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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.

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The purpose of this study was to determine the extent to which 1966-69 elementary teacher education graduates of selected Indiana institutions of higher education are prepared to teach modern mathematics in schools as measured by: (1) the attitudes of the graduates towards modern mathematics programs and towards mathematics, (2) the exposure to topics in modern mathematics provided in the undergraduate program taken by the graduates, and (3) the modern mathematics teaching procedures presented in taken by the graduates.To make the assessment, three instruments were employed. The Rice Attitude Scale was sent to 977 of the 5883 elementary teacher education graduates and 84 percent of the forms were returned. The Reys Scorecard based on the CUPM Level-I proposals was administered to the twenty-nine instructors in the eight institutions who taught the full sequence of required mathematics courses for elementary education majors. A Checklist of topics which might be presented in the professional courses relevant to the teaching of mathematics in the elementary school was developed for the study and administered to the twenty-two instructors whothe professional courses taught such courses in the eight institutions during the three year period.The attitude scale yielded two scores: the "A-score" - a measure of attitudes towards modern mathematics programs, and the "B-score" - a measure of attitudes towards mathematics. The analysis of the effect of sources of variance showed: "age," "sex," and "grade level taught" had no significant effect on either score; "institution attended," and "experience teaching a modern mathematics program" affected both scores; and "further mathematics courses taken," and "year of graduation" significantly affected the B-score. The Newman-Keuls multiple comparison test showed that graduates of one institution had significantly higher scores on certain variables. Of all the graduates in the sample, 86 percent had favorable attitudes towards modern mathematics programs and 92 percent had favorable attitudes towards mathematics and of these, 22 percent and 39 percent respectively had strongly favorable attitudes. The percentages varied slightly according to institution attended and experience in a modern mathematics program.The analysis of responses to the Reys Scorecard showed that all the topics listed under the CUPM course title "Structure of the Number System" were presented by all instructors with the majority of instructors in four institutions claiming full coverage. Ten out of the fourteen topics listed under the CUPM course title "Geometry" were presented by all instructors. None of the topics listed under the CUPM course title "Algebra" were presented by the majority of instructors in each of four institutions.The items listed on the Checklist completed by instructors of the professional methods courses were grouped under topic headings. Most of the topics thus listed were presented by all instructors. The topic "Specific methods of developing certain concepts" included the unifying concepts of modern mathematics and was presented by all instructors with the majority of instructors in four institutions reporting full discussion. Methods of teaching topics peculiar to modern mathematics were discussed as thoroughly as methods of teaching topics common to traditional mathematics. Four topics related to the experimental projects were not presented by the majority of instructors in most institutions.The research showed the preparation of graduates in the eight institutions to be more adequate than that reported in similar studies. Approximately nine out of every ten graduates had favorable attitudes towards modern mathematics programs and towards mathematics. CUPM Level-I recommendations were fulfilled with the exception of topics in Algebra. The graduates were introduced to modern mathematics teaching procedures but not to the experimental mathematics curriculum projects.

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No description available.

This research sought to investigate the sources and type of tasks used in the teaching of trigonometry in Zambia’s secondary schools, and to investigate the criteria used and decisions made by teachers in their selection and implementation of tasks. The study was conducted in three different school types located in high cost, medium cost and low cost respectively. One participant was chosen from each of the different categories of schools. The research was located within an interpretive paradigm. Data were collected through semi-structured interviews, lesson observations and document analysis which include: lesson plans for five consecutive days, pupils’ activity books and three textbooks predominantly used by the teachers. Document analysis was informed by the task analysis guide and essential themes which were used to tease out teachers’ task practice with regard to criteria used and decisions made in the selection and implementation of tasks. Essential themes that were qualitatively established were validated and explicated by the qualitative analysis. The findings of the study indicate that teachers picked tasks from prescribed textbooks. The study further suggests that teachers selected a mix of low and high level tasks, procedures without connections and procedures with connections tasks to be specific. There were no memorisations and doing mathematics tasks. Their choice of tasks was based on the purpose for which the task was intended. Some tasks were selected for the purpose of practicing the procedures and skills, other tasks for the promotion conceptual development. Most of high level tasks decline to low level tasks during implementation. The findings also indicate that teachers selected and implemented a variety of tasks and concepts. Furthermore, teachers presented tasks in various forms of representations and in a variety of ways. However, the results of this study could not be generalized because of the small sample involved. The results presented reflect the views and task practices of the target group. A possibility for future study would be to consider a large population, drawn across the country.

