn how to solve a problem using two separate systems, creating more confusion than aiding in learning (Uttal, Scudder & DeLoache, 1997). Teachers must therefore provide instruction which is guided and constrained when teaching students to work with manipulatives, ensuring students understand concepts and not simply how to work with manipulatives (Uttal, Scudder & DeLoache, 1997).