This study is concerned with children's conceptions of division in both computational and problem-solving settings. Division was chosen because it is a mathematical topic with which many children have difficulty. Even though division is often introduced in the primary grades and reviewed every year following, late intermediate students still have difficulty understanding this concept. For this investigation, the researcher chose to use a semi-structured individual interview as a means of collecting data about Grade 7 students' conceptions of division in different contexts. During the interview, each student was asked to describe his or her thinking while working through a series of computations and word problems involving division with whole numbers or with decimal fractions. Both whole numbers and decimal fractions were used in the interview items in order to investigate whether or not students' conceptions of division changed as they worked with one, then the other. Twelve students were chosen for this study. It was found that these seventh graders varied in their demonstrations of different meanings of division. Some students demonstrated only the partitive meaning, some the quotitive, some that division is the inverse of multiplication, while others demonstrated a variety of meanings of division. It was noted that students who had an understanding of both the partitive and quotitive meanings of division were more successful solving the problems presented. This could be due in part to the notion that implicit models of division, such as the partitive model, influence problem-solving behaviour. It was also found that some students hold particular mathematical beliefs about division and about the form of the divisor which influence their problem-solving ability. Often these beliefs or misconceptions are a result of an overgeneralization of whole number rules. A student's choice of operation could be influenced by a number of factors including a student's implicit model of division, a student's mathematical beliefs, and the implied action in a problem. Some students used immature strategies such as verbal cues or "try all the operations and see which produces the most reasonable result" to determine the operation. These strategies indicated a lack of understanding of the meaning of the division operation. In some cases, students were able to reason qualitatively but were unable to relate that reasoning to mathematical symbols. Although they could give an approximate answer, they could not perform any further calculations. Implications for instruction resulting from this study include assessing students' conceptual understanding of the division concept and the algorithm through interviews and group discussions prior to and during instruction. Related to this is the notion of teachers ascertaining if students hold mathematical beliefs or misconceptions which may influence new learning and/or the application of knowledge. Teachers must be aware of students' thinking in order to plan instruction which will place those beliefs in context. Instructional activities should be planned which emphasize understanding of the division concept and of the long division algorithm. There should be a linking of conceptual knowledge and procedural knowledge by pairing activities using concrete materials with symbolic representations. The division concept should be discussed in terms of both whole numbers and decimal fractions. The calculator could be used to explore relationships between the divisor, the quotient, the dividend, and the remainder in these different number systems. / Education, Faculty of / Graduate

This study examines the use of locally relevant curricular materials Understanding Images: Bill Reid and Understanding Images: Gathie Falk by three art teachers. The materials were developed by the researcher and modelled on the concept of discipline-based art education. The major purpose of this investigation was to determine if relevant instructional support material which addresses the historical and critical domains together with studio production were developed and made available would visual art teachers be inclined to offer a more balanced program and one which parallels the prescribed curriculum for junior and secondary art education in British Columbia. Secondary interests of this investigation were to determine if an understanding of the integration of the historical, critical and production domains was reflected in 1) the quality of dialogue between the teacher and the student, 2) the quality of talk among students and 3) the student art work. The descriptive, qualitative study followed the in-class activities of three art teachers in three junior secondary schools. The major instrument was the researcher who, in the role of non-participant observer, collected field notes. Further data were collected by questionnaires, sample interviews, random conversation with students, samples of student art work and photographs of classroom activity. The framework for the study was based on Eisner's (1979) model of educational criticism in which he identified three major aspects: the descriptive, the interpretive, and the evaluative aspect. (p. 211) As a result of the findings, strengths and limitations of the instructional materials were identified and implications for development and implementation of similar instructional materials for visual art education were made. / Education, Faculty of / Graduate

