title: Digital competencies of high school mathematics teachers in Pakistan

authors: Jafri, Mairaj

abstract: The dynamic demands of the contemporary educational landscape, which includes a variety of digital tools and resources, require teachers to develop digital competencies. This need is particularly pertinent for mathematics teachers in developing countries like Pakistan, where there is a requirement to bridge the digital divide and equip teachers with the knowledge and skills to integrate digital resources into their teaching practices. Prior research has acknowledged the importance of integrating digital resources in education; however, there is limited research on the challenges and opportunities that high school mathematics teachers encounter when using digital resources in resource-constrained environments like Pakistan.
This study aimed to investigate the digital competencies of high school mathematics teachers in Pakistan, focusing on their knowledge, beliefs, practices, and experiences in integrating digital resources into mathematics teaching and learning. To achieve this aim, the study adapted the “Digital Competencies for Teaching Mathematics with Technology” (DCTMT) framework. Employing a mixed-methods explanatory sequential design, the study was divided into two phases for data collection. In Phase 1, quantitative data were collected through an online survey, which received a total of 306 responses. I analysed the survey data using descriptive (Mean, Mode, Median, and Standard Deviation) and inferential (intra- and inter-construct Spearman’s rho (⍴) correlation tests) statistics. To further understand and explain important quantitative results, semi-structured interviews were conducted in Phase 2 with six (Phase 1) teachers. I analysed the qualitative data using pre-identified themes and sub-themes based on the constructs of the DCTMT framework.
The results of both phases indicated that teachers held firm beliefs about various aspects of mathematics education. Teachers expressed strong beliefs about pedagogical practices and held positive beliefs about the importance of digital resources for teaching and learning mathematics. Correlations were observed between beliefs, teachers' reported ability to create videos, knowledge of dynamic graphing software (DGS) and equation editors, and participation in professional training. The findings revealed that most teachers possessed some level of digital competency. Teachers predominantly relied on videos and graphics, indicating potential bias and a gap in their professional development and training. They lacked access to (particularly at school) and possessed a weak knowledge of mathematics-specific digital resources like Dynamic Graphing Software (DGS). Other factors, such as lack of resources, inadequate formal training, and limited professional development opportunities, hindered their ability to integrate digital resources into their teaching and learning of mathematics. However, the results indicated that teachers could overcome some of these challenges through resilience and self-learning initiatives.
The study findings suggest that equipping teachers with appropriate resources and targeted professional development could enhance their digital competencies. This would consequently promote equitable and diverse use of digital resources in mathematics education. Within the confines of resource-constrained environments, these findings support for nurturing teachers' resilience and cultivating a self-learning attitude among them. Teachers who equip themselves with digital skills receive training and have the confidence to integrate digital resources to develop digital competencies, irrespective of resource constraints.
This thesis contributes to the understanding of high school mathematics teachers' digital competencies in Pakistan and indicates the opportunities and obstacles they encounter while using digital resources. This research inquiry provides empirical evidence for the modified DCTMT framework and reveals significant interconnections between the five constructs of the framework. The study reveals critical insights into the intricate relationship between beliefs, access to resources, and competencies in utilizing digital tools for mathematics education. This thesis establishes a compelling link between training, self-learning, teachers' resilience, and their digital competencies, highlighting the dynamic interplay that shapes mathematics teachers' digital competencies. This thesis offers implications for teachers’ professional development, curriculum design, and policy formulation. It emphasizes the importance of supporting teachers with the resources and knowledge to integrate digital resources and enhance mathematics education in resource-constrained contexts.

