In 2 experiments, I studied the effects of an Equivalence Based Instruction (EBI) math intervention on the emergence of untaught selection responses and abstraction to production responses. In Experiment I, using a multiple baseline design, I implemented the EBI intervention among a group of 17 first grade participants with varying levels of math prerequisites and verbal behavior development. The intervention sought to develop a comprehensive relational network for the part-whole relations involved in addition and subtraction operations. This intervention, informed by Verbal Behavior Development Theory, Relational Frame Theory, and research on math proficiency, utilized visual and verbal stimulus presentations of fact families to establish the concepts underlying addition and subtraction. The key concept was that of a fact-family, in which two parts are equivalent to the whole and the whole is equivalent to the sum of its parts. The goal of the EBI intervention was to establish a relational network involving pictures, number bonds, sentences, and equations such that the part-whole relations involved in fact-families could be related to both addition and subtraction. The EBI intervention consisted of 3 phases to build this relational network. In Phase I, participants learned to match sentences describing complete fact-families with pictures and number bonds. In Phase II, participants learned to match sentences describing incomplete fact-families with number bonds. In Phase III, participants learned to match incomplete number bonds with addition and subtraction equations presented in various topographies. Before and after each phase of the intervention, I assessed the degree to which participants acquired untaught responses as well as their performance on production, or problem-solving, probes. Results revealed that the combinatorially entailed response (i.e., matching pictures with number bonds) emerged for all participants, while the mutually entailed response (i.e., selecting sentences) emerged for only some participants. Participants generally improved their problem-solving following the intervention; however, further examination was needed to supplement initial visual analyses of the graphs. Accordingly, I conducted a series of statistical analyses to evaluate individual and group-level differences in responding during the EBI intervention. These analyses also sought to reveal whether math prerequisites or level of verbal behavior development were associated with performance during Phases I, II, and III. Results showed that the EBI intervention was associated with standardized math performance and problem-solving accuracy, and results suggested that verbal behavior development has a meaningful relation with rate of learning. In Experiment II, I aimed to evaluate the educational significance of the repertoires involved in the EBI intervention by conducting a correlational study with 32 additional first grade participants. This experiment revealed that the response-types targeted in Phase III of the intervention were significantly associated with standardized math performance.

