Establishing Conceptual Bases for the Measurement of Volume

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Profiling Teachers:
Constructivist- and Behaviorist-Oriented Mathematics

Boris Handal
The University of Sydney
 
borishandal@optusnet.com.au

AbstractIntroductionMethodologyResults and Discussion
ConclusionReferences

The Study 

The purpose of the study was to determine whether teachers’ beliefs and practices could be characterized in terms of behaviorist and constructivist dimensions. The focus of the study was the Standard course, which is a syllabus with a mandatory thematic component (Board of Studies New South Wales, 1996; Handal, 2000; 2002). The Standard course represents the lowest mathematical level of the 1996 Years 9 and 10 Mathematics Syllabus and Standard students are generally considered as pupils who have not been successful in mathematics in previous stages. The other two levels are the Intermediate and the Advanced courses. The educational principles of the 1996 Years 9 and 10 Syllabus are based on the constructivist ideas underlying the National Statement on Mathematics for Australian Schools  (Australian Education Council, 1991). The thematic approach is an instructional strategy closely associated to constructivist practices because it makes use of instructional strategies such as problem solving, cooperative learning, exploratory work, hands-on activity, and application of mathematics to real-life situations (Freeman & Sokoloff, 1995; Handal, 1991; Seely, 1995).

The study was conducted in three phases. In the first phase, a questionnaire was devised in order to identify secondary mathematics teachers’ beliefs and practices in the teaching of mathematics thematically. The process of designing a questionnaire was adapted from the Concerns-Based Approach Model outlined by Hall and Hord (1987). The model recommends a detailed description of the main components of an innovation and of its acceptable variations. Consequently, and in order to secure content validity, a literature review was conducted on the teaching and learning of mathematics thematically. In addition, a document content analysis of the Standard course curriculum documents was carried out. Some of the questionnaire items were drawn or adapted from previous surveys and in some cases the items were adapted to the thematic focus of this study (Anderson, 1997; Andrews & Hatch, 1999; Benbow, 1993; Frank, 1990; Kifer & Robitaille, 1992; McGinnis, Shama, Graeber, & Watanabe, 1997; Peterson, Fennema, Carpenter, & Loef, 1989; Zambo, 1994). The process of developing the questionnaire also involved consultation with four senior university lecturers in mathematics education from two Faculties of Education in Australia . In addition, interviews were conducted with three policymakers involved in the development of the Standard course and two Standard course textbook writers. The purpose of these interviews was to capture the main ideas underpinning the structure and philosophy of the course. After the design of the first draft, the questionnaire was tried out with five teachers of the Standard course. These teachers were asked to go through the questionnaire and to comment on its design and content. This process was necessary in order to ensure that the questionnaire items remained close to the spirit of the Standard course in terms of teaching and learning thematically.

In the second phase, a set of six questionnaires was posted to 69 schools representing the total number of high schools delivering the Standard course in six school districts of Metropolitan Sydney. The socioeconomic disadvantage effect was taken into account by selecting an almost equal number of schools considered within the Disadvantaged Schools Program (DSP) (Graetz, 1995). A prepaid self-addressed envelope accompanied the questionnaires along with a letter addressed to the school principal assuring anonymity and confidentiality. The letter also asked the school principal to hand the questionnaires to the teachers of the Standard course in the school. All mathematics faculties were contacted by phone in the following weeks to ensure the completion and return of the questionnaires. Table 1 summarizes the school sample in the six school districts.

Table 1

Disadvantaged Schools Program (DSP) Schools and non-DSP High Schools in the NSW Public Education System by school districts included in the sample

Adapted from Disadvantaged Schools Program NSW (1999).

Note: Selective high schools are not included in this summary.

In the third phase, a series of in-depth interviews were carried out in order to further explore instructional, curricular, and organizational issues in the teaching and learning of themes in the Standard mathematics course. Fifteen teachers indicated on their questionnaires their willingness to participate in the follow-up interview component of the study. Ten teachers were selected on the basis of obtaining as much as possible, an equal representation of the five independent variables, namely, gender, teaching socioeconomic status, faculty position, years of experience, and academic qualifications. An additional criterion was that the teachers simultaneously held high constructivist-oriented beliefs and high behaviorist-oriented practices, in order to explore factors inhibiting a smooth conversion of beliefs into practice. The sample represented teachers from the six school districts with the exception of the Port Jackson district, due to the fact that no teachers from that area offered to participate in the interviews.

AbstractIntroductionMethodologyResults and Discussion
ConclusionReferences