Typescript, etc. / Digitized by Kansas State University Libraries

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.

An exploratory investigation into the effect of co-operative group learning, involving tutoring, on the achievement and attitudes of 174 grade eight pupils in new mathematics is described. Three volunteer teachers and six volunteered mathematics classes were involved. Five hypotheses concerning test performance and one concerning attitudes were advanced. Using the scores obtained in the mathematics sections of the Stanford Achievement Test (Advanced) and an entering behaviour test of prior mathematics learning, to establish similarity of the groups, instruction was carried out over a period of twelve weeks. A retention test was given two months later. Attitude scores from data collected by Semantic Differential before and after the experiment were analysed using a model for multidimensional analysis of Semantic Differential attitude data (McKie and Foster, 1972). Achievement in algebra learning and retention reached the .05 level of statistical significance, favouring the experimental group. No differences for treatment occurred for instructor effects, instructor by group interaction or attitudes at the .05 level of statistical significance. Conclusions for further research and practice are drawn. / 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

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

published_or_final_version / Education / Master / Master of Education

A key issue for the success of students entering a first year mathematics course at tertiary level is whether or not they have an integrated understanding and view of the mathematical concepts acquired at school. Various integrated applications from first year mathematics suggest that a compartmentalised view of mathematics would be detrimental to any student's chances of passing mathematics at this level. This study tried to assess whether learners do have an integrated understanding of mathematics at grade 12 level.

A key issue for the success of students entering a first year mathematics course at tertiary level is whether or not they have an integrated understanding and view of the mathematical concepts acquired at school. Various integrated applications from first year mathematics suggest that a compartmentalised view of mathematics would be detrimental to any student's chances of passing mathematics at this level. This study tried to assess whether learners do have an integrated understanding of mathematics at grade 12 level.

What can be done to bring secondary mathematics courses in tempo with the present day needs and interests of the student? The purpose of this paper is to suggest a partial answer to this question. It is doubtless true that most boys and girls in the secondary school are far more interested in sports than in mathematics. Why not draw upon this common interest and bring sports into the mathematics classroom--or even take the mathematics classroom out to the field of sports? Such a question may seem unreasonable to those who have not given much thought to the possibility of approaching certain phases of mathematics through student interests in sports. Actually, such an approach is not at all unreasonable. The sports world offers practical examples of numerous mathematical relationships. / Typescript. / "May, 1949." / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Science under Plan II." / Includes bibliographical references (leaf 32).