id: 06022049
dt: j
an: 2012b.00821
au: Izsák, Andrew; Çaǧlayan, G\”unhan; Olive, John
ti: Meta-representation in an Algebra I classroom.
so: J. Learn. Sci. 18, No. 4, 549-587 (2009).
py: 2009
pu: Lawrence Erlbaum Ass., Mahwah, NJ
la: EN
cc: H33 F93 E43
ut: word problems (mathematics); equations (mathematics); elementary algebra;
mathematics instruction; grade 8; secondary school mathematics;
teaching methods; mathematical logic; problem solving; evaluation
methods; criteria; barriers; meta-representational competence; graphs;
middle school students; research; case studies; lower secondary;
meta-representational knowledge; notation
ci:
li:
ab: Summary: We describe how one Algebra I teacher and her 8th-grade students
used meta-representational knowledge when generating and evaluating
equations to solve word problems. Analyzing data from a sequence of
four lessons, we found that the teacher and her students used criteria
for evaluating equations, in addition to other types of knowledge
(e.g., different interpretations of the equal sign) previously reported
in the literature. Moreover, the teacher and her students had trouble
understanding one another’s proposed algebraic models of problem
situations due to differences in the criteria that each applied, and
this impeded learning. These findings (a) extend an accumulating body
of evidence for the role meta-representation plays in mathematics and
science learning and (b) add a new dimension to researchers’ growing
understanding of what teachers must know in order to teach algebra and
other complex mathematics and science topics effectively.
rv: