id: 06439681
dt: a
an: 2015d.00672
au: Boester, Timothy; Lehrer, Richard
ti: Visualizing algebraic reasoning.
so: Kaput, James J. (ed.) et al., Algebra in the early grades. London:
Routledge (ISBN 978-0-8058-5472-5/hbk; 978-0-8058-5473-2/pbk). Studies
in Mathematical Thinking and Learning Series, 211-234 (2008).
py: 2008
pu: London: Routledge
la: EN
cc: H10 G40 C30 E40
ut: algebraic reasoning; visualization; geometry; generalization; spatial
structure; research; design studies; grade 6; lower secondary;
meta-representational competence; representational competencies;
graphical representations; coordinates; modes of representation;
complicated sorting; comparing the slopes of lines; ratio; patterns in
tables; similarity; early education in algebra
ci:
li:
ab: From the text: According to {\it A. D. Aleksandrov}, {\it A. N.
Kolmogorov}, and {\it M. A. Lavrent’ev} [Mathematics, its content,
methods, and meaning. Cambridge, MA: MIT Press (1969)], “Arithmetic
and geometry are the two roots from which has grown the whole of
mathematics" (p. 24). Algebra is generally understood as having derived
from the arithmetical root. In Chapter 9, the authors highlight
algebra’s indebtedness to the geometric root of mathematics, noting
that “spatial structure serves as a potentially important springboard
to algebraic reasoning, but also that algebraic reasoning supports
coming to ‘see’ lines and other geometric elements in new lights."
Their argument is not historical but rather psychological:
“Visualization bootstraps algebraic reasoning and algebraic
generalization promotes ‘seeing’ new spatial structure".
rv: