id: 02330088
dt: j
an: 1999f.03797
au: Slavit, David
ti: The role of operation sense in transitions from arithmetic to algebraic
thought.
so: Educ. Stud. Math. 37, No. 3, 251-274 (1998-99).
py: 1998
pu: Springer Netherlands, Dordrecht
la: EN
cc: C32
ut:
ci:
li: doi:10.1023/A:1003602322232
ab: As attention to the development of algebraic understandings at early grade
levels increases, theory and empirical support for these efforts are
needed. This paper outlines a theoretical perspective for studying
student understandings of mathematical operations, with a particular
focus on addition. The notion of operation sense is defined using a
perspective that incorporates the construction of mental objects. In
the context of addition, it is argued that operation sense can be used
to describe student development of additive concepts as well as
transitions into algebraic ways of thinking. The report of a case study
on the development of a young boy is then provided. The investigation
attempts to instantiate the framework in regard to student development
of an understanding of addition. Evidence was found that his attainment
of aspects of operation sense supported transitions into algebraic ways
of thinking, including a finite group setting and use of addition on
unknown and arbitrary quantities. Limitations of the framework are
discussed. (Abstract)
rv: