The purpose of this study was to examine the relationship between the developmental levels of children on certain Piagetian conservation and concept tasks and the strategies the children were capable of using in finding answers to basic addition combinations. / Two major themes were examined in the literature search. How do children recall the basic addition facts? What is known about developmental levels of children and their relationship to performance in arithmetic? / Extensive individual interviews of 52 first graders and 60 second graders were conducted. Each child was tested developmentally on Number Identity, Number Equivalence, Class Inclusion, Meaning of Addition Identity, and Meaning of Addition Parts to Whole. On each test the child was classified as Lacked Vocabulary, Nonconserver, Transition Inconsistent, Transition No Explanation, or Conserver. The child was also shown six basic addition combinations and asked for both an answer and the strategy used to obtain the answer. / In a classroom setting the children were given a 25 item facts test. The 11 teachers of students participating in the study responded to a questionnaire dealing with methods of teaching the facts and the concept of addition. / Results of the study indicated that: (1) The developmental tests are Guttman scalable for both first and second grade in the order: Conservation of Number Identity, Conservation of Number Equivalence, Meaning of Addition Identity, Meaning of Addition Parts to Whole, and Class Inclusion. (2) Children use a great variety of methods (at least 18) for getting answers to the basic addition combinations, some of which probably have not been taught to them by their teachers. (3) There is a significant relationship between where a child is developmentally and the level of the strategy he or she uses in getting answers to the basic addition combinations. The higher a child's performance on the developmental scale, the more likely the child is to use higher level strategies with the addition facts. This trend is stronger in first grade than in second. (4) The linearity of the relationship between developmental levels and fact strategy levels is diminished in first grade by those students (about one third of the cases of conservers) who are developmentally advanced but who are using low level strategies. For second grade, one sixth of the students who are conservers on some of the tests are using low level strategies. (5) There is a second major departure from linerity. While almost two thirds of the cases classified as nonconservers are not using low level fact strategies, they also rarely use strategies higher than the intermediate methods of counting on. (6) When the students in the study are subdivided into four subgroups by school/grade, correlations remain significant for first grade except for tests (Class Inclusion and Number Identity) on which almost all the students are on one end of the developmental scale. For second grade, many of the comparisons lose significance due to the halving of the number of cases when the subgroups are considered, suggesting / that the correlation is not as strong as that in first grade. (7) In first grade there is a significant correlation between the class facts test scores and both the developmental levels and the strategy level of the facts. For second grade, administering the facts test with no time limit allowed so many students to get high scores that the significant correlations present for first grade have practically disappeared. (8) The teacher questionnaire revealed that some strategies for finding answers to the addition combinations which were taught by the teachers were not often used by the students. Other strategies not taught by the teachers were apparently invented by the students. / Recommendations for further study, implications of the research, and suggestion for teachers were made. / Source: Dissertation Abstracts International, Volume: 42-06, Section: A, page: 2548. / Thesis (Ph.D.)--The Florida State University, 1981.