text: Digital competencies of high school mathematics teachers in Pakistan The dynamic demands of the contemporary educational landscape, which includes a variety of digital tools and resources, require teachers to develop digital competencies. This need is particularly pertinent for mathematics teachers in developing countries like Pakistan, where there is a requirement to bridge the digital divide and equip teachers with the knowledge and skills to integrate digital resources into their teaching practices. Prior research has acknowledged the importance of integrating digital resources in education; however, there is limited research on the challenges and opportunities that high school mathematics teachers encounter when using digital resources in resource-constrained environments like Pakistan.
This study aimed to investigate the digital competencies of high school mathematics teachers in Pakistan, focusing on their knowledge, beliefs, practices, and experiences in integrating digital resources into mathematics teaching and learning. To achieve this aim, the study adapted the “Digital Competencies for Teaching Mathematics with Technology” (DCTMT) framework. Employing a mixed-methods explanatory sequential design, the study was divided into two phases for data collection. In Phase 1, quantitative data were collected through an online survey, which received a total of 306 responses. I analysed the survey data using descriptive (Mean, Mode, Median, and Standard Deviation) and inferential (intra- and inter-construct Spearman’s rho (⍴) correlation tests) statistics. To further understand and explain important quantitative results, semi-structured interviews were conducted in Phase 2 with six (Phase 1) teachers. I analysed the qualitative data using pre-identified themes and sub-themes based on the constructs of the DCTMT framework.
The results of both phases indicated that teachers held firm beliefs about various aspects of mathematics education. Teachers expressed strong beliefs about pedagogical practices and held positive beliefs about the importance of digital resources for teaching and learning mathematics. Correlations were observed between beliefs, teachers' reported ability to create videos, knowledge of dynamic graphing software (DGS) and equation editors, and participation in professional training. The findings revealed that most teachers possessed some level of digital competency. Teachers predominantly relied on videos and graphics, indicating potential bias and a gap in their professional development and training. They lacked access to (particularly at school) and possessed a weak knowledge of mathematics-specific digital resources like Dynamic Graphing Software (DGS). Other factors, such as lack of resources, inadequate formal training, and limited professional development opportunities, hindered their ability to integrate digital resources into their teaching and learning of mathematics. However, the results indicated that teachers could overcome some of these challenges through resilience and self-learning initiatives.
The study findings suggest that equipping teachers with appropriate resources and targeted professional development could enhance their digital competencies. This would consequently promote equitable and diverse use of digital resources in mathematics education. Within the confines of resource-constrained environments, these findings support for nurturing teachers' resilience and cultivating a self-learning attitude among them. Teachers who equip themselves with digital skills receive training and have the confidence to integrate digital resources to develop digital competencies, irrespective of resource constraints.
This thesis contributes to the understanding of high school mathematics teachers' digital competencies in Pakistan and indicates the opportunities and obstacles they encounter while using digital resources. This research inquiry provides empirical evidence for the modified DCTMT framework and reveals significant interconnections between the five constructs of the framework. The study reveals critical insights into the intricate relationship between beliefs, access to resources, and competencies in utilizing digital tools for mathematics education. This thesis establishes a compelling link between training, self-learning, teachers' resilience, and their digital competencies, highlighting the dynamic interplay that shapes mathematics teachers' digital competencies. This thesis offers implications for teachers’ professional development, curriculum design, and policy formulation. It emphasizes the importance of supporting teachers with the resources and knowledge to integrate digital resources and enhance mathematics education in resource-constrained contexts.

year: 2024-07-15

title: Incremental system verification and synthesis of minimally restrictive behaviours

authors: Malik, Robi

abstract: An incremental approach to system verification is proposed, for system behaviours and safety properties described by means of finite-string languages and finite-state automata. Properties are verified with respect to subsystems of the overall system, nevertheless allowing assertions to be made about the entire system satisfying such properties. The proposed approach considers satisfaction of properties, controllability, and synthesis as successive verification steps. Furthermore, it allows the incremental augmentation of the system to be verified: after each verification step, either the desired property is verified, or a counter example is obtained, which, together with heuristics, provides the basis for the augmentation of a given subsystem for the next verification step.

text: Incremental system verification and synthesis of minimally restrictive behaviours An incremental approach to system verification is proposed, for system behaviours and safety properties described by means of finite-string languages and finite-state automata. Properties are verified with respect to subsystems of the overall system, nevertheless allowing assertions to be made about the entire system satisfying such properties. The proposed approach considers satisfaction of properties, controllability, and synthesis as successive verification steps. Furthermore, it allows the incremental augmentation of the system to be verified: after each verification step, either the desired property is verified, or a counter example is obtained, which, together with heuristics, provides the basis for the augmentation of a given subsystem for the next verification step.

year: 2000

title: Ōpōtiki Mai Tawhiti

authors: Maxwell, Te Kahautu

abstract: Ōpōtiki Mai Tawhiti competed at the Mātaatua Regional Kapa Haka Competition 2014 to qualify for the Te Matatini World Championship Kapa Haka Competition 2015, Christchurch. Ōpōtiki Mai Tawhiti placed first overall, 1st mōteatea, 1st, Haka, 1st Whakawātea, 1st Female Leader, 1st Male Leader, 1st Waiata Tira, 1st Te Reo, 1st Original Composition, 1st Costume, 2nd Waiata a Ringa, 2nd, Poi, 2nd Whakaeke.

text: Ōpōtiki Mai Tawhiti Ōpōtiki Mai Tawhiti competed at the Mātaatua Regional Kapa Haka Competition 2014 to qualify for the Te Matatini World Championship Kapa Haka Competition 2015, Christchurch. Ōpōtiki Mai Tawhiti placed first overall, 1st mōteatea, 1st, Haka, 1st Whakawātea, 1st Female Leader, 1st Male Leader, 1st Waiata Tira, 1st Te Reo, 1st Original Composition, 1st Costume, 2nd Waiata a Ringa, 2nd, Poi, 2nd Whakaeke.

year: 2014-02-22