Theses and Dissertations (Mathematics Education)http://hdl.handle.net/10500/64402015-07-02T10:08:03Z2015-07-02T10:08:03ZExploring teaching strategies to attain high performance in grade eight Mathematics : a case study of Chungcheongbuk Province, South KoreaVan der Wal, Gerhardhttp://hdl.handle.net/10500/185772015-05-08T01:03:09Z2015-02-01T00:00:00ZExploring teaching strategies to attain high performance in grade eight Mathematics : a case study of Chungcheongbuk Province, South Korea
Van der Wal, Gerhard
This study focused on teaching strategies preferred and used by grade 8 mathematics teachers, what they thought was most effective for learning mathematics as well as students’ perspectives of their mathematics classroom. The aims of this study were to investigate the teaching strategies used in the South Korean mathematical classroom and to find out how they attain a high performance in mathematics, in comparison with other countries. The target population was chosen from within the Chungcheongbuk Province and ten schools were selected for the study.
In order to determine what teaching strategies are used in the South Korean mathematics classroom, a case study using both quantitative and qualitative research methods was adopted. Data collection methods included questionnaires for the students while interviews were conducted with the teachers. The questionnaire contained fifty closed-ended questions divided into different sections to obtain data on teaching strategies used, on preferred learning styles from the students and on how they felt about mathematics and the mathematical classroom. The interview consisted of ten open-ended questions to get feedback from the mathematics teachers on what teaching strategies they used in the classroom and on what they thought were the best strategies with regard to teaching grade 8 mathematics. From the ten sampled schools there were two hundred and two students who participated in this research, and six teachers were interviewed. The results of the study showed that in the South Korean mathematics classroom a combination of direct instruction, practice and teacher guidance helps the students to learn problem-solving skills and to master mathematics. The students indicated that the teachers mostly used chalkboard instruction and that they practiced solving problems using worksheets, past exam paper questions and through homework or private study. The average student studied mathematics for about six hours a week and most attended afterschool academies for further studying mathematics. Although the South Korean students attained a high performance in mathematics it was evident that they indicated a low interest in the subject. The teachers stated in the interviews that they thought the students needed to see examples on the chalkboard, and then the students need to practice with guidance from the teacher. It was evident that the students focus a lot on guided practice, since they study for about six hours a week. The teachers also felt that the curriculum is overloaded and that there was a gap between the better and the poorer level of students in the mathematics classroom, this gap grew bigger as students lost motivation. The responses to the questionnaire showed that 65% of the students were not interested in mathematics; in spite of this South Korea is placed among the best performing countries in the world. The teachers also indicated that mathematics was very highly valued in South Korea and that parents and universities put a lot of pressure on students to perform well in this subject.
This study provides better insight into what is happening in the South Korean mathematics classroom, what methods are used and how the students felt about the mathematics classroom and the strategies that are used. Apart from commenting on teaching strategies, there was also an indication of what teaching style the students preferred. The information in this research study can provide answers to questions regarding South Korean mathematics instructional practices and will be useful for future comparative studies regarding the teaching of mathematics in other countries.
2015-02-01T00:00:00ZRelationship between learners' mathematics-related belief systems and their approaches to non-routine mathematical problem solving : a case study of three high schools in Tshwane North district (D3), South AfricaChirove, Munyaradzihttp://hdl.handle.net/10500/184132015-03-26T08:46:54Z2014-06-01T00:00:00ZRelationship between learners' mathematics-related belief systems and their approaches to non-routine mathematical problem solving : a case study of three high schools in Tshwane North district (D3), South Africa
Chirove, Munyaradzi
The purpose of this study was to determine the relationship between High School learners‟ mathematics-related belief systems and their approaches to mathematics non-routine problem-solving. A mixed methods approach was employed in the study. Survey questionnaires, mathematics problem solving test and interview schedules were the basic instruments used for data collection.
The data was presented in form of tables, diagrams, figures, direct and indirect quotes of participants‟ responses and descriptions of learners‟ mathematics related belief systems and their approaches to mathematics problem solving. The basic methods used to analyze the data were thematic analysis (coding, organizing data into descriptive themes, and noting relations between variables), cluster analysis, factor analysis, regression analysis and methodological triangulation.