One of the most striking facts disclosed in national reports is the large number of students who avoid mathematics courses, especially electives. The problem has become a serious public concern because it bears social and individual consequences: (a) a technologically advanced society demands a mathematically literate workforce, yet a large number of students drop out of mathematics; (b) inadequate preparation in mathematics seriously limits future educational and occupational opportunities of individuals. Although research on school and teacher effects has revealed the effects of school structure and policies and teaching practices on mathematics achievement, researchers have paid little attention to the course of students' academic careers. Even the few existing studies are compromised by serious methodological flaws. Researchers, thus, have not been able to provide policymakers with reliable answers to their basic concerns about mathematics participation. This study tackles these problems, employing the six-wave data from the Longitudinal Study of American Youth (LSAY). The primary purposes of this study are (a) to estimate the probability of students' dropping out of mathematics, conditional on psychological and sociological variables, including sex, socioeconomic status (SES), prior mathematics achievement, prior attitude toward mathematics, prior mathematics anxiety, and prior self-esteem, over a five-year period from grade 8 to 12, (b) to identify conditions that affect the probability, and (c) to determine whether there are critical transition points, and if so, whether certain factors have stronger effects at these points. Survival analysis is used to overcome the difficulties conventional statistical techniques have in modeling probability Analyses of mathematics participation indicate that (a) students are most likely to drop out of mathematics in grade 12; (b) males are more likely than females to participate in mathematics in grade 12; (c) the effect of SES decreases over grades; (d) prior attitude toward mathematics is as important as prior mathematics achievement, and their effects are almost constant over grades; (e) the longitudinal effect of prior mathematics achievement or prior attitude toward mathematics depends on students' sex and SES. Analyses of participation in advanced mathematics show that (a) students are most likely to drop out of advanced mathematics in grade 12; (b) males are more likely than females to participate in advanced mathematics in grade 12, and sex differences are similar across different levels of SES; (c) there is a male advantage in participation in advanced mathematics even when there is a male disadvantage in SES; (d) SES plays a critical role in the early grades, and socioeconomic differences are similar across different levels of mathematics achievement or attitude toward mathematics; (e) prior attitude toward mathematics has the strongest effect in the later grades, whereas the effect of prior mathematics achievement decreases over grades; (f) the effect of prior mathematics achievement varies across different levels of attitude toward mathematics, and vice versa; (g) the longitudinal effect of prior mathematics achievement or prior attitude toward mathematics depends on students' sex and their initial mathematics achievement and attitude toward mathematics. / Education, Faculty of / Curriculum and Pedagogy (EDCP), Department of / Graduate

It was the purpose of this study to investigate the effects of convergent/divergent teaching methods on student performance on two mathematical problem solving tasks (routine/non-routine problems). A concurrent purpose was to investigate the interaction between the convergent/ divergent teaching methods and the thinking style (either convergent or divergent) of the learner. Four grade ten classes were randomly selected from the eleven academic mathematics classes in the secondary school involved in the study. Due to subject absenteeism a total of sixty-six subjects were used for the analyses. Each subject was given the Watson-Glaser Test of Critical Thinking (Form YM) and the Torrance test of Thinking Creatively With Words (Booklet A) to determine their level on the independent measures of convergent and divergent thinking, respectively. Each subject was taught by one teacher using one method for approximately two hours. The content of these lessons involved the Fibonacci Sequence and Pascal's Triangle. At the end of treatment, each subject received a test on the dependent measures Croutine/non-routine problems). Trained observers were used to ensure consistency of teaching method. Analysis of covariance using the regression model was performed with convergent/divergent thinking styles as the covariates. There was no significant difference between convergent teaching methods and divergent teaching methods (p ≤ 0.05). Convergent thinkers scored significantly higher than did divergent thinkers on both dependent measures. However, as convergent thinking is far more highly correlated with intelligence than is divergent thinking, this result may have been confounded by intelligence. Therefore, in further studies in this area, the variance in problem solving due to intelligence should be partialled out. Only one of eight interaction effects was significant (p ≤ 0.05). This suggested that non-divergent thinkers did better with convergent (as opposed to divergent) teaching methods and that non-convergent thinkers did better with divergent (as opposed to convergent) teaching methods. The lack of other significant interactions indicated that intelligence may have been a confounding effect in this study. / Education, Faculty of / Graduate

