| Summary: | 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
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