Learners‟ mathematics-related beliefs were grouped into three Learners‟ mathematics-related beliefs were grouped into three categories, according to Daskalogianni and Simpson (2001a)‟s macro-belief systems: utilitarian, systematic and exploratory. A number of learners‟ problem solving strategies were identified, that include unsystematic guess, check and revise; systematic guess, check and revise; trial-and-error; logical reasoning; non-logical reasoning; systematic listing; looking for a pattern; making a model; considering a simple case; using a formula; numeric approach; piece-wise and holistic approaches. A weak positive linear relationship between learners‟ mathematics-related belief systems and their approaches to non-routine problem solving was discovered. It was, also, discovered that learners‟ mathematics-related belief systems could explain their approach to non-routine mathematics problem solving (and vice versa).
2014-06-01T00:00:00ZNon-euclidean geometry and its possible role in the secondary school mathematics syllabusFish, Washielahttp://hdl.handle.net/10500/167892015-06-10T01:29:21Z1996-01-01T00:00:00ZNon-euclidean geometry and its possible role in the secondary school mathematics syllabus
Fish, Washiela
There are numerous problems associated with the teaching of Euclidean geometry at
secondary schools today. Students do not see the necessity of proving results which
have been obtained intuitively. They do not comprehend that the validity of a
deduction is independent of the 'truth' of the initial assumptions. They do not realise
that they cannot reason from diagrams, because these may be misleading or inaccurate.
Most importantly, they do not understand that Euclidean geometry is a particular
interpretation of physical space and that there are alternative, equally valid
interpretations. A possible means of addressing the above problems is tbe introduction of nonEuclidean
geometry at school level. It is imperative to identify those students who have
the pre-requisite knowledge and skills. A number of interesting teaching strategies,
such as debates, discussions, investigations, and oral and written presentations, can be
used to introduce and develop the content matter.
1996-01-01T00:00:00ZAlgebraïese simbole : die historiese ontwikkeling, gebruik en onderrig daarvanStols, Gert Hendrikus.http://hdl.handle.net/10500/161222015-06-13T01:01:20Z1996-06-01T00:00:00ZAlgebraïese simbole : die historiese ontwikkeling, gebruik en onderrig daarvan
Stols, Gert Hendrikus.
Die gebruik van simbole maak wiskunde eenvoudiger en kragtiger, maar ook
moeiliker verstaanbaar. Laasgenoemde kan voorkom word as slegs eenvoudige en
noodsaaklike simbole gebruik word, met die verduidelikings en motiverings in
woorde.
Die krag van simbole le veral in die feit dat simbole as substitute vir konsepte kan
dien. Omdat die krag van simbole hierin le, skuil daar 'n groot gevaar in die gebruik
van simbole. Wanneer simbole los is van sinvolle verstandsvoorstellings, is daar geen
krag in simbole nie. Dit is die geval met die huidige benadering in skoolalgebra.
Voordat voldoende verstandsvoorstellings opgebou is, word daar op die manipulasie
van simbole gekonsentreer.
Die algebraiese historiese-kenteoretiese perspektief maak algebra meer betekenisvol
vir leerders. Hiervolgens moet die leerlinge die geleentheid gegun word om
oplossings in prosavorm te skryf en self hul eie wiskundige simbole vir idees spontaan in te voer. Hulle moet self die voordeel van algebraiese simbole beleef.; The use of symbols in algebra both simplifies and strengthens the subject, but it also
increases its level of complexity.This problem can be prevented if only simple and
essential symbols are used and if the explanations are fully verbalised.
The power of symbols stems from their potential to be used as substitutes for
concepts. As this constitutes the crux of mathematical symbolic representation, it
also presents a danger in that the symbols may not be comprehended. If symbols are
not related to mental representations, the symbols are meaningless. This is the case in
the present approach to algebra. Before sufficient mental representations are built,
there is a concentration on the manipulation of symbols.
The algebraic historical epistemological perspective makes algebra more meaningful
for learners. Learners should be granted the opportunities to write their solutions in prose and to develop their own symbols for concepts.
Text in Afrikaans, abstract in Afrikaans and English
1996-06-01T00:00:00Z