GUIDE TO
James Calleja
©2015
THE PROFESSIONAL DEVELOPMENT DESIGN TASK-‐DELINEATED
Solving mathematical tasks provides a first-‐hand experience for developing a learners’ perspective
INQUIRY-‐ORIENTED
Providing opportunities for teachers to explore and learn through inquiry
PRACTICE-‐BASED
Connecting activities to content and pedagogy situated and applicable to teachers’ classrooms
COLLABORATIVE
Working together to develop shared practice within a community of practice
This PD programme design aims to provide teachers with opportunities to: Understand inquiry learning while working on mathematical tasks; Experience models of inquiry teaching through video-based discussions; Become critical inquirers while designing, using and reflecting on their IBL practices; Present classroom experiences, share insights and collaboratively construct learning of inquiry teaching; Develop their identities as teachers of mathematics. The four PD workshops are designed to focus on four research-based IBL principles. The first session considers tasks for mathematical inquiry, the second deals with the role of open questioning, the third session addresses learning through collaboration, while the final session investigates student agency and responsibility. Workshops follow practically a consistent pattern of activities. In the introductory activity, teachers work collaboratively to solve a mathematical task. A video from a local classroom is then introduced. The video demonstrates a teacher enacting the IBL principles in a local classroom. In a third activity teachers are provided with individual reading and analysis of narrative contrasting lesson cases. To guide the reading and analysis of these cases, teachers are provided with focus questions to draw their attention to key aspects. A fourth activity includes the analysis of a published lesson video (available on YouTube) focusing on one of the four IBL principles. The ensuing whole-group discussion provides additional opportunities for teachers to further investigate teaching approaches, clarifying concepts, or problematizing issues related to teaching mathematics through inquiry. Teaching & Learning Mathematics through Inquiry | CPD Leader’s Guide |
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ENGAGING TEACHERS IN LEARNING ABOUT INQUIRY Personal experience and research-informed knowledge about adult learners are carefully considered and integrated in the design of the activities supporting and promoting ‘Teaching Mathematics through Inquiry’. As adult learners, teachers … Want to know what is expected of them Value learning related to classroom prac8ce Need to see links with their problems of teaching Prefer to be consulted, heard and valued Learn best in an unhurried and non-‐threatening environment Like to integrate what they learn with what they already know Learn with and from other teachers
At the beginning of the first session, the following three main aims of the professional development sessions are communicated and discussed: 1. Exploring what inquiry-based learning is and how it may be enacted by teachers in their classroom; 2. Discussing, analysing and evaluating inquiry teaching from the teachers’ perspective of classroom experiences; 3. Creating a learning community where teachers learn with each other and from one another. Each workshop then starts by delineating objectives specific to that particular session. During the sessions, participants are also expected to assume active roles in setting goals, determining activities, and deciding about the process and the outcome of their professional learning.
Teaching & Learning Mathematics through Inquiry | CPD Leader’s Guide |
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GUIDELINES FOR THE PROFESSIONAL DEVELOPMENT LEADER PD leaders need to have expertise in the field of professional development, teacher learning and inquiry-based learning. Thus, they need to be aware that: Learners bring particular practice-based knowledge, experiences, skills and beliefs about mathematics, teaching and learning; Knowledge about teaching is constructed uniquely and individually through interaction with a variety of tools, resources and contexts; Knowledge
about
teaching
may
be
developed
and
improved
by
participating in collaborative activities with others working in a range of contexts and facing different/similar challenges; Learning about teaching mathematics through inquiry ideally involves an active, inquiry and reflective process; The person leading the PD should guide discussions, link arguments to the content of PD (for example: the use of questioning techniques or collaborative work), and focus on the organizational framework of the program. It is also critical to invest time and effort to cultivate and establish a community of learners who trust each other. During the lesson video analysis, for instance, this trust-building component may be important to establish a working relationship where teachers feel free to critically analyse incidents and provide their own personal understanding and meanings – even if these may not be aligned with an inquiry-based learning perspective. This approach has been shown to be important for fostering successful teacher learning. The PD leader must engage learners to develop communication, to listen carefully to each other, to raise questions and concerns, and to constructively criticise thinking and ideas presented. Hence, it is vital to support learners to feel at ease enough for making their practice public. The PD leader is also responsible for creating a climate in which teachers feel confident and safe to present, debate and evaluate ideas. It is his/her role to cultivate such an atmosphere where learning about teaching mathematics through inquiry is both supportive and non-threatening.
Teaching & Learning Mathematics through Inquiry | CPD Leader’s Guide |
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FACILITIES FOR LEADING THE SESSIONS The ‘Teaching Mathematics through Inquiry’ activities require participants to discuss and work collaboratively. Thus, professional development sessions would be more successful in a room: Having an arrangement where participants are facing each other is more likely to support small-group discussions
Equipped with an interactive board, a projector and a sound system, as CPD leaders would need to make use of power-point presentations and show videos
Equipped with a white board for whole-class presentations and discussions
Teaching & Learning Mathematics through Inquiry | CPD Leader’s Guide |
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