Visit the COVID-19 Corona Virus South African Resource Portal on https://sacoronavirus.co.za/
Exploring learners' mathematical understanding through an analysis of their solution strategies
- Authors: Penlington, Thomas Helm
- Date: 2005
- Subjects: Mathematics -- Study and teaching (Elementary) , Mathematics -- Problems, exercises, etc. , Problem solving -- Study and teaching , Reasoning , Mathematical ability
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1934 , http://hdl.handle.net/10962/d1007642
- Description: The purpose of this study is to investigate various solution strategies employed by Grade 7 learners and their teachers when solving a given set of mathematical tasks. This study is oriented in an interpretive paradigm and is characterised by qualitative methods. The research, set in nine schools in the Eastern Cape, was carried out with nine learners and their mathematics teachers and was designed around two phases. The research tools consisted of a set of 12 tasks that were modelled after the Third International Mathematics and Science Study (TIMSS), and a process of clinical interviews that interrogated the solution strategies that were used in solving the 12 tasks. Aspects of grounded theory were used in the analysis of the data. The study reveals that in most tasks, learners relied heavily on procedural understanding at the expense of conceptual understanding. It also emphasises that the solution strategies adopted by learners, particularly whole number operations, were consistent with those strategies used by their teachers. Both learners and teachers favoured using the traditional, standard algorithm strategies and appeared to have learned these algorithms in isolation from concepts, failing to relate them to understanding. Another important finding was that there was evidence to suggest that some learners and teachers did employ their own constructed solution strategies. They were able to make sense of the problems and to 'mathematize' effectively and reason mathematically. An interesting outcome of the study shows that participants were more proficient in solving word problems than mathematical computations. This is in contrast to existing research on word problems, where it is shown that teachers find them difficult to teach and learners find them difficult to understand. The findings of this study also highlight issues for mathematics teachers to consider when dealing with computations and word problems involving number sense and other problem solving type problems.
- Full Text:
The role of computational thinking in introductory computer science
- Authors: Gouws, Lindsey Ann
- Date: 2014
- Subjects: Computer science , Computational complexity , Problem solving -- Study and teaching
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:4690 , http://hdl.handle.net/10962/d1011152 , Computer science , Computational complexity , Problem solving -- Study and teaching
- Description: Computational thinking (CT) is gaining recognition as an important skill for students, both in computer science and other disciplines. Although there has been much focus on this field in recent years, it is rarely taught as a formal course, and there is little consensus on what exactly CT entails and how to teach and evaluate it. This research addresses the lack of resources for integrating CT into the introductory computer science curriculum. The question that we aim to answer is whether CT can be evaluated in a meaningful way. A CT framework that outlines the skills and techniques comprising CT and describes the nature of student engagement was developed; this is used as the basis for this research. An assessment (CT test) was then created to gauge the ability of incoming students, and a CT-specfic computer game was developed based on the analysis of an existing game. A set of problem solving strategies and practice activities were then recommended based on criteria defined in the framework. The results revealed that the CT abilities of first year university students are relatively poor, but that the students' scores for the CT test could be used as a predictor for their future success in computer science courses. The framework developed for this research proved successful when applied to the test, computer game evaluation, and classification of strategies and activities. Through this research, we established that CT is a skill that first year computer science students are lacking, and that using CT exercises alongside traditional programming instruction can improve students' learning experiences.
- Full Text:
An investigation of teachers’ experiences of a Geoboard intervention programme in area and perimeter in selected Grade 9 classes: a case study
- Authors: Mkhwane, Fezeka Felicia
- Date: 2018
- Subjects: Mathematics -- Study and teaching (Secondary) -- South Africa , Teachers -- Training of -- South Africa , Manipulatives (Education) , Effective teaching , Shapes -- Study and teaching (Secondary) -- South Africa , Problem solving -- Study and teaching
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/61646 , vital:28045
- Description: 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.
- Full Text: