Madduma Bandara Ekanayake | National Institute of Education, SriLanka (original) (raw)

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Papers by Madduma Bandara Ekanayake

The major purpose of this study was to address the instructional needs of proof-type geometry pro... more The major purpose of this study was to address the instructional needs of proof-type geometry problem solving. It was designed to address two research questions: (Q 1). What are the predictive indicators of successful proof-type geometry problem solving? (Q 2). Based on needs with an emphasis on formative evaluation, what is one design solution to support students solving proof-type problems in geometry? The overall study focused on a learning need assessment in the first phase of the study (Study 1) and a development process to translate instructional needs identified into a supportive instructional environment for proof-type geometry problem solving in the second phase (Study 2). The review of literature revealed that proof-type geometry problems have different learning requirements compared to other mathematical problems types. The solution process for proof-type geometry problems demands the adoption of a non-algorithmic approach in which students could activate problem-solving strategies that are domain specific. These strategies include heuristics such as using auxiliaries (parallel lines, bisectors and perpendiculars), alternative proving methods (indirect proof, reductio ad absurdum, method of contradiction). Equally important are the role of domain-general strategies during the solution of proof-type geometry problems such as working backward and logical inferencing. The literature review suggested that geometry content knowledge, general processes, and mathematical reasoning could be potential predictive indicators of successful proof-type geometry problem solving. However, the relative importance of these variables during the construction of geometry proofs had not been subjected to an empirical evaluation. Study 1 takes up the above issue by determining the relative importance of these variables in proof type geometry problem solving. Data were collected from 166 Sri Lankan students on three independent variables: Geometry Content Knowledge (GCK), General Problem-Solving processes (GPS) and Mathematical Reasoning Skills (MRS); and a dependent variable Proof-Type Geometry problem-solving (PTG). The relationship among these variables was examined through a multiple linear regression analysis procedure. This analysis showed that geometry content knowledge, general problem-solving processes, and mathematical reasoning are predictive indicators of First of all my heartfelt thanks are due to supervisors: Dr Mohan Chinnappan and Dr Christine Brown. You were not tired of your novice student. Not only your valuable scholarly guidance, but also your kind moral support was useful to overcome various academic and personal difficulties. I remember your companionship, encouragement and inspiration in my effort to make it a success. I gratefully remember my wife Shanthi and her broad understanding. You had to be a father to our sons Nipuna and Anuna. During my long overseas period, you would have spent a hard time without my assistance. Your patience really helped me to continue this study. Dear sons, I should thank you also as you did not cry for you rights. I worship my father and mother. You were not only parents, but were also teachers in my early grades at school. When you were alive, you wanted to empower me to become helpful rather than powerful to others. Dear Chandana and Anula, your contribution is extraordinary. You sacrificed your time to make time for me. In addition, both of you forced me to complete this. Your kids Lakshitha and Madusha made me fresh. My sincere thanks to Mr. Peter Keble and Mr. G.B. Wanninayake for their valuable contribution in completing this dissertation. My thanks are also due to the principals, teachers, and participant students of the schools.

International Journal of Science and Mathematics Education, 2011

Within the domain of geometry, proof and proof development continues to be a problematic area for... more Within the domain of geometry, proof and proof development continues to be a problematic area for students. Battista (2007) suggested that the investigation of knowledge components that students bring to understanding and constructing geometry proofs could provide important insights into the above issue. This issue also features prominently in the deliberations of the 2009 International Commission on Mathematics Instruction Study on the learning and teaching of proofs in mathematics, in general, and geometry, in particular. In the study reported here, we consider knowledge use by a cohort of 166 Sri Lankan students during the construction of geometry proofs. Three knowledge components were hypothesised to influence the students' attempts at proof development: geometry content knowledge, general problem-solving skills and geometry reasoning skills. Regression analyses supported our conjecture that all 3 knowledge components played important functions in developing proofs. We suggest that whilst students have to acquire a robust body of geometric content knowledge, the activation and the utilisation of this knowledge during the construction of proof need to be guided by general problem-solving and reasoning skills.

Education is shaping with the advances of new information and communication technologies (ICT). M... more Education is shaping with the advances of new information and communication technologies (ICT). Most countries all over the world have accepted the need of incorporating ICT to promote the quality of learning. Sri Lanka also invests a large amount of funds to provide ICT education and ICT based education. Each of 200,000 teachers are to be equipped with a personal computer by 2009. The purpose of this is to make all teachers use computers in their everyday academic work i.e,. in instructional process and classroom management. The benefit comes to all 2,000,000 students when the plan becomes a reality.

