Proefschrift Universiteit van Amsterdam. / Auteursnaam op omslag: Jaap Kamps. Met index, lit. opg. - Met samenvatting in het Nederlands.

Proefschrift--Utrecht. / Includes bibliographical references.

Thesis--Leyden. / In Periodical Room.

Inaug.-diss.--Jena. / Lebensabriss. "Aufzählung der zur arbeit benutzten werke von Fries selbst, und einigen abhandlungen über ihn": p. 7-9.

Metakognitiewe strategieë en wiskundetaal speel ’n kritiese rol in onderwysers se onderrigstrategieë en die verbetering van hulle wiskunde-onderrigstyl. Die waarskynlikheid bestaan dat wanneer ʼn onderwyser se metakognisie ontwikkel word, sy of haar onderrig ook sal verbeter (Jing & Yang, 2008, p. 1). Metakognisie fasiliteer die onderrig en leer van wiskundekennis (Gourgey, 2001, p. 18), en taal is die instrument wat in ʼn onderwyskonteks die kommunikasie vir die aanleer, verstaan en ontwikkeling van wiskundekonsepte en -prosesse fasiliteer (Jamison, 2000). ʼn Empiriese kwalitatiewe ondersoek – om te bepaal wat Graad 1-onderwysers se persepsies van metakognisie en wiskundetaal tydens die onderrig en leer van wiskunde is – is in hierdie studie uitgevoer. Die ondersoek het op vyf Graad 1-onderwysers gefokus. ʼn Gerieflikheidsteekproef is gebruik om die groepie onderwysers (wat vir die navorser toeganklik was) uit te nooi om aan die studie deel te neem. Video-opnames is gemaak van ʼn fokusgroeponderhoud, sowel as van ʼn wiskundeles en twee individuele onderhoude. Al die onderwysers het aan die fokusgroeponderhoud deelgeneem. Een van die onderwysers (Deelnemer B) het ingestem dat ʼn video-opname van haar wiskundeles gemaak kon word. ʼn Individuele onderhoud is voor en na die video-opname met deelnemer B gevoer om ʼn beter en meer diepgaande begrip van haar persepsies oor wiskundeonderrig te verkry. Die video-opnames van die fokusgroeponderhoud, wiskundeles en individuele onderhoude is verbatim getranskribeer, waarna a priori kodes uit die literatuurstudie gekies is. Die kodes is in temas en kategorieë gegroepeer. Data is ontleed, en gevolgtrekkings geformuleer. Resultate is daarna geïnterpreteer en aanbevelings gemaak. Ten spyte van die beperkte veralgemenings wat op grond van die resultate moontlik is, kom die navorser nogtans tot die slotsom dat graad 1-onderwysers se persepsies oor metakognisie en wiskundetaal in die onderrig en leer in wiskunde in graad 1-klasse belangrik is en groot gewig dra. / MEd (Mathematics Education), North-West University, Potchefstroom Campus, 2015

Metakognitiewe strategieë en wiskundetaal speel ’n kritiese rol in onderwysers se onderrigstrategieë en die verbetering van hulle wiskunde-onderrigstyl. Die waarskynlikheid bestaan dat wanneer ʼn onderwyser se metakognisie ontwikkel word, sy of haar onderrig ook sal verbeter (Jing & Yang, 2008, p. 1). Metakognisie fasiliteer die onderrig en leer van wiskundekennis (Gourgey, 2001, p. 18), en taal is die instrument wat in ʼn onderwyskonteks die kommunikasie vir die aanleer, verstaan en ontwikkeling van wiskundekonsepte en -prosesse fasiliteer (Jamison, 2000). ʼn Empiriese kwalitatiewe ondersoek – om te bepaal wat Graad 1-onderwysers se persepsies van metakognisie en wiskundetaal tydens die onderrig en leer van wiskunde is – is in hierdie studie uitgevoer. Die ondersoek het op vyf Graad 1-onderwysers gefokus. ʼn Gerieflikheidsteekproef is gebruik om die groepie onderwysers (wat vir die navorser toeganklik was) uit te nooi om aan die studie deel te neem. Video-opnames is gemaak van ʼn fokusgroeponderhoud, sowel as van ʼn wiskundeles en twee individuele onderhoude. Al die onderwysers het aan die fokusgroeponderhoud deelgeneem. Een van die onderwysers (Deelnemer B) het ingestem dat ʼn video-opname van haar wiskundeles gemaak kon word. ʼn Individuele onderhoud is voor en na die video-opname met deelnemer B gevoer om ʼn beter en meer diepgaande begrip van haar persepsies oor wiskundeonderrig te verkry. Die video-opnames van die fokusgroeponderhoud, wiskundeles en individuele onderhoude is verbatim getranskribeer, waarna a priori kodes uit die literatuurstudie gekies is. Die kodes is in temas en kategorieë gegroepeer. Data is ontleed, en gevolgtrekkings geformuleer. Resultate is daarna geïnterpreteer en aanbevelings gemaak. Ten spyte van die beperkte veralgemenings wat op grond van die resultate moontlik is, kom die navorser nogtans tot die slotsom dat graad 1-onderwysers se persepsies oor metakognisie en wiskundetaal in die onderrig en leer in wiskunde in graad 1-klasse belangrik is en groot gewig dra. / MEd (Mathematics Education), North-West University, Potchefstroom Campus, 2015

