Problem-based Learning as a learning model for secondary school mathematics preservice teachers. #PBLmathEd

Many issues co-exist for preservice teachers� learning, such as the incredible amount of mathematics in curricula, acquiring and teaching 21^{st} century skills while managing inclusive education issues, the diversity of students� abilities, and the increasing knowledge of �best-practice� pedagogical strategies. Recent literature on preservice teacher learning calls for inquiry-based education models aligned with inservice teacher professional learning community models that are classroom practice-based and begin with an identified �problem of practice�. A Problem-based Learning model authentically related to mathematics problem solving and the problem solving of teachers� daily professional practice would be beneficial for secondary school mathematics preservice teacher learning.

Problem-based learning (PBL) is a way of learning that incorporates collaboration amongst small groups of learners, each with their own expert (called tutors), focusing on relevant and realistic problems that the learners might encounter in their future professional practice. PBL is not about creating a realistic environment that replicates the learners� professional practice but instead focuses on creating an authentic environment in which learners can develop the necessary knowledge and skills to be successful in their professional practice.

Teacher cognition, which consists of teacher knowledge and beliefs, is a viable theoretical framework for unpacking and understanding teacher learning in relation to the mathematics teaching and learning context. Problem solving knowledge appears in teachers� behaviours in their daily classroom practice, and, as a thinking process in curriculum documents and exercises in textbooks. Teacher efficacy is the belief a teacher possesses concerning his/her/their capabilities to perform in a way to affect student learning outcomes, and is relevant to the classroom contextual nature of teaching through the consideration of possible instructional strategies, attending to student engagement, and performing classroom management. A PBL model for secondary mathematics preservice teacher learning is a different and valuable learning model�well articulated by teacher cognition, and connected to mathematics, problem solving, and teachers� learning through problems of practice.

Selected references:

Borg, S. (2015). *Teacher cognition and language education.* (2nd ed.). London, UK: Bloomsbury.

Dorier, J.-L., & Maass, K. (2014). Inquiry-based mathematics education. In S. Lerman (Ed.), *Encyclopedia of Mathematics Education* (pp. 300-304). Netherlands: Springer.

Hmelo-Silver, C. E. (2004). Problem-based learning: What and how do students learn? *Educational Psychology Review, 16*(3), 235-266.

Hoaglund, A., Birkenfeld, K., & Box, J. (2014). Professional learning communities: Creating a foundation for collaboration skills in pre-service teachers. *Education, 134*(4), 521-528.

OECD. (2005). *Teachers matter: Attracting, developing and retaining effective teachers*. Paris, France: Organisation for Economic Co-operation and Development.

Pyper, J. S. (2014). Pre-service mathematics teacher efficacy: Its nature and relationship to teacher concerns and orientation. *Alberta Journal of Educational Research, 60*(1), 81-97.

Savery, J. R. (2006). Overview of problem-based learning: Definitions and distinctions. *Interdisciplinary Journal of Problem-Based Learning, 1*(1), 9-20.