Methodology

Data collection

Most research on teachers’ beliefs and conceptions is interpretive in nature and employs qualitative methods of analysis. Data can be obtained by using many techniques such as Likert-scale questionnaires, interviews, classroom observations, stimulated recall interviews, linguistic analysis of teacher talk, paragraph completion tests, responses to simulation materials such as vignettes describing hypothetical students or classroom situations, and concept generation and mapping exercises such as the Kelly Repertory Grid Technique (Fransella & Bannister, 1977). Some studies used a combination of these techniques, rather than a single technique.

The collection of data will primarily involve qualitative methods. It will also involve some quantitative methods. It is primarily on qualitative because this study will be more on descriptive than statistical data.

Interviews and classroom observations will be the primary data sources. Questionnaires will serve important additional data sources.

The first stage of the overall research will involve data collection using a specifically designed questionnaire, and distributed to 150 qualified secondary mathematics teachers who have teaching experience between 1 to 5 years throughout Brunei. The questionnaire will cover the following areas:

1. subject demographics such as gender, age, position held, nature of teacher training, length of teaching experience, classes currently taught, class size, level and subject taught over three years.
2. Teachers’ memories of mathematics lessons.
3. Teachers’ current and past attitude to mathematics
4. Teachers’ beliefs about mathematics and mathematics pedagogy.
5. Teachers’ view of effective teaching including how effective teaching should be

carried out.

6. Their most commonly used teaching approaches (frequency of use of a variety

teaching strategies)

7. Factors inhibiting them from carrying out effective teaching

Teachers will be chosen from the top six performing government schools in mathematics PMB and from the bottom six underperforming government schools. Elite schools or colleges like Maktab Sains Paduka Seri Baginda Sultan (MSPSBS) will be not be included in this survey as in elite school, the teaching method used does not play a crucial role in promoting students’ understanding. The selection of these schools are done deliberately, it is to see if there is a correlation between practice and achievement. The criteria for the selection of teachers will include the following elements:

§ have teaching experience between one to five years

§ qualified teachers (meaning they have attained at least a diploma in education).

§ teaching at lower secondary level.

In this study, I described for those teachers who have teaching experience between one to five years as beginning teachers. Beginning teachers are deliberately chosen because these teachers reveal about their beliefs as they try hard to in their teaching practice. And their beliefs about Mathematics and Mathematics pedagogy are likely to be challenged during the first few years of teaching because their pedagogical ideals do not always fit to the real world of teachings. In Brunei, based on the inspection made by the inspectorate department, these are the group of teachers who are observed to be proactive and who are very susceptible to changes, who are willing to upgrade themselves in order to perform better.

The study will be focusing on qualified teachers because it is important that teachers have acquired teaching skills through a proper teacher education program. The reason to choose teachers teaching lower because this is the time when most introductions of topics (teaching of concepts) is taught.

The responses from the questionnaire will be analysed. Since it is anticipated that there is a tendency that some of the teachers will not willing to participate Therefore, for a start, about ten teachers will be identified and approached from the data analysis. And it is expected that this number will go down. Data from observations carried out by the Inspectorate department during a period from 2001 to 2004 will also be used to support the identification of teachers.

Preferably, the selection will be further narrowed to three teachers who practice the explain practice approach and three teachers who employ a constructivist approach.

Qualitatively, the study will involve a series of audio-taped interviews and at least three observations per teacher. All interviews will be carried out on one to one basis.

First interview will be unstructured interview. This interview is done to gather more in depth information about teachers’ beliefs (mathematics and mathematics pedagogy).

Observations are conducted to obtain teaching practice data. It will be at least three observations per teacher and will be done on regular basis. These observations will be discussed in subsequent interviews. These interviews will be semi structured. It is to discuss about the teachers teaching episodes of the observations such as teaching method employed, objectives and goals of the lesson and so on. These interviews will be conducted as soon as possible after the observations. So that the teachers still have fresh memories about their teachings.

Another interview will be focusing on relationships between beliefs and practice. This includes factors and the role of interventions on their practices.

A take home questionnaire will be given to the teachers to seek their opinions about this study.

Data Analysis

Data analysis will be organized using components of a beliefs and practice model. Data will be classified into one of three areas:

(a) beliefs (subdivided into beliefs about mathematics, beliefs about

mathematics teaching and mathematics learning).

(b) actual teaching practice

(c) factors that influence on relationships between beliefs and practice

To make consistent comparisons, each teacher’s beliefs about the nature of mathematics, the mathematics teaching, and the mathematics learning will be categorized using teaching model presented by Kuhs and Ball (1986) namely:

(a) Learner-focused: mathematics teaching that focuses on the learner’s personal construction of mathematical knowledge;

(b) Content-focused with an emphasis on conceptual understanding: mathematics teaching that is driven by the content itself but emphasizes conceptual understanding;

(c) Content-focused with an emphasis on performance: mathematics teaching that emphasizes student performance and mastery of mathematical rules and procedures; and

(d) Classroom-focused: mathematics teaching based on knowledge about effective classroom.

Another model which might be used to categorize these teachers’ beliefs is to use either a transmission (traditional teacher-centered) model in which teacher delivers knowledge and skills, or child-centered in which children are actively involved in constructing their mathematical knowledge.