Wiskunde as taal van die wetenskap en tegnologie is een van die weinige vakke wat spesifiek as voorvereiste vir die bestudering van sekere studierigtings gestel word. Leerlinge met Wiskunde-angs word verhoed om hul ware potensiaal in Wiskunde te verwesenlik en word sodoende gediskwalifiseer om hul regmatige plek in die beroepswereld in te neem. Die doel van hierdie studie was om te bepaal of hipnoterapie aangewend kan word om Wiskunde-angs tot werkbare vlakke te beperk sodat leerlinge optimaal in Wiskunde kan presteer. Die aard, oorsake, aanvang, herkenning, verklaring, gevolge, voorkoms en meting van Wiskunde-angs, die verband daarvan met Wiskundeprestasie en die hulp wat onderwysers en hulpprogramme kan lewer, is nagegaan. Daarna is hipnose en hipnoterapie beskou om te bepaal of dit as terapeutiese hulpmiddel pedagogies verantwoordbaar is. 'n Hipnoterapieprogram is in werking gestel en daar is bevind dat die proefpersone almal tot 'n mindere of meerdere mate daarby gebaat het. / Mathematics as the language of science and technology is one of few subjects used as entrance requirement to certain fields of study. Mathematics anxiety prohibits certain pupils to reach their full potential in Mathematics and thus to obtain their rightful place in the world of work. The aim of this study was to determine whether hypnotherapy can be used to lower Mathematics anxiety levels to such an extend that pupils can optimally achieve in Mathematics. The nature, causes, extent, recognition, explanation, consequences, incidence and measurement of Mathematics anxiety, its relationship to achievement in Mathematics, as well as the help that can be rendered by teachers and treatment programmes were studied. Hypnotherapy was then examined to determine whether its use was pedagogically justifiable. A hypnotherapy treatment programme was introduced which was found to be to some extent beneficial to all the subjects used. / Psychology of Education / M. Ed. (Voorligting)

Within the framework of comprehensive research that has been done on the mathematics achievement of first-year university students, research literature contains relatively few studies concerning the prediction of the mathematics achievement of final year students. An ex post facto empirical study was undertaken to rectify this situation to some extent. The aims of this study were: • To develop prediction models with which to predict the mathematics achievement of third-year students at the PU for CHE. • To develop a prediction analysis for continuous data by means of which the mathematics achievement of third-year students can be predicted in terms of a pass/fail dichotomy by using the fundamentals of Boolean algebra. • To determine, as a secondary aim, the differential influence of several independent variables on the mathematics achievement of male and female students in their third year. Of the set of independent variables in this study, five indicated previous achievement, 10 were aptitude variables (including an estimated IQ score) and 21 were measures of different interests, while a measure of the algebraic preparedness of prospective mathematics students on the PU for CHE was also included. The mathematics achievement of students at the end of the first semester of the first year was used in part of the investigation as an independent variable. Four criteria were defined to quantify the mathematics achievement of students at the PU for CHE. In three of these, unsuccessful attempts to obtain a pass in mathematics courses were taken into consideration. The aptitude variables in this study were measured with the Senior Aptitude tests (Human Sciences Research Council), the 19-Field Interests Questionnaire (Human Sciences Research Council) and the algebraic preparedness of students was measured by means of a 60-item multiplechoice test developed by this researcher and of which measures of validity and reliability were reported. The data of two groups of subjects considered as study populations, were used in the study. The group of first-year students following mathematics courses for the first time in 1982 was employed as an experimental group. Of the 154 first-year students in this group, 58 were able to advance to the third year and wrote the examination in least one mathematics course in that year. The class of first-year students registered for mathematics courses for the first time in 1983 was used as a crossvalidation group in order to validate the prediction models. This group consisted of 138 students, of which 54 advanced to the third year. Six hypotheses were examined in this study by means of several statistical techniques. By means of singular correlations it was shown that certain independent variables exerted a bigger influence on the mathematics performance of third-year students than others and that the correlations of some independent variables with mathematics achievement decreased from the first year to the third year. Regarding other variables, the opposite tendency was found. By means of factor, regression, discriminant and Boolean analysis, it was further found that the mathematics achievement of male and female students on the third year level was influenced differently by independent variables. The hypothesis that a higher percentage of the variance of mathematics performance in the case of females than that of males can be accounted for, could not be accepted for all criteria of mathematics achievement. The validity of prediction models could also not be accepted for all criteria of mathematics performance, even if the mathematics achievement of students at the end of the first semester in the first year was included as an independent variable in the regression analysis. Finally it was found that prediction models for the pass/fail dichotomy for mathematics achievement, developed by means of Boolean analysis, were on the average more successful in terms of validity than the discriminant functions developed by using discriminant analysis. This result indicated a promising future for the use of Boolean analysis in the prediction of academic achievement. / Proefskrif (DEd)--PU vir CHO, 1988

