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Professional development for teachers of mathematical modelling in Singapore
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Type
Thesis
Author
Tan, Liang Soon
Supervisor
Ang, Keng Cheng
Abstract
The purpose of this study is to conceptualize, implement, and evaluate a school-based professional development (SBPD) programme for teachers in mathematical modelling. The proposed SBPD programme is new in the context of local schools in Singapore. It aims to help novice teachers develop competencies to make appropriate decisions in the teaching of mathematical modelling. For the purpose of evaluating the SBPD programme, this study addresses the following research questions:
1. What aspects of a mathematics teacher’s competencies in teaching mathematical modelling are developed through his/her participation in the SBPD programme?
2. What are the reasons for the development (or the lack of development) of these aspects of a teacher’s competencies to teach mathematical modelling in relation to the SBPD programme?
A wide selection of relevant literature has been reviewed to establish the theoretical framework within which the SBPD programme is conceptualized. The SBPD programme is characterized by three dimensions of learning deemed essential for effective professional development of teachers – the content, process and context dimensions. The content dimension is focussed on developing the teacher’s knowledge and skills in the teaching of modelling. The process dimension is characterized by the transformative learning cycles for teachers to elicit, enact and reorganize their orientations in a mathematical modelling classroom. The context dimension takes into account the school contextual factors and adjusts the SBPD programme implementation accordingly.
A multiple-case study approach was adopted. The SBPD programme was implemented in three secondary schools in Singapore. Data collected across the classroom and SBPD programme levels include lesson observations, formal interviews, teachers’ commentaries, and analysis of relevant lesson artefacts of teachers’ practice in the teaching of modelling. An analytic tool adapted from Schoenfeld’s framework for goal-based decision-making (Schoenfeld, 2010) was used to examine participating teachers’ orientations, resources, goals and teaching decisions.
The findings of this study indicate that the SBPD programme positively influences teachers’ knowledge and resources, goals, and orientations in planning, designing, and enacting modelling learning experiences. Teachers were able to plan developmentally appropriate modelling lessons and design learning opportunities for students to reason mathematically their choices of modelling ideas and steps. Teachers had moved from compartmentalized teaching of the modelling stages to facilitating students’ learning experiences in the modelling process.
This study also reveals that the development of the teacher’s competencies in the teaching of mathematical modelling had resulted from an interaction between the content and process dimensions of the SBPD programme. The teacher’s independent modelling learning experiences, his knowledge of the modelling task solution space, and his use of Ang’s framework for teaching modelling (Ang, 2015) are necessary resources that were activated in the teaching of modelling. The teacher’s experience in the transformative learning cycles has helped him develop and reorganize his orientations, resources and goals in the teaching of modelling.
In addition, teachers who participated in this study had begun to value students’ mathematical reasoning during the modelling process and became more sensitised to their learning difficulties. They had internalized the use of Ang’s framework for teaching modelling, developed more coherent lesson images and better questioning techniques. They also became oriented towards the learning goal of getting students to formulate the mathematical problem from the real world situation. The outcomes that were achieved suggest that the conceptualization of the SBPD programme may be capable of wide and flexible applications.
1. What aspects of a mathematics teacher’s competencies in teaching mathematical modelling are developed through his/her participation in the SBPD programme?
2. What are the reasons for the development (or the lack of development) of these aspects of a teacher’s competencies to teach mathematical modelling in relation to the SBPD programme?
A wide selection of relevant literature has been reviewed to establish the theoretical framework within which the SBPD programme is conceptualized. The SBPD programme is characterized by three dimensions of learning deemed essential for effective professional development of teachers – the content, process and context dimensions. The content dimension is focussed on developing the teacher’s knowledge and skills in the teaching of modelling. The process dimension is characterized by the transformative learning cycles for teachers to elicit, enact and reorganize their orientations in a mathematical modelling classroom. The context dimension takes into account the school contextual factors and adjusts the SBPD programme implementation accordingly.
A multiple-case study approach was adopted. The SBPD programme was implemented in three secondary schools in Singapore. Data collected across the classroom and SBPD programme levels include lesson observations, formal interviews, teachers’ commentaries, and analysis of relevant lesson artefacts of teachers’ practice in the teaching of modelling. An analytic tool adapted from Schoenfeld’s framework for goal-based decision-making (Schoenfeld, 2010) was used to examine participating teachers’ orientations, resources, goals and teaching decisions.
The findings of this study indicate that the SBPD programme positively influences teachers’ knowledge and resources, goals, and orientations in planning, designing, and enacting modelling learning experiences. Teachers were able to plan developmentally appropriate modelling lessons and design learning opportunities for students to reason mathematically their choices of modelling ideas and steps. Teachers had moved from compartmentalized teaching of the modelling stages to facilitating students’ learning experiences in the modelling process.
This study also reveals that the development of the teacher’s competencies in the teaching of mathematical modelling had resulted from an interaction between the content and process dimensions of the SBPD programme. The teacher’s independent modelling learning experiences, his knowledge of the modelling task solution space, and his use of Ang’s framework for teaching modelling (Ang, 2015) are necessary resources that were activated in the teaching of modelling. The teacher’s experience in the transformative learning cycles has helped him develop and reorganize his orientations, resources and goals in the teaching of modelling.
In addition, teachers who participated in this study had begun to value students’ mathematical reasoning during the modelling process and became more sensitised to their learning difficulties. They had internalized the use of Ang’s framework for teaching modelling, developed more coherent lesson images and better questioning techniques. They also became oriented towards the learning goal of getting students to formulate the mathematical problem from the real world situation. The outcomes that were achieved suggest that the conceptualization of the SBPD programme may be capable of wide and flexible applications.
Date Issued
2016
Call Number
QA11.2 Tan
Date Submitted
2016