Teaching for Metacognition Project: Construction of Knowledge by Mathematics Teachers Working and Learning Collaboratively in Multitier Communities of Practice

Abstract

Teaching for metacognition project affirms a gradual shift in the centre of gravity away from the University-based, “supply side”, “offline” forms of knowledge production conducted by university scholars for teachers towards an emergent school-based, demand-side, online, in situ forms of knowledge production conducted by teachers with support from fellow teachers, lead and senior teachers, and other experts such as university scholars and curriculum specialists. The project facilitates the participation of mathematics teachers in two-tier communities of practice. In this chapter, we describe the design of the project and the learning of two teams of teachers from two schools participating in the project. It is apparent from the findings that the teachers worked and learned collaboratively whilst participating in a first-tier and a second-tier community of practice. Their participation in the communities of practice enabled them to develop a deeper understanding of metacognition and also teaching for metacognition.

Appendices

Appendix A

Appendix B

Teacher noticing—Round 2 You may use the following prompts to guide you in viewing the videorecord for the four lenses. The prompts are adopted from McDuffie et al. (2014)
Teaching lens • How does the teacher elicit students’ thinking and respond? – What opportunities does the teacher create for diverse learners to communicate their mathematical thinking—show what they know? – How does the teacher implement the task in a way that maintains or changes the cognitive demand? – What resources and knowledge does the teacher use/draw upon to support students’ math understanding?	Learning Lens • What specific math understandings and/or confusions are indicated in students’ work, talk, and/or behaviour? – How do students communicate what their understandings and sense making of others’ thinking? – In what ways does student engagement reflect conceptual and/or procedural learning? – What resources or knowledge do students draw upon to understand and solve the math task?
Task lens • What is the nature of the task/s used in the lesson? – What makes this a good and/or problematic task? How could it be improved? What is/are the central math idea/s in this task? – How does the task make thinking visible? – What resources or knowledge does this task activate and/or connect to?	Power and participation lens • Who participates? • Does the classroom culture value and encourage most students to speak, only a few, or only the teacher? • Where does the majority of the math “work” take place in the classroom? – Who holds authority for knowing mathematics? Do some students hold more status than others? – What evidence indicates that differences in approaches and perspectives are/are not respected and valued?

Appendix C

Thinking about thinking: metacognition
Metacognitive knowledge– Reflecting on What we know • Awareness of knowledge • Awareness of thinking • Awareness of thinking strategies Write down examples of each for mathematics lessons	Metacognitive regulation– Directing our learning • Planning approaches to tasks • Monitoring activities during learning • Checking outcomes Write down examples of each for mathematics lessons
A Culture of Metacognition in the Classroom What conditions support a metacognitive classroom environment?	Strategies for learning • Predicting outcomes/evaluating work • Questioning by the teacher/self-assessing • Self-questioning/selecting strategies • Using directed or selected thinking • Using discourse/critiquing/revising Write down examples of each for mathematics lessons