This study investigated four research questions concerning strategies students used in solving the multiplication and division combinations. / In 1943, Brownell identified several strategies students used to solve the multiplication combinations, such as counting and rote memory. Recent research has indicated that the strategies students use may be related to how they are taught. Teaching techniques advocated today are somewhat different from those used during the 1940's. Has this caused a change in the strategies students use? / If students use thinking strategies on the multiplication combinations, do they also use them on the division combinations? / Brownell claimed that students mastered the combinations by adopting more and more mature thinking strategies until they reached mastery, where strategy A is more mature than strategy B if it is more mathematically sophisticated, or is more time efficient or demonstrates a deeper understanding of the operation on the part of the student. Brownell claimed however that the maturity level of the strategies students use has no correlation with their achievement in those combinations. Brownell claimed students could become so efficient at using an immature strategy as to score well on a test. Recent findings seem to refute this claim. Can evidence be found to refute Brownell's claim? / Most elementary mathematics textbooks advocate teaching the division combinations by relating them to the multiplication combinations. In light of the recent findings concerning the relationship between teaching and student's strategy use, what is the nature of the interrelationship between students' achievement on the multiplication and division combinations, the strategies they use, and the maturity levels of those strategies? / Ninety-five fourth-graders from two elementary schools were given a division combination test, followed the next day by a test on the multiplication combinations. Both tests were given via a slide projector, at the rate of one combination every six seconds. Based on the results of these tests, a stratified random sample consisting of half the subjects from each school was selected for individual, tape-recorded interviews. The tapes were analyzed to identify what strategy each student used on each combination asked in the interview. A panel of judges was asked to rank the strategies identified by level of maturity. Using these rankings, multiplication and division maturity indices were computed for each subject. The maturity indices, test scores, and the distributions of the strategies were then analyzed to answer the research questions. / The results of the analyses indicate that these students use the same strategies to solve the multiplication and division combinations: (a) Habituation, (b) solution, (c) repeated addition, (d) skip counting, (e) rote memory, (f) recitation of tables, (g) single digit counting, and (h) guessing. Brownell and Carper's categories were too broad and masked some of these strategies. Positive relationships were discovered between strategy maturity and achievement in both multiplication and division. Positive relationships were also discovered between multiplication and division strategy maturity levels, between multiplication strategy maturity and division achievement, between multiplication achievement and division strategy maturity, and between multiplication and division achievement. / These results lead to the conclusion that students do use thinking strategies on both multiplication and division combinations, that there is a relationship between achievement and strategy maturity for both multiplication and division, and that perhaps the key to multiplication and division achievement is the level of multiplication strategy maturity a student has reached. / Source: Dissertation Abstracts International, Volume: 41-05, Section: A, page: 1989. / Thesis (Ph.D.)--The Florida State University, 1980.

This study examined student attitude toward mathematics and the use of positive instances or negative instances in learning 15 standard concepts of college algebra. Specifically, the study sought to find answers to: What differences appear among students taught only with positive instances compared with students receiving negative instances, as well? Do these treatments affect the students' attitude toward mathematics? In what way? / The study was conducted during the fall quarter of 1979. All subjects were freshmen at Florida A&M University in Tallahassee, Florida. The 71 students involved in the study were assigned to their particular treatment group by chance of registration. Group I received both positive and negative instances of the 15 concepts taught. The students in Group II, however, received only positive instances of the same 15 concepts. All students took a pretest and a posttest over the standard algebraic concepts involved in this study. This test had been developed in another research project and validity and reliability has been established. The same subjects were pretested and posttested on attitude. A one-way analysis of variance was used to test the null-hypotheses at the .05 level of significance. This statistical analysis was used for both the concept investigation and the attitudinal study. / This study indicated that for the concepts studied, students receiving both positive and negative instances (Group I) did significantly better than those (Group II) receiving only positive instances. The total number of instances received by both groups was identical. / Surprisingly, Group II had much higher scores on the pretreatment attitudinal opinionaire than Group I. This difference was surprising because of the very similar pretest concept scores for these two groups. However, at the end of the study the attitude scores for both groups were found to be virtually the same. Interestingly, the attitude toward mathematics for both groups improved. Group I had a significant improvement of attitude, but Group II did not. / This study suggests that providing students with both positive and negative instances may enhance their grasp of an algebraic concept. It also provided evidence that attitude improvement may result from exposure to a combination of both types of instances. This evidence may serve to promote additional investigation in this area. / Source: Dissertation Abstracts International, Volume: 41-11, Section: A, page: 4630. / Thesis (Ph.D.)--The Florida State University, 1980.

