Date of Award


Document Type


Degree Name

Master of Arts in Education



First Advisor

Nancy Polette

Second Advisor

Jeanne Donovan


The purpose of this experimental study was to investigate the operational and recall ability of second grade children, after instruction and the use of manipulative aids , to understand the multiplication of three. Multiplication of numbers at the early stages, in most mathematics programs, provides for rote memorization and drill instead of concept understanding. Most practices and drills require only answers to the facts, which provide little indication that a student can explain or show how that answer was obtained. Memorizing the multiplication facts is important, but at this early age the operation on those numbers to obtain an answer is as important for retaining the knowledge. It should be l earned that an answer can be figured out by several other methods.

The major hypothesis for this study was: Long-term recall of concrete operational concepts of multiplication will be significantly improved because of the daily manipulative experiences. The use of manipulative aids gives the child concrete experiences which can be treated to show the "why" of the fact. The mental growth descriptions, as stated by Jean Piaget , indicate that at this pre-operational level of understanding a child needs to act upon the objects in order to build an understanding.

The experiment included twenty-three second grade children in one classroom of a suburban public school in St. Louis, Missouri. The class was randomly divided into an experimental and a control group . Before any instruction was begun in the multiplication of three a pretest was administered to the whole class. The following three days the class received instruction on multiplication of three. This instruction included listing and answering the facts, drawing pictures for each fact, completing pages in the mathematics book, quick quizzes, oral game drills, and suggested practice with parents at home. On the fourth day a whole class test was administered to determine operational abilities and understanding.

At this time the class was divided into the previously determined groups . For four days, one-half hour each day, the experimental group remained with the investigator while the control group went to another room for addition/subtraction work with a teach-aide. The experimental group participated in manipulative aid work using concrete, movable objects to further their understanding of the fact and answer. At the end of this time all work on multiplication of three was completed. After a two week interval a posttest was administered to determine short - term recall . Another posttest was administered at the six week interval to determine long-term recall.

The gain scores of all these tests were compared to decide significant/not significant gain for both the experimental and control groups. Also compared were the gain scores of male and female children . Data was also analyzed to compare the mean gain scores of the children who had an early birthdate in the school year to those who had a late birthdate in the school year.

The results of this experimental study indicate that there were no significant differences in the mean gain scores of the experimental group over the control group. Children in both groups made a moderate gain in correct answers by the end of this study. Females made more consistent gains as compared with the males in this study. The children with late birthdays made more significant gains than the children with early birthdays.

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Creative Commons Attribution-NonCommercial 4.0 International License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License

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