The major purpose of this study was to address the instructional needs of proof-type geometry pro... more The major purpose of this study was to address the instructional needs of proof-type geometry problem solving. It was designed to address two research questions: (Q 1). What are the predictive indicators of successful proof-type geometry problem solving? (Q 2). Based on needs with an emphasis on formative evaluation, what is one design solution to support students solving proof-type problems in geometry? The overall study focused on a learning need assessment in the first phase of the study (Study 1) and a development process to translate instructional needs identified into a supportive instructional environment for proof-type geometry problem solving in the second phase (Study 2). The review of literature revealed that proof-type geometry problems have different learning requirements compared to other mathematical problems types. The solution process for proof-type geometry problems demands the adoption of a non-algorithmic approach in which students could activate problem-solving strategies that are domain specific. These strategies include heuristics such as using auxiliaries (parallel lines, bisectors and perpendiculars), alternative proving methods (indirect proof, reductio ad absurdum, method of contradiction). Equally important are the role of domain-general strategies during the solution of proof-type geometry problems such as working backward and logical inferencing. The literature review suggested that geometry content knowledge, general processes, and mathematical reasoning could be potential predictive indicators of successful proof-type geometry problem solving. However, the relative importance of these variables during the construction of geometry proofs had not been subjected to an empirical evaluation. Study 1 takes up the above issue by determining the relative importance of these variables in proof type geometry problem solving. Data were collected from 166 Sri Lankan students on three independent variables: Geometry Content Knowledge (GCK), General Problem-Solving processes (GPS) and Mathematical Reasoning Skills (MRS); and a dependent variable Proof-Type Geometry problem-solving (PTG). The relationship among these variables was examined through a multiple linear regression analysis procedure. This analysis showed that geometry content knowledge, general problem-solving processes, and mathematical reasoning are predictive indicators of First of all my heartfelt thanks are due to supervisors: Dr Mohan Chinnappan and Dr Christine Brown. You were not tired of your novice student. Not only your valuable scholarly guidance, but also your kind moral support was useful to overcome various academic and personal difficulties. I remember your companionship, encouragement and inspiration in my effort to make it a success. I gratefully remember my wife Shanthi and her broad understanding. You had to be a father to our sons Nipuna and Anuna. During my long overseas period, you would have spent a hard time without my assistance. Your patience really helped me to continue this study. Dear sons, I should thank you also as you did not cry for you rights. I worship my father and mother. You were not only parents, but were also teachers in my early grades at school. When you were alive, you wanted to empower me to become helpful rather than powerful to others. Dear Chandana and Anula, your contribution is extraordinary. You sacrificed your time to make time for me. In addition, both of you forced me to complete this. Your kids Lakshitha and Madusha made me fresh. My sincere thanks to Mr. Peter Keble and Mr. G.B. Wanninayake for their valuable contribution in completing this dissertation. My thanks are also due to the principals, teachers, and participant students of the schools.

International Conference on Advances in ICT for Emerging Regions (ICTer2012), 2012

This paper discusses the results of a tutor mentor development program that utilized a community ... more This paper discusses the results of a tutor mentor development program that utilized a community building model to train online tutors and mentors in higher education institutions and professional organizations in Sri Lanka. Based on WisCom; an instructional design model for developing online wisdom communities, this tutor mentor development program which utilized a blended format of face-to-face and online activities in MOODLE, attempted to build a learning community between trainees, both academics and professionals who represented diverse disciplines and organizations. A regression model examined predictors of learner satisfaction, using four independent variables: Community Building, Interaction, Course Design, and Leamer Support. Interaction emerged as a strong predictor of Learner Satisfaction explaining 50.2% of the variance in Leamer Satisfaction. This finding shows the importance of designing interactive learning activities to support learning online, and contradicts the general belief that Sri Lankan participants would be less likely to interact online because they come from a traditional education system that encourages passivity and reception of ideas from a more learned teacher. Qualitative analysis showed evidence of several types of learning online as a result of collaborative group interaction, as well as issues that contributed to non-participation. Factors that motivated participants to stay engaged in learning could be classified into three categories: (1) general enjoyment, interest and motivation; (2) collaborative learning and community building; and (3) knowledge building. These results suggest that the online learning design based on Wi sCorn led to learner satisfaction and supported interaction and collaborative learning in the Sri Lankan socio-cultural context.