The purpose of this study was to demonstrate that by learning the place-value method of teaching long division, prospective elementary school teachers will both gain an understanding of and improve their teaching of long division. / In the early Sixties, the mathematical content of prospective elementary school teachers' programs was the focus of attention of many mathematics educators. / Noting some dissatisfaction of the results of this effort, and claiming that elementary teachers tend to teach as they have been taught, some mathematics educators in the Seventies have advocated and experimented with the notion that the pedagogical content should not be isolated from mathematical theory. In trying to develop mathematical understanding of long division through a study of its pedagogy, the present study essentially agrees with this point of view. This effort evolved gradually from four previous studies at The Florida State University, which dealt with the subject matters of numeration systems, geometry, or probability. / At the same time, long division has been one of the most troublesome topics for elementary students to master. Since the Fifties a repeated subtraction technique has been emphasized, based upon a study by Van Engen and Gibb in 1956. Since 1970, emphasis has been shifting toward use of a multiplicative, distributive, or partitioning approach. The long division technique of the present study is in the spirit of the latter, using money as a concrete model, and emphasizing an understanding of the process in terms of place-value and distributivity. / Twenty-one prospective elementary school teachers at The Florida State University were the subjects of this study. Ten of them were chosen, each to teach long division to one of 10 randomly-selected fifth-graders from the University's Developmental Research School (DRS). These teaching sessions were videotaped. All 21 prospective teachers were then taught the place-value method of teaching long division, following which they took a revised form of Van Engen and Gibb's examination as a test of their understanding. The same 10 prospective teachers taught long division, again each to one of another group of 10 randomly-selected DRS fifth-graders. Once more these teaching sessions were videotaped. All videotapes were evaluated by three mathematics education doctoral students, using a revised form of three observation instruments developed by Dodd (Thornton) in 1974. / The data indicated that learning the place-value technique for teaching long division can favorably affect the mathematical understanding and teaching performance of prospective elementary school teachers. As a result of studying this technique not only did the 21 prospective elementary school teachers display comprehension on the mathematical understanding test, but also the videotaped microteaching was judged significantly better after the instruction than before. / Source: Dissertation Abstracts International, Volume: 42-06, Section: A, page: 2547. / Thesis (Ph.D.)--The Florida State University, 1981.

The major issues addressed in this study were the effect which certain distractors have on student performance when solving mathematics problems in a multiple-choice format, and the processes used by students in solving these problems. / Phasse I of the investigation consisted of administering three forms of a test to students in grades eight and eleven. Two of the forms were of a multiple-choice nature and one form was constructed response (no choices were given; the student was expected to solve the problem and supply a unique answer). The two multiple-choice forms were identical except for one of the answer choices. One form had the major distractor (answer to step one in a two-step problem) and the other form did not have this distractor. The problem statement was the same in all three forms. The questions were one- and two-step problems dealing with percent (discount, interest and sales tax). / Phase II of the study consisted of interviews with individual students from grades eight and eleven. The purpose of the interviews was to learn as much as possible about the processes used by students when solving problems where the answer must be selected from a list of four possible choices. / Each student was asked to think aloud as he/she attempted to solve each of eight problems. After the student selected an answer, the interviewer asked probing questions to obtain as much information as possible about the process used, including any use of the answer choices before a final answer was selected. / An ANOVA was used for data analysis on Part I. The results were that the mean score for the constructed response test form was significantly lower than the mean score for either of the two multiple-choice forms. / While there is no statistical evidence from Part I that the presence of step-one distractors has an effect on student performance, there is some evidence to this effect from Part II of the study. Of those two-step problems presented, 42% of the responses of students from the average and low ability groups were the intermediate answers. Also, 52% of the incorrect responses by the average ability group on two-step problems were the intermediate answers. / Phase II of the study revealed that very few students use short cuts or mental computations in arriving at answers. There seems to be a direct relationship between a student's mathematical ability and when the student first looks at the answer choices. The low ability students look at the choices early in the problem-solving process and the high ability students usually first look at the choices late in the process (often after finding the answer). Also, the average ability student is somewhat inconsistent in the processes used to solve similar two-step problems; the low ability student is very inconsistent. / The processes used by the low ability students in selecting an answer choice were as follows: (1) Solve the problem and then look at the choices (and select the matching one). (2) Solve the problem, look at the choices and select the number closest to the student's answer. (3) Look at the choices and search for a process which would yield one of them. (4) Force the answer to be one of the choices (by dropping a zero, moving the decimal, etc.) (5) Guessing. (6) Not selecting a choice at all. / Source: Dissertation Abstracts International, Volume: 41-07, Section: A, page: 2983. / Thesis (Ph.D.)--The Florida State University, 1980.