Within the framework of comprehensive research that has been done on the mathematics achievement of first-year university students, research literature contains relatively few studies concerning the prediction of the mathematics achievement of final year students. An ex post facto empirical study was undertaken to rectify this situation to some extent. The aims of this study were: • To develop prediction models with which to predict the mathematics achievement of third-year students at the PU for CHE. • To develop a prediction analysis for continuous data by means of which the mathematics achievement of third-year students can be predicted in terms of a pass/fail dichotomy by using the fundamentals of Boolean algebra. • To determine, as a secondary aim, the differential influence of several independent variables on the mathematics achievement of male and female students in their third year. Of the set of independent variables in this study, five indicated previous achievement, 10 were aptitude variables (including an estimated IQ score) and 21 were measures of different interests, while a measure of the algebraic preparedness of prospective mathematics students on the PU for CHE was also included. The mathematics achievement of students at the end of the first semester of the first year was used in part of the investigation as an independent variable. Four criteria were defined to quantify the mathematics achievement of students at the PU for CHE. In three of these, unsuccessful attempts to obtain a pass in mathematics courses were taken into consideration. The aptitude variables in this study were measured with the Senior Aptitude tests (Human Sciences Research Council), the 19-Field Interests Questionnaire (Human Sciences Research Council) and the algebraic preparedness of students was measured by means of a 60-item multiplechoice test developed by this researcher and of which measures of validity and reliability were reported. The data of two groups of subjects considered as study populations, were used in the study. The group of first-year students following mathematics courses for the first time in 1982 was employed as an experimental group. Of the 154 first-year students in this group, 58 were able to advance to the third year and wrote the examination in least one mathematics course in that year. The class of first-year students registered for mathematics courses for the first time in 1983 was used as a crossvalidation group in order to validate the prediction models. This group consisted of 138 students, of which 54 advanced to the third year. Six hypotheses were examined in this study by means of several statistical techniques. By means of singular correlations it was shown that certain independent variables exerted a bigger influence on the mathematics performance of third-year students than others and that the correlations of some independent variables with mathematics achievement decreased from the first year to the third year. Regarding other variables, the opposite tendency was found. By means of factor, regression, discriminant and Boolean analysis, it was further found that the mathematics achievement of male and female students on the third year level was influenced differently by independent variables. The hypothesis that a higher percentage of the variance of mathematics performance in the case of females than that of males can be accounted for, could not be accepted for all criteria of mathematics achievement. The validity of prediction models could also not be accepted for all criteria of mathematics performance, even if the mathematics achievement of students at the end of the first semester in the first year was included as an independent variable in the regression analysis. Finally it was found that prediction models for the pass/fail dichotomy for mathematics achievement, developed by means of Boolean analysis, were on the average more successful in terms of validity than the discriminant functions developed by using discriminant analysis. This result indicated a promising future for the use of Boolean analysis in the prediction of academic achievement. / Proefskrif (DEd)--PU vir CHO, 1988

Proefschrift Universiteit van Amsterdam. / Met index, lit. opg. - Met samenvatting in het Nederlands.