This research tested whether Reform-Based Approaches (RBAs) in the learning and teaching of calculus could lead to improved conceptual understanding. The study adopted positivistic paradigm, quantitative approach and pre- and post-test in a quasi-experimental design. The theoretical framework was Constructivism. The interventions were grounded on learner-centred RBAs including Interactive Engagement (IE), Peer Discussion (PD) and Good Questions (GQ). The experimental group comprised 119 volunteering students from a population of 461 registered for Mathematics as a service subject for the National Diploma (ND) in science or engineering at a South African university. Those not in the experimental group were taught through teacher-centred traditional approaches which have been the norm. However, only 71 out of those in the traditionally taught cohort volunteered to write both Pre- and Post-tests. As such, the total number of subjects in the study was 190, i.e., 119 from the Reform-Based cohort and 71 from the Traditional cohort. The instrument, the Calculus Concept Inventory for Technicians (CCIT), consisted of 19 questions on functions, differentiation and integration. Based on a pilot test, the instrument was improved. The Reform-Based cohort did not receive any participation reward and test scores did not contribute to promotion scores. The students wrote Pre-tests in the second week after commencement of lectures and Post-tests during the last week of lectures. The data were analysed using various statistical tools, tests and measures such as Chi-squares, Student t-tests, Pearson’s Product Moment correlation, Cronbach alpha, KR-20, the Difficulty Index, and Item Discrimination Point Biserial Index (PBI). The raw gain and normalised gains were also employed in data analyses. The main finding of this study was that RBA made a significant impact on the conceptual understanding of calculus of the experimental group. The gain achieved by the experimental group was in a low range and corresponded to the low use of IE (25% of contact time). A combination of RBA with Traditional teaching is recommended. Also, RBA will be most successfully introduced if supplemented and complemented through supportive environments.

M.Ed. (Mathematics) / Mathematics is the gate and key of the sciences .•• Neglect ·of Mathematics works injury to all knowledge, since he who is ignorant of it cannot know the other sciences or things of this world. And what is worse, men who are this ignorant are unable to perceive their own ignorance and do not seek a remedy (Kline 1960: 1). Perhaps the most unfortunate fact about Mathematics is that it requires man to reason, whereas most human beings are not convinced that reasoning is worth while. But a little investigation of the ways of our society does show that the ability to reason enhance the very existence of man. The engineer reasons continually in order to design or produce a new device. The scientist observes or experiments and draws conclusions from the evidence he obtains. The modern every-day man needs to reason in a very similar way to secure his foothold in society. Technological development has made it easier for man to cope with the demands of every-day life, providing that the individual who has to concentrate his efforts on the development of his immediate surroundings, possesses the knowledge required to reach and sustain a perceived disposition. The view that mathematics somehow exists apart from everyday human affairs is a dangerous myth that cannot be sustained. It is dangerous because in addition to being philosophically unsound, it has damaging results in education. If mathematics is a body of infallible, objective knowledge, then mathematics bears no social responsibility. The underachievement of sectors of the population, the sense of cultural alienation from mathematics felt by many groups of students; the relationship of mathematics to human affairs such as the transmission of social and political values; its role in the distribution of wealth and power - all of this is irrelevant to mathematics. Once it is admitted though, that mathematics is a living social construct, then the aims of teaching mathematics need to include the empowerment of learners to create their own mathematical knowledge; mathematics can be reshaped, at least in school, to give all groups more access to its concepts, and to the wealth and power its knowledge brings. Such a dynamic view of mathematics, in the mind of the teacher, has classroom consequences. In terms of the aims of teaching mathematics / the most radical of these consequences are to facilitate the active construction of understanding, built on learners own knowledge, and the exploration and autonomous pursuit of the learner's own interest and thus that of the society at large. An emperical investigation was launched to determine the impact of modern-day approach to mathematics teaching, and to access the consequences of a perceived view of mathematics manifesting in the respective worlds of the individuals subjected to this manner of teaching. This investigation indicated that the mathematics teacher has a social responsibility towards his pupils and to society at large. Achievement of this goal implies a radical change in the approach to mathematical teaching, which can only be resolved by adopting a stance of excellence / with a commitment to incorporate a restructured strategy which will assist the student in his pursuit to achieve his personal aspirations.