The major purpose of this study was to address the instructional needs of proof-type geometry pro... more The major purpose of this study was to address the instructional needs of proof-type geometry problem solving. It was designed to address two research questions: (Q 1). What are the predictive indicators of successful proof-type geometry problem solving? (Q 2). Based on needs with an emphasis on formative evaluation, what is one design solution to support students solving proof-type problems in geometry? The overall study focused on a learning need assessment in the first phase of the study (Study 1) and a development process to translate instructional needs identified into a supportive instructional environment for proof-type geometry problem solving in the second phase (Study 2). The review of literature revealed that proof-type geometry problems have different learning requirements compared to other mathematical problems types. The solution process for proof-type geometry problems demands the adoption of a non-algorithmic approach in which students could activate problem-solving strategies that are domain specific. These strategies include heuristics such as using auxiliaries (parallel lines, bisectors and perpendiculars), alternative proving methods (indirect proof, reductio ad absurdum, method of contradiction). Equally important are the role of domain-general strategies during the solution of proof-type geometry problems such as working backward and logical inferencing. The literature review suggested that geometry content knowledge, general processes, and mathematical reasoning could be potential predictive indicators of successful proof-type geometry problem solving. However, the relative importance of these variables during the construction of geometry proofs had not been subjected to an empirical evaluation. Study 1 takes up the above issue by determining the relative importance of these variables in proof type geometry problem solving. Data were collected from 166 Sri Lankan students on three independent variables: Geometry Content Knowledge (GCK), General Problem-Solving processes (GPS) and Mathematical Reasoning Skills (MRS); and a dependent variable Proof-Type Geometry problem-solving (PTG). The relationship among these variables was examined through a multiple linear regression analysis procedure. This analysis showed that geometry content knowledge, general problem-solving processes, and mathematical reasoning are predictive indicators of First of all my heartfelt thanks are due to supervisors: Dr Mohan Chinnappan and Dr Christine Brown. You were not tired of your novice student. Not only your valuable scholarly guidance, but also your kind moral support was useful to overcome various academic and personal difficulties. I remember your companionship, encouragement and inspiration in my effort to make it a success. I gratefully remember my wife Shanthi and her broad understanding. You had to be a father to our sons Nipuna and Anuna. During my long overseas period, you would have spent a hard time without my assistance. Your patience really helped me to continue this study. Dear sons, I should thank you also as you did not cry for you rights. I worship my father and mother. You were not only parents, but were also teachers in my early grades at school. When you were alive, you wanted to empower me to become helpful rather than powerful to others. Dear Chandana and Anula, your contribution is extraordinary. You sacrificed your time to make time for me. In addition, both of you forced me to complete this. Your kids Lakshitha and Madusha made me fresh. My sincere thanks to Mr. Peter Keble and Mr. G.B. Wanninayake for their valuable contribution in completing this dissertation. My thanks are also due to the principals, teachers, and participant students of the schools.

International Journal of Science and Mathematics Education, 2011

Within the domain of geometry, proof and proof development continues to be a problematic area for... more Within the domain of geometry, proof and proof development continues to be a problematic area for students. Battista (2007) suggested that the investigation of knowledge components that students bring to understanding and constructing geometry proofs could provide important insights into the above issue. This issue also features prominently in the deliberations of the 2009 International Commission on Mathematics Instruction Study on the learning and teaching of proofs in mathematics, in general, and geometry, in particular. In the study reported here, we consider knowledge use by a cohort of 166 Sri Lankan students during the construction of geometry proofs. Three knowledge components were hypothesised to influence the students' attempts at proof development: geometry content knowledge, general problem-solving skills and geometry reasoning skills. Regression analyses supported our conjecture that all 3 knowledge components played important functions in developing proofs. We suggest that whilst students have to acquire a robust body of geometric content knowledge, the activation and the utilisation of this knowledge during the construction of proof need to be guided by general problem-solving and reasoning skills.

Education is shaping with the advances of new information and communication technologies (ICT). M... more Education is shaping with the advances of new information and communication technologies (ICT). Most countries all over the world have accepted the need of incorporating ICT to promote the quality of learning. Sri Lanka also invests a large amount of funds to provide ICT education and ICT based education. Each of 200,000 teachers are to be equipped with a personal computer by 2009. The purpose of this is to make all teachers use computers in their everyday academic work i.e,. in instructional process and classroom management. The benefit comes to all 2,000,000 students when the plan becomes a reality.

