The purpose of this study was to design a local theory explaining the relationship between metacognitive language and networks as constructs of a local instructional theory in the context of a fourth-year intermediate phase mathematics education methodology module. The local instructional theory was designed to facilitate an adapted lesson study through a problem-based learning instructional philosophy. A problem-based learning task was then designed outlining the education needs and resources of a South African primary school, characteristic of schools in a rural area. In particular the task describes a fictitious teacher’s concern for teaching a Grade 6 mathematics class the concept of place value. Two groups of students, who volunteered to participate in this research, collaboratively designed and presented research lessons across two educational design-based research cycles for two rural schools in North West, as a form of service learning. In implementing the local instructional theory phases, participants were required to follow the lesson study approach by investigating, planning, developing, presenting, reflecting, refining and re-presenting the research lesson and its resources. These design sessions were videorecorded, transcribed and then coded in Atlas.ti through interpretivistic and hermeneutic analysis. The coded data were then imported into NodeXL to illustrate embedded networks. Not only social network data but also metacognitive network data were visualised in terms of metacognitive networks. The results show that across the local instructional theory phases, constructs of metacognition, metacognitive language and networking emerged on a social (stratum 1), interpersonal (stratum 2) and social-metacognitive (stratum 3) level. Collectively, these strata form the architecture of the theory of metacognitive locale that explains the relationship between the constructs. The findings suggest that when students express their metacognitive processes through a metacognitive language (e.g. I am thinking or feeling), their interpersonal metacognitive networks develop into shared metacognitive experiences which foster their metacognitive locale, a dimension of their metacognitive language and networking. / PhD (Mathematics Education), North-West University, Potchefstroom Campus, 2015

The purpose of this study was to design a local theory explaining the relationship between metacognitive language and networks as constructs of a local instructional theory in the context of a fourth-year intermediate phase mathematics education methodology module. The local instructional theory was designed to facilitate an adapted lesson study through a problem-based learning instructional philosophy. A problem-based learning task was then designed outlining the education needs and resources of a South African primary school, characteristic of schools in a rural area. In particular the task describes a fictitious teacher’s concern for teaching a Grade 6 mathematics class the concept of place value. Two groups of students, who volunteered to participate in this research, collaboratively designed and presented research lessons across two educational design-based research cycles for two rural schools in North West, as a form of service learning. In implementing the local instructional theory phases, participants were required to follow the lesson study approach by investigating, planning, developing, presenting, reflecting, refining and re-presenting the research lesson and its resources. These design sessions were videorecorded, transcribed and then coded in Atlas.ti through interpretivistic and hermeneutic analysis. The coded data were then imported into NodeXL to illustrate embedded networks. Not only social network data but also metacognitive network data were visualised in terms of metacognitive networks. The results show that across the local instructional theory phases, constructs of metacognition, metacognitive language and networking emerged on a social (stratum 1), interpersonal (stratum 2) and social-metacognitive (stratum 3) level. Collectively, these strata form the architecture of the theory of metacognitive locale that explains the relationship between the constructs. The findings suggest that when students express their metacognitive processes through a metacognitive language (e.g. I am thinking or feeling), their interpersonal metacognitive networks develop into shared metacognitive experiences which foster their metacognitive locale, a dimension of their metacognitive language and networking. / PhD (Mathematics Education), North-West University, Potchefstroom Campus, 2015