Thesis (PhD)--University of Stellenbosch, 2004. / ENGLISH ABSTRACT: The globalisation of business is probably the most important topic of discussion in business around the world. Globalisation impacts on business processes, and changes in the processes of economic and political liberalisation signify a radical shift in thinking about how the world works and how it should be organised. The process of change consequently means having to deal with increasing complexity. It is the complexity of change that prompts the urgency to improve the thinking of management in an organisation. As adult learners, managers need different competencies to operate; in addition their thinking skills need to be developed, as they are the key drivers in an organisation going through transformation. In a needs' assessment in a financial services organisation operating in the global environment, a need for training of middle managers to help them improve their thinking skills in order to become more effective thinkers was determined. The need to train adults to develop cognitive skills prompted a specific thinking skills intervention and the facilitation thereof. A Thinking Skills Programme aimed at teaching thinking dispositions and thinking skills was implemented as a programme to teach the managers to become effective thinkers. The study was approached from a programme evaluative perspective. The purpose of the programme was an improvement-orientated evaluation and was designed to evaluate the outcomes of the programme. Qualitative data was collected through a pre- assessment and postassessment process. Open-ended questionnaires as well as other qualitative methods were used in the assessment to capture the data. The data analysis was done through content analysis. In the process of determining the patterns and processes in the preassessment, observations, semi-structured interviews, field notes and post-assessment, the researcher looked for themes or interconnections that emerged in the units, sub-categories and categories. The sub-categories that emerged were derived from the frequency of appearance in the answers of the participants in the questionnaires. The post-assessment feedback categories indicated that a shift in effective thinking had taken place in the participants. The most significant difference in their thinking was the awareness of their thinking. They reflected on their thinking while solving problems, which is evidence of effective thinking. They used the thinking tools to help them solve problems. The intervention influenced the participants to be more creative in solving problems, which was not evident in the pre-assessment. The evaluation of the outcome of the programme through the application of a Thinking Skills Programme was successful. This was demonstrated by the fact that in the measurement of the outcome of the programme it was evident that the middle managers had become more aware of their thinking and that they applied the thinking dispositions and thinking tools in their daily managerial activities. They had become more effective thinkers. / AFRIKAANSE OPSOMMING: Die globalisering van die sakewêreld is waarskynlik die belangrikste besprekingspunt in dié sektor regoor die wêreld. Globalisering het 'n impak op sakeprosesse, en veranderings in die prosesse van ekonomiese en politieke liberalisering dui op 'n radikale verandering in denke oor hoe die wêreld werk en hoe dit georganiseer behoort te word. Die proses van verandering dui gevolglik daarop dat daar rekening gehou moet word met toenemende kompleksiteit. Dit is die kompleksiteit van verandering wat aanleiding gee tot die belangrikheid daarvan om die denkvaardighede van die bestuur in 'n organisasie te verbeter. As volwasse leerders benodig bestuurders verskillende vaardighede om hulle taak te verrig, en hulle denkvaardighede moet ontwikkel word aangesien hulle die dryfkrag is van 'n organisasie wat transformasie ondergaan. In 'n behoeftebepaling in 'n finansiële dienste organisasie wat op die wêreldmark meeding, is die behoefte geïdentifiseer aan opleiding vir middelvlak bestuurders om hulle denkvaardighede te help verbeter, ten einde van hulle meer effektiewe denkers te maak. Die behoefte om volwassenes op te lei in die ontwikkeling van kognitiewe vaardighede het aanleiding gegee tot In spesifieke denkvaardigheidsintervensie en die fasilitering daarvan. 'n Denkvaardigheidsprogram gemik op die onderrig van denkdisposisies en -vaardighede is as 'n program ingestelom bestuurders op te lei om effektiewe denkers te word. Die studie is benader vanuit 'n programevaluasie-perspektief. Die doel van die program was 'n verbeteringsgeoriënteerde evaluasie en dit is ontwerp om die uitkomstes van die program te evalueer. Kwalitatiewe data is versamel deur middel van 'n pre- en postassesseringsproses. Oopeindevraelyste asook ander kwalitatiewe metodes is in die assessering gebruik om data te versamel. Die data-analise is gedoen deur inhoudsanalise. Vir die bepaling van die patrone en prosesse in die pre-assessering, is observasies, semigestruktureerde onderhoude en veldaantekeninge gebruik. Vir die postassessering het die navorser gesoek na temas of interkonneksies wat na vore gekom het in die eenhede, subkategorieë en kategorieë. Die subkategorieë wat na vore gekom het, is geïdentifiseer op grond van die frekwensie van voorkoms in die antwoorde van die deelnemers wat die vraelyste voltooi het. Die terugvoeringskategorieë in die postassessering het aangetoon dat 'n verandering in effektiewe denke by die deelnemers plaasgevind het. Die mees beduidende verandering in hulle denke was die bewustheid van hulle denke. Deelnemers het gereflekteer op hulle denke tydens probleemoplossing, wat as bewys dien van effektiewe denke. Hulle het die denkinstrumente gebruik om hulle te help om probleme op te los. Die intervensie het tot gevolg gehad dat die deelnemers meer kreatief tydens probleemoplossing was, wat nie tydens die pre-assessering geblyk het nie. Die evaluering van die uitkoms van die program deur die toepassing van 'n Denkvaardigheidsprogram was suksesvol. Dit is gedemonstreer deur die feit dat in die meting van die uitkoms van die program dit duidelik geblyk het dat die middelvlak bestuurders meer bewus geraak het van hulle denke en dat hulle die denkdisposisies en denkinstrumente in hulle daaglikse bestuursaktiwiteite toegepas het. Hulle het meer effektiewe denkers geword.

This study examined the effects of specially designed thinking journal activities that have been attributed with encouraging reflective thinking, on instruction using generic, or content-free problem solving software. Sixty-three fourth grade students participated in four instructional sessions using a software package called Moptown Hotel. Students completed separate posttests that measured (1) performance on problems of the same kind as those used in instruction, and (2) transfer of skills to other kinds of problems. Scores of students who wrote thinking journals prior to testing were compared with scores of students who did not. Results indicate that students who wrote thinking journals performed the same as students who did not when tested on problems similar to those practiced in class. Tests in which students transferred their skills to word problems, however, produced significant differences. There was no significant difference between scores when averaged over all four weekly occasions. However, for the final session alone, students who wrote thinking journals scored higher on tests of problem solving transfer than students who did not (p < .01). The study also examined the relationship between the degree of metacognitive thought displayed in students' journal entries, and their measured problem solving ability. Results indicate that students who had higher average reflectivity scores also had higher average problem solving performance and transfer scores (p < .05). It was also noted that the significant relationship between reflectivity and scores of problem solving ability was only observed in male students. It was concluded that under the right conditions, and for the right kinds of problems, thinking journal writing can help students understand their own thinking processes, resulting in improved problem solving behavior. The study also raises the question of whether there are differences between the ways that male and female students apply metacognitive awareness gained through journal writing experiences.

