Mathematics textbooks are by far the most commonly used didactic tool in classroom teaching. Currently, there is very limited research into how teacher guides, accompanying these textbooks, support the teacher’s work in the classroom. The purpose of the study was to examine to what extent teacher guides support and guide teacher in teaching mathematics. Question raised by the study was – how are variation and concretization addressed in the teacher guides? Variation theory directs focus to critical aspects of the object of learning and can be used as basis to evaluate teacher guides. Concepts like variation and concretization have been useful tools when analysing the teacher guides. To support the study’s phenomenographical approach, a coding system was developed and used as a tool in analysis. Developing the coding system was critical in order to compare the four teacher guides, as well as for the reliability and validity of the study. Data were collected from four, first grade teacher guides in mathematics. An analysis covering an overall perspective has been performed. Several specific topics have also been analysed in a more inductive approach. The results indicate that teacher guides, anchored in the Swedish curricula in mathematics, do not support teachers in how to move from concrete learning to abstract learning. Critical details are being omitted which might affect the goal of abstract thinking.

Abstract Students in grades 3 and 4 attending a traditional public elementary school in a northeastern state did not meet proficiency levels in mathematics as measured by the state's assessment system. Published reports indicated that students attending the Montessori programs were more proficient in solving math problems compared to students in traditional schools. However, researchers had not compared Montessori and traditional teachers' perceptions of teaching elementary mathematics. The purpose of this qualitative case study was to explore the perceptions of traditional and Montessori teachers regarding teaching basic problem solving skills in mathematics. Koehler and Grouws' model provided the theoretical framework. Data collection included semistructured interviews with 6 traditional and 4 Montessori elementary teachers, field notes, and journaling. Data were analyzed using a coding scheme that incorporated the theoretical model's categories. Findings indicated that both groups of teachers reported that concrete (manipulatives) to abstract (pen and paper) learning was an effective approach to teaching basic math concepts and problem-solving skills. Social change will be realized when struggling elementary students in both Montessori and traditional settings begin to meet proficiency levels in mathematics and benefit from instruction that balances concrete and abstract learning skills. As such, students will be able to explore, develop, and become more actively engaged in learning math and problem solving in all elementary grades. The project deliverable, a position paper supporting the principal theme of concrete to abstract learning, may be used to promote effective instructional practices in mathematics, hence, positive social change.

The aim of this study was to conduct a thorough theoretical study on the relevant aspects involved in knowledge management and organizational learning, and thence assess the level of organisational learning within the ferrometallurgical industry. From the outcomes of the assessment, recommendations to improve the state of affairs were to be made. Knowledge can be defined as actionable information. The creation, acquisition, sharing and leveraging of knowledge in today's industries are critical. Knowledge is now termed the fourth productive resource, and some authors claim, with some justification, that the widespread knowledge within a company is the only source of sustainable competitive advantage. With this in mind, it is obvious that companies need to nurture knowledge creation and effective utilisation thereof in order to meet organisational goals. Knowledge can be codified if it is explicit, but needs to be transferred using personalisation if it is tacit. Implicitness of tacit knowledge further confounds the issue. Knowledge management practices underpin the process of organisational learning. The level of organisational learning within the ferrometallurgical industry in South Africa was assessed, using a survey questionnaire obtained from the Harvard Business School. The results show that the industry lags behind the medians in the ten constructs measured, and much work will be required to significantly improve the situation. Key areas of concern are in the areas of psychological safety, time for reflection, education and training, and collection of information. As a consequence, a practical strategy for improving the state of knowledge management and organisational learning in the ferrometallurgical industry was developed. / Thesis (M.B.A.)--North-West University, Vaal Triangle Campus, 2010.

The aim of this study was to conduct a thorough theoretical study on the relevant aspects involved in knowledge management and organizational learning, and thence assess the level of organisational learning within the ferrometallurgical industry. From the outcomes of the assessment, recommendations to improve the state of affairs were to be made. Knowledge can be defined as actionable information. The creation, acquisition, sharing and leveraging of knowledge in today's industries are critical. Knowledge is now termed the fourth productive resource, and some authors claim, with some justification, that the widespread knowledge within a company is the only source of sustainable competitive advantage. With this in mind, it is obvious that companies need to nurture knowledge creation and effective utilisation thereof in order to meet organisational goals. Knowledge can be codified if it is explicit, but needs to be transferred using personalisation if it is tacit. Implicitness of tacit knowledge further confounds the issue. Knowledge management practices underpin the process of organisational learning. The level of organisational learning within the ferrometallurgical industry in South Africa was assessed, using a survey questionnaire obtained from the Harvard Business School. The results show that the industry lags behind the medians in the ten constructs measured, and much work will be required to significantly improve the situation. Key areas of concern are in the areas of psychological safety, time for reflection, education and training, and collection of information. As a consequence, a practical strategy for improving the state of knowledge management and organisational learning in the ferrometallurgical industry was developed. / Thesis (M.B.A.)--North-West University, Vaal Triangle Campus, 2010.