Selecting and sequencing mathematics tasks: seeking mathematical knowledge for teaching
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Date
2013
Authors
Galant, Jaamia
Journal Title
Journal ISSN
Volume Title
Publisher
Faculty of Education, University of the Free State
Abstract
In this article, I present an initial analysis of an empirical study that was undertaken
in an attempt to elicit what subject-matter knowledge, pedagogic content knowledge
and curriculum knowledge teachers bring to bear on decisions for teaching. The
analysis is based on interview data with 46 Grade 3 teachers, who were presented
with two mathematical tasks taken from the 2010 NDBE Grade 2 and Grade 3
Numeracy Workbooks. Teachers were required to justify the selection and sequencing
of the two mathematical tasks for teaching multiplication. In so doing, they provide
some indication of what they know or do not know about the mathematical concepts
in the tasks; about the connections between mathematical concepts; about the
representations of those concepts, and about how learners learn those concepts.
Teachers’ responses varied from an articulation of the pedagogic and mathematical
intentions of the tasks, to the use and consequences of pictorial representations in
the tasks and how learners would respond to the tasks. The variation in responses
reflected different criteria that teachers used to justify the selection and sequencing
of the tasks. The analysis raises critical questions regarding the interplay between
teachers’ subject-matter knowledge, their pedagogic content knowledge and
curricular knowledge, which they bring to bear on pedagogic decisions. The analysis
raises further critical questions concerning the pedagogic and mathematical
explicitness of tasks in the NDBE Numeracy Workbooks. The analysis suggests that
careful consideration must be given to the construction of mathematical tasks
in Grade 3, and probably the Foundation Phase, to ensure that the mathematical
purpose of tasks is explicit, and that ‘contextual noise’ is not introduced that distracts
from the pedagogic and mathematical intent of the tasks.
Description
Keywords
Subject-matter knowledge, Pedagogic content knowledge, Curricular knowledge, Mathematical tasks, Numeracy workbooks
Citation
Galant, J. (2013). Selecting and sequencing mathematics tasks: seeking mathematical knowledge for teaching. Perspectives in Education: Primary mathematics: addressing the crisis, 31(3), 34-48.