Math Manipulatives Design

The purposes of the undertaken study were: (1) to examine the effectiveness of selected math manipulatives (cuisenaire rods, uniflex cubes) on the math performance (comparing, adding, subtracting fractions and adding and subtracting integers) of below-average eight grade students; and (2) utilize the effectiveness findings to determine whether the existing research on manipulatives using samples of elementary and secondary students generalizes to middle school level students. This chapter of the study describes and discusses all of the methods and procedures used in both the collection and analysis of math performance data.

As noted in the presented review of the research, studies of the effects of math manipulatives using middle school students were mixed with some showing positive results and others showing neutral or negative results. This means that the existing work in the field did not provide a firm foundation for the formulation of a directional hypothesis. For this reason, the hypothesis tested in the study was formulated as a null thesis. This null hypothesis was:

Null Hypothesis: Level of math performance will not significantly differ depending upon whether students were in the experimental or the control groups.

The boundaries (delimitations) beyond which this study does not seek to generalize can be delineated as follows:

1. The study is restricted solely to eighth grade students;

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) for both groups; no differences were observed between experimental and control conditions prior to the study; score values indicated that both groups were approximately two years below grade level in math achievement. Experimental Treatment All students in the experimental condition received ten days of lessons using math manipulatives. These lessons covered: comparing fractions using cuisenaire rods; adding fraction using cuisenaire rods; subtracting fractions using cuisenaire rods; adding integers using uniflex cubes; and subtracting integers using uniflex cubs. Students were given the rods and told that they were going to use the largest one for the rod that equals 1. The other nine rods were said to represent the following: 1/10, 2/10 or 1/5; 3/10,4/10 or 2/5; 5/10 or 1/2; 6/10 or 3/5; 7/10, 8/10 or 54/5 and 9/10. Students were then asked to determine the value of each rod when the rod chosen to be 1 changed. The learning process for the first unit served as a model for finding the value of the other rods when the unit rod changed. This instruction allowed the children to touch, hold and create concrete representations of fractions. Rods were also used in finding common denominations. For example, when addin

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