Specific to the recommendation of the National Council of Teachers of Mathematics (1980) to identify and analyze problem solving strategies and the settings in which the development of these strategies could be optimized, this study is a compilation of three case studies which describe what elementary school children say and do when solving verbal mathematics problems in small groups. Persuant to this goal, three four-member groups were selected and asked to reach a consensus within each group on the solution to a variety of routine and non-routine problems. In this relatively unstructured setting, transcriptions of verbal interactions, written records of all computations, and observer notes were compiled for each group. The resulting identification and description of the problem solving behaviors which occurred were analyzed in terms of two broad interactive functions by which children seek to understand verbal problems: the construction of mental representations or physical displays of the problems and the evaluations of these constructions. Representations, in this perspective, are constructed at two levels: a contextual level at which the problem situation is linguistically interpreted and a structural level at which a statement of a problem underlying mathematical structure is defined. Evaluations also occur which allow group members to monitor their understanding and direct the course of the problem solving effort. The findings indicate that intermediate aged children when solving problems in small groups display general patterns of behavior. These patterns of behavior include: the manner in which the groups approach and effectively isolate the contextual elements of a verbal problem, the propensity of groups to change the mode in which a problem is represented by utilizing manipulatives, diagrams, tables and other physical displays, and the manner in which groups monitor the course of problem solving and reach consensuses on solution proposals. Within this general pattern, however, specific subject and task variables characterize individual groups, affecting both the group interaction and the incidence of specific problem solving behaviors. These findings suggest practical classroom applications for group problem solving formats in the elementary school classroom. Additional research, however, must provide the link between group problem solving and individual performance.

published_or_final_version / Education / Master / Master of Education

published_or_final_version / Education / Master / Master of Education

published_or_final_version / Education / Master / Master of Education

The purpose of this study was to extend our current knowledge about what happens in physical science classrooms. The focus was the context of problem tasks. This involved the study of the situations, events and factors that relate to the solving of problem tasks at high school in order to understand their role and nature. e problem tasks that were central to this study were well defined, narrow in focus, and invariably involved the calculation of some quantity through the use of a formula and algebraic manipulation. The main questions that guided the study were as follows: What is happening in physical science classrooms? What is the nature and role of problem solving within this context? What are some of the consequences of organising teaching and learning in this manner? How do external forces influence what happens? The study aimed at describing the activities that the teachers and students were involved in and understanding how they understood their own actions. An interpretive research approach was chosen for this purpose, having as its basis a detailed descriptive foundation using classroom observation. Two high school science classrooms were studied in detail over a period of a year. The data gathered included field notes from over a hundred classroom visits, extensive video and audio records, questionnaires, classroom documents and formal an informal interviews with teachers, students and examiners. Through a process of careful and systematic analysis of the data, six assertions emerged. These assertions are supported by both particular evidence in the form of analytic narrative vignettes, quotes and extracts, and general evidence consisting of frequency data and summary tables. The analysis reveals that problem tasks occupied most of the teaching and learning time, and that the students found this experience of school science boring. Most of the problem tasks were routine in nature and of low conceptual demand. The majority of the students were unable to solve the more difficult tasks encountered in their tests and examinations. In addition, a significant number could not solve the routine problem tasks. This suggests that the predominant instructional strategies were ineffective. It was found that participants had an uncritical belief in the efficacy of teacher explanations and student practice on problem tasks. Further, the participants had different views of the role of problem tasks. A significant finding was that the examination exerted a powerful focusing influence on the classroom environment, the instructional activities and on the problem tasks used . It appeared that the ultimate goal of school physical science was to solve these types of problem task in preparation for the high stakes examination, rather than the learning of science. The study has implications both for practice and for research on the teaching and learning of school physical science. These implications are discussed in terms of instructional strategies aimed at promoting a deeper understanding of physical science. In order to improve practice it is advocated that the role of problem tasks in learning science be made explicit while at the same time new types of instructional task need to be designed to achieve our goals for school science. / Thesis (Ph.D.)-University of Natal, Durban, 1999.

