by
Robert W. Jones∗
This experimental study conducted by Mr. Jones on the Pine Ridge Indian Reservation uses drill as the subject of the study. The study is designed to show whether or not drill has value as a re-teaching and retention gaining device in the area of multiplication with Indian children from an educationally deprived area.
The reteaching of multiplication and division skills has been a traditional trauma for sixth grade teachers in the Pine Ridge Area. Those students who could not wholly or partially re-grasp the skills were forced to proceed through the rest of the mathematics skills for the remainder of the school year with little or no success experiences, thereby lowering their self-concept and attitude toward school. Their school attendance would be low and their behavior would be poor.
The difficulties that have ensued in multiplication and division, even after having received additional assistance from federal programs, show that there is a need for research in this area. Research could perhaps indicate what methods and procedures bring about more favorable results with these children.
The sixth grade students in Mr. Jones' room participated in a month long project of practicing and drilling on the multiplication and division facts of one and two digit numbers. There were twenty-five students in the room; twelve in the control group, thirteen in the ex- perimental group. The student's previous daily work over the first three quarters of the school year determined who went into which group. Those who had been having problems with multiplication and division, by averaging less than 70% on their daily work, were put in the experimental group; the others were placed in the control group.
The main objective of the study was to determine the relationship and value of daily drill on the learning of multiplication and division facts, as opposed to little or no drill on the multiplication and division facts. A fifteen minute timed test consisting of twenty facts was administered to all twenty-five of the pupils at the beginning of the
study. Following three weeks of daily practice on facts with the experimental group, the test was administered again.
During this same three week period, the control group worked on an area in mathematics other than multiplication and division, thereby restricting their use of knowledge of multiplication and division.
The first week of the project for the experimental group was spent initiating
∗ Robert W. Jones received a National Education Association Award in 1973 for Outstanding Contributions to Education. He received his Master's Degree from Black Hill State College in 1974. Mr. Jones is currently Teacher Supervisor at the American Horse Day School, in Allen, South Dakota.
the plans and discussing the needs and values of daily drilling on our facts. The plans were to test ourselves, check the facts most often missed, analyze what gave us the most trouble, and study these "trouble spots" each day for a few minutes.
When the initial timed test was given, the most apparent trouble spot in the classroom was in division where zero was a place holder in the quotient. Problems containing multiplicands or divisors over eleven contained the greatest number of errors, with all division facts missed more frequently than their corresponding multiplication facts.
Starting the third day of our plan, we decided to use no more than ten minutes of each opening exercise period to work on our math facts. It was decided to keep this period separate from our regular math time, to use it as we needed, and to end each short period with a "mini-quiz" of fifteen facts.
Each morning we discussed and analyzed certain trouble spots in our area, (spending more than one morning on the same area in some cases) followed by the daily quiz which was patterned after the day's discussion. The children questioned, discussed, and made many suggestions to one another and to me. Most of them also drilled themselves during free time and at home.
The areas we studied which we found to be most constructive in helping the children develop more understanding of their facts were these:
An association of "greater than" and "less than" 6x9 > 5/9
Grouping by 10's
4x22=4x 20+2 or 4x10+4x10+2 Families of facts
Showing the relationship of multiplication and division 4x5=20, 20/4=5, 20/5=4 Emphasis on relationship in multiplication and division
Estimating partial quotients
19 / 124 — 19 is almost twenty, and twenty will go into 124 just as many times as 2 goes into 12.
Making practice patterns in facts
Making individual multiplication facts charts, using them to reverse and show division Stressing all facts with one product or quotient
The quizzes each day were based on the concepts discussed. The facts were either given orally, written one at a time on the chalk board, on an overhead projector or on flash cards. The children had only to write the answer.
SUMMARY
The study's results show that drill, extended over a three week period of time, can be used successfully with Indian children from an educationally deprived area.
Those in the experimental group showed higher retention and speedier recall of multiplication and division facts after continuous exposure to the facts, in comparison to the control group's lessening in ability to readily recall and retain multiplication and division facts after limited exposure to the facts.
The experimental group showed a great deal of enthusiasm toward this study and the test data revealed much improvement in either their time or accuracy or both. Initially, the experimental group averaged twelve mistakes in fourteen minutes, seven-tenths seconds. Only one of the children in that completed the test in less than fourteen minutes. At the conclusion of the experiment, the experimental group's average was six mistakes in thirteen minutes, eight-tenths seconds. Six completed the test in less than fourteen minutes resulting in a thirty percent increase in accuracy and a six percent increase in time.
The control group initially averaged four mistakes in thirteen minutes, eight-tenths seconds. Four of the twelve children participating in the control group completed the test in less than fourteen minutes. At the conclusion of the experiment, the control group's average was two mistakes in fourteen minutes, seven-tenths seconds resulting in a ten percent increase in accuracy and a six percent decrease in time.
The experimental group showed an overall increase in both accuracy and time, whereas the control group only showed an increase in accuracy. This phenomenon may be attributed to the fact that the control group was in the same room with the experimental group when the drill exercises were being conducted, thereby being. exposed to the drill but not the exercises which develop expertise.
The girls showed the greatest increase for the experimental group and the greatest decrease for the control group.
The girls of the experimental group showed an average increase, from pre-test to post-test, of eight items and an overall averaged high of sixteen items correct on the post-test. The boys, not fairing as well, showed an average item increase of six items and an overall averaged high score of thirteen items correct on the post-test.
The girls in the control group showed a zero item increase and an overall averaged high of sixteen items correct on the posttest, in comparison to their male counterparts' average of two items increased and an overall averaged high of eighteen items correct on the post-test.
The girls of both groups related to the teacher showing more emotional concern toward the program. Those of the experimental group were very positive in attitude toward the study and showed much positive concern towards the results of their post-test. The girls of the control group were negative in attitude toward the test, relating to the teacher that they felt they were being "left out," and had difficulty in understanding why they, too, could not participate in the drill activities.
The boys showed less concerned attitudes toward the program. The boys of the experimental group seemed to be more apathetic overtly than the girls toward the study. The boys of the control group were less concerned about being "left out," however, a few did mention their wanting to participate in the drill games.
During the three weeks of the study, the attendance was very high for the experimental group. Their attendance for this same three week period averaged one person absent per week, in comparison to the control group's average of four people absent per week during the study. This, perhaps, resulting from a feeling of non-involvement and non- importance on the behalf of the control group participants.
The attitude of the students toward the program was also reflected by their parents at Parent-Teacher Conferences. Of the thirteen students participating in the experimental group, only three did not have representation at the conferences. The ten parents or guardians representing members of the experimental group attending conferences, also revealed the students' positive attitude toward the study. Each representative stated that their child or ward had mentioned some of the things he was doing in the study. These same parents or guardians shared their child's or ward's concerns toward the program and wanted to learn more about it and its results.
Four of the ten parents or guardians coming to conferences as representatives of children in the experimental group had not
previously been in attendance at any of this year's Parent-Teacher Conferences.
The twelve control group participants were represented by only five parents. These same five parents traditionally attend most of the Parent-Teacher Conferences. They claimed no awareness of the program and could recall no mentioning of the study by their children.