id: 05179753
dt: j
an: 2007b.00083
au: Martineza, Mara; Brizuela, Bárbara M.
ti: A third grader’s way of thinking about linear function tables.
so: J. Math. Behav. 25, No. 4, 285-298 (2006).
py: 2006
pu: Elsevier, New York, NY
la: EN
cc: C32 H22 I22
ut: primary education; grade 3; functions; understanding; propaedeutics;
concept formation; learning; elementary algebra; abstract reasoning;
generalization; variables
ci:
li: doi:10.1016/j.jmathb.2006.11.003
ab: Summary: This paper is inscribed within the research effort to produce
evidence regarding primary school students’ learning of algebra.
Given the results obtained so far in the research community, we are
convinced that young elementary school students can successfully learn
algebra. Moreover, children this young can make use of different
representational systems, including function tables, algebraic
notation, and graphs in the Cartesian coordinate grid. In our research,
we introduce algebra from a functional perspective. A functional
perspective moves away from the mere symbolic manipulation of equations
and focuses on relationships between variables. In investigating the
processes of teaching and learning algebra at this age, we are
interested in identifying meaningful teaching situations. Within each
type of teaching situation, we focus on what kind of knowledge students
produce, what are the main obstacles they find in their learning, as
well as the intermediate states of knowledge between what they know and
the target knowledge for the teaching situation. In this paper, we
present a case study focusing on the approach adopted by a third grade
student, Marisa, when she was producing the formula for a linear
function while she was working with the information of a problem
displayed in a function table containing pairs of inputs-outputs. We
will frame the analysis and discussion on Marisa’s approach in terms
of the concept of theorem-in action (Vergnaud, 1982) and we will
contrast it with the scalar and functional approaches introduced by
Vergnaud (1988) in his Theory of Multiplicative Fields. The approach
adopted by Marisa turns out to have both scalar and functional aspects
to it, providing us with new ways of thinking of children’s potential
responses to functions.
rv: