The introduction of a new approach to mathematics teaching and learning in Thailand

This study aimed to address the need to make informed curriculum decisions by providing information on instructional approaches and learning outcomes in secondary school mathematics, particularly in the topic of function, that offered possibilities for the use of the graphing calculator. The study investigated the implementation of a more active, inductive approach, including the integration of the graphing calculator, with the algebraic topic of function with Thai mathematics students. The teaching approach was designed in response to the requirements of the Thai National Education Act 1999 and contrasts with the traditional transmission approach currently seen in Thai classroom. In order to move from the traditional teaching and learning strategies, learning processes under the Thai National Education Act 1999 focus on the principle that students are most important in the learning processes, and are capable of learning and self-development. The teaching and learning process should enable the students to develop themselves at their own pace and to the best of their potentiality. The study investigated students' responses to a new teaching approach, their use of the graphing calculator and their developing understanding of the function concept.

The teaching experiment included two classes of Year 10 Thai mathematics students who studied in a public school located in the north eastern part of Thailand. Twenty-four students volunteered to participate in these two classes, twelve in each. Three students from each class volunteered to take the roles of key informants. The two classes were taught, Class 2 commencing their program two weeks after Class 1. Both classes were taught by the researcher (called teacher-researcher in the report) assisted by one of the regular teachers at the school. The teacher-researcher is a Thai secondary mathematics teacher with more than twenty years experience. The influence of instruction was monitored through analysis of classroom observations, the teacher-researcher's and classroom teacher's field notes, teacher-researcher and classroom teacher discussions, students' diaries and the key informants' interviews after some teaching episodes. This enabled reflection on each teaching episode with Class 1 and some modifications to the materials for Class 2.

At the completion of the teaching program, a function concept questionnaire and function test were administered to the six key informants. The questionnaire and the test were designed to investigate students' concept definition and concept image of function, and to assess each of three aspects of the conceptual knowledge of function, including interpreting a function, modelling a functional situation, and translating between different functional representations and within the same representation. Based on a sequence of student cognitive development and the research theoretical framework (ActionProcess- Object perspective), all six key informants' responses to the questionnaire and the test were classified into four categories, namely an action, a process, a pre-object and an object conception of function. Results indicated that the six key informants were able to use action, process and object conceptions of function as required in various situations. They were mostly able to perform actions on functions whenever there were required. In some situations, they were able to link the necessary processes and properties to solve a problem, but in other situations they were not successful. Although the students had experienced all necessary processes and properties, they had not sufficient time to build the quality links that would enable them to solve problems more reliably.

The inductive nature of the teaching program was more limited than originally envisaged. The nature of material, based on the Thai mathematics syllabus, made the use of a more inductive approach with the integrated use of the graphing calculator difficult to achieve. When teaching the classes, the teacher-researcher also had difficulties in moving away from his familiar strategies. Both students and teachers needed a greater time to adapt to these changes.

The attitude questionnaire was administered with all students in order to investigate students' confidence in using the graphing calculator and their attitudes toward the collaborative use of the graphing calculator. Findings indicated positive attitudes toward integrating the graphing calculator in the teaching and learning of mathematics. They also indicated that they preferred to work using the graphing calculator on their own first, and then discuss and share results shown on its screen with each other, as well as asking for help when facing difficulties.

Data from classroom observations and the key informants' interviews after the lessons were used to determine how and why the graphing calculators were employed in the problem contexts and learning situations. The study indicated that the graphing calculator could be used by the students as a tool to promote their conceptions of function in all three views (an action, a process and an object view of function). The study classified three roles of the graphing calculator used by the students, including a conceptual action representation tool (CART), a conceptual process representation tool (CPRT) and a conceptual object representation tool (CORT). However, students in the study usually attempted to use an algebraic or arithmetic strategy to solve a problem, rather than apply the graphing calculator. The study also identified three stages of the students learning to use the graphing calculator, namely "awareness", "learning the process" and "application of the process". In the stage of the application of the process, the study also identified three roles of the students during the period of using the graphing calculators: student as receiver, an assistant and partner.

Results from the study were used to formulate a set of recommendations for Thai educational authorities aimed at assisting teachers and students to move towards meeting the requirements of the 1999 Education Act.

Please note: The data of this study was collected entirely in Thailand. All lessons and interviews were conducted in the Thai language and teaching materials were also written in the Thai language. The materials presented in the appendices are translations of the printed materials used in the study. Excerpts of dialogue from the lessons and interviews have also been translated into English. The translations are as near as possible to the original statements in Thai.