Die tesis is voorgelê ter verwerwing van die graad: Magister in Opvoedkunde aan die: Cape Peninsula University of Technology, 2012. Afrikaanse abstrak: Hierdie navorsing het die gebruik van probleemoplossings-onderrigtegnieke deur onderwysers in die Rekenaartoepassingstegnologie (RTT) –klaskamer ondersoek. Kriteria ten opsigte van probleemoplossingsvaardighede soos uiteengesit in die Nasionale Kurrikulumverklaring (NKV ) en die Nasionale Kurrikulum- en Assesserings- Beleidsverklaring (NKABV) vir RTT was toegepas in hierdie studie. RTT word slegs vanaf graad 10 in die verdere onderwys- en opleidingfase (VOO) as „n keusevak aangebied. Dus was die navorser se fokus op die omliggende sekondêre skole wat RTT aanbied. Die navorsing konsentreer op die onderwyser en sy toepassing van probleemoplossings-onderrigtegnieke. Die navorser het gebruik gemaak van gevallestudie as navorsingsontwerp en konstruktivisme as raamwerk toegepas. Klaskamer-observasies, onderhoude en beide formele en onderwyser - geskepte dokumente het gedien as bronne vir data. Die data was tematies ontleed om die betekenis daarvan te ontgin. Die analise van die data dui aan dat respondente nie aan die vereistes gestel deur die NKABV en NKV, ten opsigte van die aanbieding en assessering van probleemoplossings-onderrigtegnieke, voldoen nie. Die navorser beveel aan dat „n moontlike oplossing vir die onderwyser-respondente se gebrek aan kennis en onderrigvaardighede met betrekking tot probleemoplossings-onderrigtegnieke kan wees dat daar spesifieke kursusse oor hierdie onderwerp aangebied word. Die navorsing skep ook ʼn geleentheid vir tersiêre instellings om hulle kurrikula en opleidingsprogramme sodanig aan te pas ten einde die leemtes, soos uitgewys deur die navorsing, aan te spreek. / This research explored the utilization of problem solving techniques by Computer Applications Technology (CAT) teachers in grade 11. The requirements and criteria as set out in the National Curriculum Statement (NCS) and the National Curriculum and Assessment Policy Statement (CAPS), were applied in this study. CAT is only introduced in grade 10 in the Further Education and Training (FET) phase. The researcher thus focussed on the surrounding schools that offer CAT as a subject. The research focussed on the teacher and the teaching of problem solving techniques in CAT. The researcher used a case study design and employed a constructivism as the theoretical framework. Classroom observations, interviews and both teacher generated and formal documents served as data sources. A thematic analysis approach was adopted to make sense of the data. The analysis of the different data sources indicated that the respondents did not fully comply with the requirements set by the NCS and CAPA with reference to the teaching of problem solving techniques in CAT. The researcher recommends that courses are presented to address the gaps in the knowledge and skills of teachers in CAT referring to problem solving techniques. This creates both the opportunity and challenge to tertiary institutions to align their curricula and training programmes to address the gaps identified by this research.

The study was undertaken with three Grade 9 teachers at three selected schools which are part of RUMEP’s Collegial Cluster Schools’ programme that I coordinate. Collegial clusters are communities of teachers who aim at improving their practice by working on their own professional development. The purpose of this study was to investigate the selected Grade 9 teachers’ experiences of a Geoboard intervention programme. It also wanted to investigate the role that a Geoboard can play in the teaching and learning of area and perimeter of two-dimensional shapes. The research was a case-study within the interpretive paradigm. A variety of data collection techniques was used. These included baseline assessment tasks, observations during the intervention programme, post intervention assessment tasks and semistructured interviews with the participating teachers and a few learners from each participating school. The collected data was analysed using both the quantitative and qualitative methods. My research findings reveal that a Geoboard, as a manipulative, developed confidence in the participating teachers. In the interviews with teachers, it transpired that teachers’ skills in teaching area and perimeter of two-dimensional shapes had been sharpened. According to the interviews with learners, the use of a Geoboard led to better conceptual understanding of the area and perimeter, as learners no longer had to rely on formulae. Kilpatrick et al. (2001) refer to conceptual understanding as an integrated functional grasp of mathematical ideas. The post intervention assessment task showed a positive shift in learners’ performance. The average learner performance improved from 29% in the baseline assessment task to 61% in the post intervention assessment task. This shows that the use of a Geoboard led to meaningful learning of area and perimeter of two-dimensional shapes. The overall research findings reveal that the use of manipulatives has a positive impact in the teaching and learning of area and perimeter. Learners’ responses to the interview questions showed that there was better understanding of the two concepts, which enabled them to construct their own knowledge. They further said the Geoboard allowed them to be hands-on, which contributed to their active involvement in the lesson.