This study investigated the effectiveness of using minicalculators to teach the basic concepts of average at the fourth grade level. The two purposes of this study were: to investigate the possibility that using minicalculators in connection with a unit on averages (arithmetic mean) will facilitate students' acquisition of an understanding of the average of a set of numbers and their abilities to use this knowledge in new situations. / To conduct the study, the researcher used two intact fourth grade classes in one elementary school as the population sample. These classes were assigned randomly to either a calculator group or non-calculator group. A computational pretest (covering the four basic arithmetic operations) was administered to both groups a week before the instruction began. Data from this pretest were used to determine if there was any bias with regards to the mathematical abilities of the two groups. Each group received seven days of instruction by a graduate student in mathematics education. Students in the calculator group solved the problems using a minicalculator. Students in the non-calculator group solved the problems using written computational procedures (paper and pencil). A posttest and a transfer test on averages were administered to each group on the two days following the instructional period. These tests were also given as retention tests after a period of one month. / Mann-Whitney U Test analysis showed significant differences (at .05 level of significance) favoring the calculator group over the non-calculator group on a test of the basic concepts in average (posttest). No significant differences between both groups were observed on the retention posttest, the transfer test and the retention transfer test. As a further investigation of the results of this study, the researcher analyzed the errors made by the students in both groups on the posttest, transfer test and the retention tests. / The conclusions of this study were: (1) The minicalculator was an advantage in avoiding computational errors on all the tests administered to students in the calculator group. (2) The use of minicalculators does not help students in retaining the process required to solve two-step average problems and in applying this knowledge in new situations. (3) The written computational procedures (paper and pencil) seemed to be an advantage in retaining the process required to solve the average problems and in retaining how to apply this knowledge in new situations. / Source: Dissertation Abstracts International, Volume: 41-07, Section: A, page: 2980. / Thesis (Ph.D.)--The Florida State University, 1980.

Purpose. The purpose of this study was to determine if students in a college algebra classroom who were trained to take T-Notes would perform better on exams than students who were not trained in note taking. / Method. Twenty-five college freshmen or sophomores enrolled in the investigator's College Algebra sections at Abraham Baldwin College, a two-year unit of the University System of Georgia, were the subjects of the study. / The study was conducted in an actual classroom setting with the note taking training incorporated into the mathematics lectures. The dependent variables were the course midterm exam and final exam. / One section was chosen at random to receive the training in note taking with T-Notes. A pretest was administered to all students and notes were examined from both groups to determine if there were any significant differences between the groups initially. / During the training period, the instructor always wrote problems on the broad; using the T-Note format. The no training group received the same mathematics instruction, but T-Notes were not used. Approximately once a week notes were collected from both groups. The training group received feedback on their T-Notes, while the no training group were told their own particular note taking strategies were being studied. / Findings. Using an ANCOVA, Treatment by College Algebra Course Repeater with MSAT, on both the midterm exam and the final exam, a significant interaction was found (p $<$.05). The mean for students repeating college algebra was significantly higher for those who received note taking training than for those who did not receive note taking training. / Students in the training group continued to use T-Notes throughout the posttraining period and reported using their notes more than the group which received no training. All students in the training group indicated they found T-Notes to be a helpful technique. / Source: Dissertation Abstracts International, Volume: 50-02, Section: A, page: 0379. / Major Professor: Eugene D. Nichols. / Thesis (Ph.D.)--The Florida State University, 1988.

The purposes of this study were: (1) to investigate the effectiveness of the computer-student interactive method in presenting statistical concepts and in instructing students in the applications of these concepts, and (2) to develop instruments that test for the understanding of these concepts and the mastery of these application skills. / The computer-student interactive method provided an experiential learning environment in which students were allowed to use computers to experiment with and investigate the concepts of random sampling and the central limit theorem. / The students in two sections of Business Statistics, STA 2014, at a community college participated in this study. A traditional lecture method was used with the control group to present a unit on random sampling and the central limit theorem to one section of 29 students. The computer-student interactive method was used with the experimental group of 23 students. / The experimental group performed significantly better than the control group on a concepts test administered at the conclusion of the study. There was no significant difference in the performance of the two groups on an applications test. / Concept and application retention tests were given three weeks after the conclusion of the study. There was no significant difference in the degree of retention for both groups on either test. / A mathematics attitude was administered before and after the study. There was no significant favorable change in attitude toward mathematics over the course of the study. / After an analysis of the results from the study, the researcher concluded that the computer-student interactive method is effective in presenting abstract statistical concepts to community college business statistics students. / Source: Dissertation Abstracts International, Volume: 51-02, Section: A, page: 0441. / Major Professor: E. T. Denmark. / Thesis (Ph.D.)--The Florida State University, 1990.

Source: Dissertation Abstracts International, Volume: 40-06, Section: A, page: 3171. / Thesis (Ph.D.)--The Florida State University, 1979.

Source: Dissertation Abstracts International, Volume: 38-05, Section: A, page: 2656. / Thesis (Ph.D.)--The Florida State University, 1977.