Key developmental understandings in mathematics: A direction for investigating and establishing learning goals

Research output: Contribution to journalArticle

Abstract

Although mathematics educators seem to agree on the importance of teaching
mathematics for understanding, what they mean by understanding varies greatly.
In this article, I elaborate and exemplify the construct of key developmental understanding
to emphasize a particular aspect of teaching for understanding and to
offer a construct that could be used to frame the ideniification of conceptual learning
goals in mathematics. The key developmental understanding construct is based
on extant empirical and theoretical work. The construct can be used in the context
of research and curriculum development. Using a classroom example involving
fractions, I illustrate how focusing on key developmental understandings leads
to particular, potentially useful types of pedagogical thinking and directions for
inquiry.
Original languageEnglish (US)
Pages (from-to)359-371
Number of pages13
JournalMathematical Thinking and Learning
Volume8
Issue number4
StatePublished - 2006

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Mathematics
Learning
mathematics
Curriculum
learning
Teaching
Research
curriculum development
Vary
Direction compound
educator
classroom
Thinking

Keywords

  • Mathematical concept
  • Instructional goals
  • Reflective abstraction

Cite this

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abstract = "Although mathematics educators seem to agree on the importance of teachingmathematics for understanding, what they mean by understanding varies greatly.In this article, I elaborate and exemplify the construct of key developmental understandingto emphasize a particular aspect of teaching for understanding and tooffer a construct that could be used to frame the ideniification of conceptual learninggoals in mathematics. The key developmental understanding construct is basedon extant empirical and theoretical work. The construct can be used in the contextof research and curriculum development. Using a classroom example involvingfractions, I illustrate how focusing on key developmental understandings leadsto particular, potentially useful types of pedagogical thinking and directions forinquiry.",
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