M.Ed. (Subject Didactics) / Each child has his own personality and individuality. Children are learning in different ways, at different tempo's and achieve different heights of success with.their efforts. The degree to which the learner is able to master new concepts, is closely related to the reference framework and given pre-knowledge. However, the learning process is not always successful. Various reasons for this phenomena can be identified. This study focuses on the role which misconceptions play in this regard. In general, misconceptions can be defined as a distortion or misinterpretation of the learned concepts. synonyms used to describe this phenomena includes words. like "previous knowledge", "preconceptions" and "alternative frameworks" Misconceptions in Mathematics are numerous. In various studies conducted, misconceptions were identified in almost all areas of Mathematics. Likewise a great deal of misconceptions were found existing among students concerning the handling of fractions. It is an impossible task to research all misconceptions in Mathematics in one study. For this reason it was decided to do research on only one aspect, namely fractions where possible misconceptions can occur. With the empirical research which was conducted, certain misconceptions in the area of fractions were identified. These misconceptions include, amongst other, the following: 1. The sum of and difference between two fractions. There is very little or no notion of the smallest denominator. 2. Multiplying and division of fractions. The student is uncertain about the role which the numerator and the denominator play in the solution. As fractions play such an important role in Mathematical success, it is suggested that a plan of action will be set as soon as possible in order to prevent misconceptions influencing the student learning process.

During the years since 1929 it has been the privilege of the writer to serve as a teacher in the science department of the high school at Stockton, California. During those years he has been associated with students of all four years of the high school, with a slight majority of the time spent with students of the first two years of high school. Inevitably, certain observations occurred. With those observations, certain convictions, beliefs, and desires to assist, developed concerning the students who pass through our schools. It is only natural, therefore, that one in such a position should be imbued with the desire to do something about it". It is with the outgrowth of that desire that the following pages deal. Therefore, it is deemed of value to enumerate a few of the observations which led to the formulation of the outline with which the pages that follow are to be concerned. 1. Many students have need for a broad, more comprehensive, and generally non-mathematical background in science, as considered in a purely personal and cultural aspect. 2. Many of the students when in the ninth grade have the intelligence, but not the maturity, to grasp some of the ideas and facts presented in the ninth grade general science. 3. Many highly intelligent students, capable of genuine culture, do not reach college. However, they are in serious need of a general scientific background for later thought, reading, interest, and general use in everyday life. 4. Many students who do go to college will not major in the scientific field and, therefore, do not need merely one special science in high school, but one in whose study there is the possibility of broader application. 5. Many students in the upper classes in high school need a chance to do exploratory work in the field of science in an attempt to orient themselves in choosing a vocation. 6. Many students who will go to college are forced to take a particular science when both their needs and interest suggest a more general contact with science. It seems quite evident that the students mentioned above are to be found in all classes in the high school. However, the majority are in what may be called the middle fifty percent, that is, the two quartiles between the extremely bright on the one hand and those in the quartile of lowest ability. It is toward the better student of this middle group that attention is directed chiefly. Further, it is this group which has been neglected grossly in the past. In the early days when our public school system was in process of development, the schools were chiefly concerned with training men for the law, medicine, or for the ministry. This gave attention to a very select group and placed emphasis on the classics and specialized scientific field. To return to the type of student served by the schools, not until the early nineteen twenties did the poorer student come in for this share in attention and concern. The educational trend of that decade might be compared to a pendulum, which, having been started at the peak of its swing, rushes past the central point to become almost suspended for a time on the opposite side, and then to oscillate between these two extremes--attention to the very able student on the one hand and concern for the "slow" student and the "problem" child on the other hand. Therefore, is not action long overdue in caring for the needs, desires, and abilities of the great middle group, which, in the last analysis, go to make up the backbone our national life, thought, and culture? It is with the intention of serving this group and giving it some of the attention which it has been denied for so long, that this outline was developed.

