Dialogic learning: experiences in a mathematics club

Abstract

The reformed Hong Kong mathematics curriculum for the 21st century consists of three components, namely generic skills, values and attitudes and, lastly, traditional cognitive development. The first two are newly emphasized and expanded. Theoretically, these components correspond closely with communication, socioculture and constructivism respectively, which are the central concepts of dialogic learning (DL). In DL, students are autonomously engaged in egalitarian dialogue, in which they share, reflect and form a learning community. Through DL, a student is expected to develop into an all-rounded and life-long learner. Contrary to the reform, dialogue is still deficient in mathematics classrooms. The role of this study is to present examples of students’ experiences in DL, found in the mathematics club of a secondary girls’ school.

This study aims to explore and investigate: (1) the existence of DL in the club, (2) what the members learnt and (3) how they did it. This is an ethnographic research, which emphasizes first hand understanding, grounded theories and thorough intricacies. Therefore, I observed the students’ activities as a participant, interviewed them, and then described, analyzed and interpreted my findings accordingly.

Based on my synthesis of relevant literature and the insight I gained from decades of teaching and otherwise interacting with students, I constructed a pentahedral framework to help investigate DL in a more comprehensive and intensive way. It involves the development of various generic skills and the cultivation of values and attitudes, which are usually unrecognized in examination syllabuses and the old curriculum. It consists of five facets, concerning cognitive knowledge, sharing and negotiation, learning skills, metacognition and values and attitudes.

And here are the findings. All significant elements of DL from literature have been identified to exist in the club. As for what the students learnt, they recalled fruitful experiences in all five facets of the DL pentahedron. These findings were then combined with the learning histories of three subjects to yield four representative learning patterns, namely those of a ‘cognitive developer’, a ‘communicative daily life explorer’, a ‘eureka torchbearer’ and a ‘frustrated sharer-explorer’.

These 4 learning patterns were further combined with (i) the purposes for mathematics study from pure examination results to ‘liberation’ and (ii) the understanding of mathematics learning from pure cognitive knowledge to inclusion of generic skills and values and attitude, to form a conceptual model of learning styles. The styles of the ‘eureka torchbearer’ and the ‘communicative daily life explorer’ were found to be exemplars of the ideals of people who favour the most liberal implementation of the curriculum reform. The ‘frustrated sharer-explorer’ was stuck with the style favoured by conservatives who are against hasty reforms. The ‘cognitive developer’ was somewhere in between.

These findings may contribute to the framework of policy debate on mathematics education. In the school and classroom level, they may help teachers overcome learning disaffection and other difficulties, in both theory and practice. Organizers of extracurricular activities may also be inspired by the students’ rich experiences of dialogic learning.