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; the extent to which findings may generalize beyond middle school groups cannot be known on the basis of the findings of this study.
2. The study utilized only one researcher-designed instrument to measure math performance. While steps were taken to boost the validity and reliability of the instrument (e.g., by showing it to the faculty adviser and obtaining approval), whether findings would be the same if other instruments (perhaps standardized math tests) had been used cannot be known on the basis of the findings of th...