Conceptual Foundation of PLATINUM project

The conceptual foundation of PLATINUM project is inquiry-based approach to mathematics teaching and learning.  In this project we explore both didactic and pedagogic processes and practices and blend methods and resources to achieve development in teaching and learning.
We utilise a developmental research approach in which partners ‘walk the walk’ of inquiry-based practice and share findings with others.

The main purpose of inquiry is to engage participants deeply with concepts that they should learn or develop – in contrast with procedural learning or learning by rote. Where mathematics is concerned, inquiry approaches in problems and tasks encourage students to get involved with the mathematics, asking and trying to answer questions, and exploring/investigating processes and concepts. For their teachers/lecturers the challenge is to offer suitable problems/tasks through which their students can come to understand the mathematics being presented to them in lectures. This challenge brings lecturers themselves into an inquiry process where their teaching of mathematics is concerned – conceiving suitable approaches to their students’ engagement and bringing these into their practice with students.

In the PLATINUM project, we seek to document, analyse and report outcomes from the two layers of inquiry outlined above. Thus, teacher-researchers within the project seek, not only, to engage with their students in inquiry in practice, but also, to provide an account of their activity, the outcomes, issues and tensions arising from it, that they can share with other practitioners beyond the project.
Thus, our inquiry model constitutes three layers as follows (Scheme).

Scheme:  Model of three layers of inquiry

Inquiry in

1. engaging with mathematics in inquiry-based teaching-learning situations with students;

2. exploring teaching processes, the didactics and pedagogies involved in student inquiry, and their use in teaching-learning situations to achieve desired student outcomes;

3. the entire developmental process in which participants reflect on practices in the other two layers, and gather, analyse, and feed back data to inform practice and develop knowledge in practice.

These layers are deeply inter-related. Teachers/lecturers, inquiring into their teaching, focus centrally on their students’ learning through inquiry. Teacher-researchers, reflecting and analyzing data from the other two layers, feed back what is learned to the practices they are in the process of developing. The whole constitutes an inter-related developmental process represented by the figure above.

Important to the inquiry process in its three layers, is the concept of ‘community’. An inquiry community in PLATINUM consists of teachers and/or students working together in inquiry ways to achieve learning and development. Central to our model is the belief that engagement with others, into concepts we seek to learn/develop, enriches engagement and provides opportunity for individuals to broaden their own thinking and to clarify their own conceptions. This provides opportunity for colleagues to look critically at the practices in which they engage, and to introduce and explore changes to practice. Such a critical approach within a supportive environment enables participants to address problems and issues with teaching and learning which might otherwise be beyond individual resolution.

In the project, we expect our analysis of data to allow us to report on the outcomes of our activity with evidence to support what we claim regarding our developments in teaching-learning through inquiry.

References

• Jaworski B. (2006) Theory and Practice in Mathematics Teaching Development: critical inquiry as a mode of learning in teaching. Journal of Mathematics Teacher Education. Special Issue: Relations between theory and practice in mathematics teacher Education. Vol. 9 number 2, pp. 187-211. Link
• Jaworski, B. (2008). Building and sustaining inquiry communities in mathematics teaching development. Teachers and didacticians in collaboration. In K. Krainer (Volume Ed.) & T. Wood (Series Ed.) International handbook of mathematics teacher education: Vol. 3. Participants in Mathematics Teacher Education: Individuals, teams, communities and networks (pp.309-330). Rotterdam, The Netherlands: Sense Publishers. Link
• Jaworski, B. (2014). Unifying Complexity in Mathematics Teaching-Learning Development: A Theory-Practice Dialectic. In Y. Li et al. (eds.), Transforming Mathematics Instruction: Multiple Approaches and Practices, Advances in Mathematics Education, 439-458. New York: Springer. Link
• Goodchild, S. (2008). A quest for ‘good’ research: the mathematics teacher educator as practitioner researcher in a community of inquiry. In Jaworski, B., & Wood,T. (eds.) (2008). International Handbook of Mathematics Teacher Education: vol. 4 The Mathematics Teacher Educator as a Developing Professional, 201-220. Rotterdam, The Netherlands: Sense Publishers. Link