The purposes of the study were: (1) to develop and test a new measure, of appreciation of poetry, and (2) to determine the relationship between appreciation of poetry and (a) creative performance in poetry, (b) silent reading ability, and (c) subjective assessment by a teacher of a student's level of appreciation. Following a review of some of the major attempts this century to define and measure appreciation of literature, the procedures adopted in the study were outlined. Based on the findings of the research, it was decided to employ poetry rather than prose in the new measure, and design it specifically for the junior secondary level. The test, called the Poem Comparison Test, consisted of twelve poems. Each poem was in two versions, the original and an inferior imitation, and the subject was asked to rate each of the two versions. In order to measure creative performance in poetry three other measures were also developed specifically for the study. These measures were: the Rhyme Test, the Rhythm Test, and the Imagery Test. So that the subjects' responses would be as little restricted as possible, all three of these tests employed an open-ended format. Two outside markers were employed to score the Rhythm Test and the Imagery Test. Silent reading ability was measured by the Gates-McGinitie Reading Test, Survey E, Form 2M. The subjective assessment of the students' level of appreciation was measured by a questionnaire, also developed specifically for the study, and given to the teachers of the students involved in the study. The subjects were grade eight and grade ten students in a large metropolitan secondary school in an average socio-economic section of the city. The testing took place in April, 1975, and complete data were obtained for 95 students. The main questions that the study was designed to answer were: (1) Is there a significant, positive correlation between appreciation of poetry and creative performance in poetry? (p>.5) (2) Is there a significant, positive correlation between appreciation of poetry and silent reading ability? (p>.5) (3) Is there a significant, positive correlation between students' appreciation of poetry and their teachers' assessment of their level of appreciation? (p>.5) (4) Do appreciation of poetry and creative performance in poetry increase from grade eight to grade ten? (a=.01) (5) Are girls better than boys in appreciation of poetry and creative performance in poetry? (a=.01) Based on the data obtained, the following conclusions were drawn: (1) There is not a significant, positive correlation between appreciation of poetry and creative performance in poetry (2) There is not a significant, positive correlation between appreciation of poetry and silent reading ability (3) There is not a significant, positive correlation between students' appreciation of poetry and their teachers' assessment of their level of appreciation, (4) Appreciation of poetry increases from grade eight to grade ten, but creative performance in poetry does not. (5) Girls, are better than boys in creative performance in rhyme and rhythm, but not in appreciation of poetry or creative performance in imagery. The overall conclusions for the study were: (1) there is a factor of appreciation of poetry which is distinguishable from both creative performance in poetry and silent reading ability, and (2) that the measure of appreciation of poetry developed specifically for this study could provide a valid tool for both the researcher and the classroom teacher. / Education, Faculty of / Graduate

Myra McIlvaine Marshall / Typescript / M.A. Florida State College for Women 1933 / Includes bibliographical references

"The purpose of this paper is to examine the place of science in the secondary school program. It is assumed that the place of science in the curriculum has to be justified in such a study. Justification for teaching science is approached in this paper through a study of the nature of the society that creates and maintains the school; the nature of learning and the individual; and the unique contributions that science education can make for a better adjustment of the individual to his environment. It is hoped that this paper might stimulate other science teachers to explore some of the varied references mentioned herein"--Introduction. / "July, 1949." / Typescript. / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Arts under Plan II." / Advisor: Mode L. Stone, Professor Directing Paper. / Includes bibliographical references (leaves 64-66).

"Homemaking courses, in harmony with all of the other courses in which the students participate in high school, should contribute to the maximum extent possible in the development of their personalities. Typically such courses are taught in ways which involve pupils at a minimum in determining the purposes which the course should serve and the appropriate activities for pupils to engage in to achieve these purposes. This study is an effort to test the hypothesis that more effective learning, with respect to the objectives stated above, will occur if pupils are involved more directly in the determination of the purposes to be achieved by a course, and the activities appropriate for achieving those purposes. Stated more specifically, the purpose of this study is to test the hypothesis that pupils learn more effectively when taught through processes involving pupil-teacher planning than when taught through processes which place all responsibility for planning on the teacher"--Introduction. / "August, 1959." / Typescript. / "Submitted to the Graduate School of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Advisor: Herman Frick, Professor Directing Paper. / Includes bibliographical references (leaf 32).

"The problem of this study is to discover and describe some of the existing relationships between art teachers and core teachers in eight Florida secondary schools which have some form of core or basic education in their curriculums. In this study, these relationships are taken to exist in seven basic areas as follows: (1) scheduling, (2) planning, (3) use of materials and facilities, (4) ways of working, (5) problems, (6) sample activities, and (7) evaluation"--Introduction. / Typescript. / "May, 1954." / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements of the degree of Master of Arts." / Advisor: Ivan E. Johnson, Professor Directing Study. / Includes bibliographical references (leaves 105-106).

"The purpose of this paper is to compile an annotated bibliography of science books, chosen to meet established criteria for book selection and to implement the ninth grade general science program as recommended by the Florida State Department of Education. The bibliography has been arranged by units of work as recommended for the science program, then in order of relative readability"--Introduction. / Typescript. / "August, 1953." / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Advisor: Sara Krentzman Srygley, Professor Directing Paper. / Includes bibliographical references (leaf 109).