The results reported here are the product of the research titled: Using history in the teaching of mathematics. The subjects are students in two classes of algebra II course at Florida State University High School-- 36 students-- makes and females whose ages are mostly 18 and a few 17 and 16 years old. Algebra II is a course that is usually taken by high school seniors in 12th grade and a few 11th or 10th grade students which explains why the ages of the students are mostly 18 and a few 17 and 16 years old. In this investigation, both quantitative study and qualitative study were employed. The quantitative study was the main study-- a teaching experiment using quasi-experimental methodology that involves two groups-- group 1 and group 2. Group 1 is the control group, where various algebraic/mathematical concepts, or topics were taught or explained to students with the necessary formulas. Group 2 was the experimental group in which the accounts of the historical origin of algebraic/mathematical concepts and the mathematicians (Lewis Carroll, Archimedes, Pythagoras, and Sophie Germain) who brought forward or created the concepts were used to augment pedagogical lessons and exercises used for this study as the main feature of pedagogy. The qualitative study augmented the main quantitative study; it was a follow-up interview for students to probe further an in-depth rationale for the research theme, using history in the teaching of mathematics. The statistical analysis results indicated that there is a significant difference in the mean of score for the control group students and the mean of scores of the experimental group is greater than the mean on scores of student's performance in the control group; and the interview questions responses indeed corroborate the fact that the use of history in teaching mathematics does improve learning and understanding of algebraic/mathematical concepts. / Typescript. / "Submitted to the Department of Curriculum and Instruction in partial fulfillment of the requirements for the degree of Doctor of Philosophy." / Advisors: Elizabeth Jakubowski, Herbert Wills III, Professors Co-Directing Dissertation. / Includes bibliographical references (leaves 202-205).

Submitted in fulfilmentnof the requirements for the degree of Doctor of Education in the Department of Philosophy of Education at the University of Zululand, 2002. / This study advocates to examine the efficacy of values clarification with particular reference to its impact on critical thinking and effective communication for secondary school learners. The capability of discerning and focussing on critical aspects of situations and seeing the patterns characterising those situations is a far more holistic capability than those commonly defined in competency-based approaches. Such holistic capabilities represent the links between disciplinary knowledge and professional skills. Secondary school educators find certain values important for their learners and these are articulated by means of the curriculum and studied or taught through values clarification. Values clarification is a process of helping the individual to arrive at his or her own values in a rational and justifiable way without a set of values being imposed. Values education therefore exists in order to strengthen the transfer of values in the school while critical thinking aims to develop a reflexion on values and a value development by means of analysing and comparing opinions and communicating effectively about them. Moral development is dedicated to the stages of cognitive development for learning values and the skills to reflect on them. In this way they are both cognitive, skills-oriented educational tasks. It is clear that education is concerned with critical thinking and many skills have been formulated that learners need to acquire in order to facilitate thinking critically and communicating effectively. Critical thinking manifests itself in a plethora of skills such as identifying assumptions (both stated and unstated both one's own and others), clarifying, focussing, and remaining relevant to the topic; understanding logic and judging sources by their reliability and credibility. This calls for not only skills but dispositions such as being openminded, considerate, impartial as well as suspending judgement, taking a stance when warranted, and questioning one's critical thinking skills. By implication, this reflects on teaching values clarification and critical thinking, since critical thinking derives from the fact that learners should be taught to think, to solve problems and to communicate, and to encourage involvement in their own learning. Learners need to think critically as citizens in society — being able to detect bias, recognizing illogical thinking, avoiding stereotyping of group members, reaching conclusions based on solid evidence and guarding against propaganda. For this reason critical thinking must pervade the secondary school curriculum. In conclusion, the fundamental purpose of education should have its manifestation in the acquisition of knowledge (knowing what?) and skills (knowing how); and the manipulation thereof to think critically and communicate effectively.

Cubism has often been referred to as “a dead art.” It is the objective of this thesis to present evidence gained through working with high school art students that the study of Cubism, at the secondary level, can result in greater creativity and a genuine appreciation of the abstract. In addition to the study of Cubist artists and their techniques, a correlation was made between art of the early 1900’s and other areas such as Social Science, Music and Literature of this time. By this method, the students were given a broader insight into the motives of the Cubist artists. The personal involvement of each student in the progressive changes from objective representation of subject matter to quasi-nonrepresentational painting provided them with more open attitudes in understanding art of the past and of the present. Photographs of student work from an advanced art class at Reynolds High School are offered as evidence to support this thesis.

My research problem was to experiment with four high school art classes in drawing and painting the figure, to draw conclusions about how they relate to working with the figure, and to recommend methods that appeared to be most successful in broadening viewpoints, developing skills and increasing interest and involvement in art. This problem was selected because teenage students, in the vast majority of cases, have great difficulty in drawing or painting figures and, therefore, strenuously avoid it. I discovered that a subjective approach that recognizes personal feelings, along with one that requires close looking, seemed to get the most exciting, results and to be the best received by the students.

This study investigated the causes of difficulty experienced by Standard Nine Venda pupils in acquiring hierarchical geographical concepts. The study also focussed on intervention methods to assist pupils acquire concepts so that they could be able to transfer them to other situations. The literature was surveyed for background information on the role of prior knowledge, the transfer for attained concepts, instructional organization in acquiring concepts, and language and concept acquisition.

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