Knowledge and beliefs of pre-service secondary mathematics teachers in Sri Lanka and the impact on their instructional practices

Abstract

The mathematics education research literature emphasizes the importance of understanding mathematics teachers’ knowledge and beliefs, due to the significant role they play in mathematics teaching. This study investigates the characteristics of Sri Lankan pre-service secondary mathematics teachers’ content knowledge for teaching mathematics (CKTM) and professed beliefs, and their impact on instructional practices, taking school algebra as an example. The study explores the prospective teachers’ CKTM in relation to two cognitive and pedagogical dimensions – subject matter content knowledge (SMCK) and pedagogical content knowledge (PCK). Two aspects of their professed beliefs are also examined – beliefs about the nature of mathematics, and beliefs about teaching and learning mathematics.

The study employs a mixed-method research design that explores the independent variables CKTM and beliefs quantitatively, using two survey questionnaires; and enquires about the dependent variable, instructional practices, through a qualitative case study in which data are collected through classroom teaching observations and follow-up post-lesson interviews. The quantitative component of the study involved a cohort of third-year (final-year) pre-service secondary mathematics teachers (Sinhala medium) in Sri Lanka. The qualitative component of the study involved four selected cases, using maximal variation sampling strategy, based on differences in knowledge and beliefs identified in the quantitative study.

Quantitative analyses of the survey responses indicate that the majority of the participants demonstrated considerably higher performances in knowing and applying skills related tasks than that of reasoning skills. It also provides insights into the PCK that pre-service teachers’ hold of which the majority did not perform well on either knowledge of teaching (KOT) or knowledge of student thinking (KOS) tasks. Results of the beliefs survey show that the Sri Lankan pre-service mathematics teachers tended to hold more flexible views on the nature of mathematics and on teaching and learning mathematics.

Qualitative analysis of the audio-taped classroom teaching observation transcripts was performed, using a list of sensitizing concepts that reflected KOT and KOS aspects, and flexible and rigid beliefs aspects. Comparison of the case teachers’ instructional practices in relation to their knowledge differences and beliefs indicates the participants’ CKTM was unlikely to influence their practices directly, whereas their flexible view orientation was found to shape their instructional practices to a certain extent.

In addition, the cumulative effect of certain embedded features of the teaching and learning mathematics culture in Sri Lanka such as examination oriented culture, shortage of time to cover the required content, and classroom situations such as students’ achievement level, students’ long term learning style, and pre-service teachers’ prior learning experiences is found to exert a considerable impact on preservice teachers’ instructional practices.

The findings of this study contribute to better understanding of the factors that play a crucial role in Sri Lanka’s pre-service mathematics teachers’ instructional practices. The study also makes a theoretical contribution by proposing an integrative theoretical framework for further studies related to mathematics teaching in the field.