The major purpose of this study was to address the instructional needs of proof-type geometry pro... more The major purpose of this study was to address the instructional needs of proof-type geometry problem solving. It was designed to address two research questions: (Q 1). What are the predictive indicators of successful proof-type geometry problem solving? (Q 2). Based on needs with an emphasis on formative evaluation, what is one design solution to support students solving proof-type problems in geometry? The overall study focused on a learning need assessment in the first phase of the study (Study 1) and a development process to translate instructional needs identified into a supportive instructional environment for proof-type geometry problem solving in the second phase (Study 2). The review of literature revealed that proof-type geometry problems have different learning requirements compared to other mathematical problems types. The solution process for proof-type geometry problems demands the adoption of a non-algorithmic approach in which students could activate problem-solving strategies that are domain specific. These strategies include heuristics such as using auxiliaries (parallel lines, bisectors and perpendiculars), alternative proving methods (indirect proof, reductio ad absurdum, method of contradiction). Equally important are the role of domain-general strategies during the solution of proof-type geometry problems such as working backward and logical inferencing. The literature review suggested that geometry content knowledge, general processes, and mathematical reasoning could be potential predictive indicators of successful proof-type geometry problem solving. However, the relative importance of these variables during the construction of geometry proofs had not been subjected to an empirical evaluation. Study 1 takes up the above issue by determining the relative importance of these variables in proof type geometry problem solving. Data were collected from 166 Sri Lankan students on three independent variables: Geometry Content Knowledge (GCK), General Problem-Solving processes (GPS) and Mathematical Reasoning Skills (MRS); and a dependent variable Proof-Type Geometry problem-solving (PTG). The relationship among these variables was examined through a multiple linear regression analysis procedure. This analysis showed that geometry content knowledge, general problem-solving processes, and mathematical reasoning are predictive indicators of First of all my heartfelt thanks are due to supervisors: Dr Mohan Chinnappan and Dr Christine Brown. You were not tired of your novice student. Not only your valuable scholarly guidance, but also your kind moral support was useful to overcome various academic and personal difficulties. I remember your companionship, encouragement and inspiration in my effort to make it a success. I gratefully remember my wife Shanthi and her broad understanding. You had to be a father to our sons Nipuna and Anuna. During my long overseas period, you would have spent a hard time without my assistance. Your patience really helped me to continue this study. Dear sons, I should thank you also as you did not cry for you rights. I worship my father and mother. You were not only parents, but were also teachers in my early grades at school. When you were alive, you wanted to empower me to become helpful rather than powerful to others. Dear Chandana and Anula, your contribution is extraordinary. You sacrificed your time to make time for me. In addition, both of you forced me to complete this. Your kids Lakshitha and Madusha made me fresh. My sincere thanks to Mr. Peter Keble and Mr. G.B. Wanninayake for their valuable contribution in completing this dissertation. My thanks are also due to the principals, teachers, and participant students of the schools.

International Conference on Advances in ICT for Emerging Regions (ICTer2012), 2012

This paper discusses the results of a tutor mentor development program that utilized a community ... more This paper discusses the results of a tutor mentor development program that utilized a community building model to train online tutors and mentors in higher education institutions and professional organizations in Sri Lanka. Based on WisCom; an instructional design model for developing online wisdom communities, this tutor mentor development program which utilized a blended format of face-to-face and online activities in MOODLE, attempted to build a learning community between trainees, both academics and professionals who represented diverse disciplines and organizations. A regression model examined predictors of learner satisfaction, using four independent variables: Community Building, Interaction, Course Design, and Leamer Support. Interaction emerged as a strong predictor of Learner Satisfaction explaining 50.2% of the variance in Leamer Satisfaction. This finding shows the importance of designing interactive learning activities to support learning online, and contradicts the general belief that Sri Lankan participants would be less likely to interact online because they come from a traditional education system that encourages passivity and reception of ideas from a more learned teacher. Qualitative analysis showed evidence of several types of learning online as a result of collaborative group interaction, as well as issues that contributed to non-participation. Factors that motivated participants to stay engaged in learning could be classified into three categories: (1) general enjoyment, interest and motivation; (2) collaborative learning and community building; and (3) knowledge building. These results suggest that the online learning design based on Wi sCorn led to learner satisfaction and supported interaction and collaborative learning in the Sri Lankan socio-cultural context.