id: 06134940
dt: j
an: 2013a.00424
au: Ding, Meixia; Heaton, Ruth; Hartman, David
ti: Teaching middle level students to generalize: from implicit to explicit.
so: Investig. Math. Learn. 5, No. 2, 14-43 (2012).
py: 2012
pu: Research Council of Mathematics Learning (RCML), Memphis, TN
la: EN
cc: D50 C70 B50 A20 F30
ut: generalization; students’ abilities; problem situations; problem
    structures; patterns; supporting students’ understanding; problem
    solving; teacher difficulties; pedagogical content knowledge
ci: 
li: 
ab: Summary: This study took a broad view of generalization, exploring how
    classroom instruction within opportunities of implicit generalization
    may be related to students’ abilities to generalize. From an
    integrated perspective of generalization and problem solving, we
    investigated twelve lessons of two middle level teachers based on three
    pattern-based problems. We found teachers’ limited awareness and
    knowledge of problem situations, especially problem structures, were
    obstacles hindering their ability to support students’ understanding
    of implicit generalization. Teachers tended to focus on particular
    “results" for individual cases rather than the “process" of
    obtaining those results, resulting in missed opportunities to develop
    students’ sense of general patterns. Without attention to implicit
    generalization, explicit generalization rarely took place in a
    meaningful way during problem solving.
rv: