id: 06580971
dt: j
an: 2016c.00585
au: Bostic, Jonathan D.
ti: Fostering justification: a case study of preservice teachers, proof-related
tasks, and manipulatives.
so: J. Math. Educ. Teach. Coll. 7, No. 1, 35-43 (2016).
py: 2016
pu: Teachers College (TC), Columbia University, New York, NY
la: EN
cc: E59 D39
ut: preservice teacher education; lower secondary; proving; justifying;
argumentation; reasoning; proofs; modes of representation; educational
media; teaching aids; manipulative materials; research; case studies
ci:
li:
ab: Summary: Instruction promoting reasoning and proof should be a part of
K‒12 mathematics teaching. Preservice teachers (PSTs) need
mathematics content instruction that helps them construct valid
justifications for mathematical notions and develop positive
perceptions of proof. This case study describes instruction with
proof-related tasks and manipulatives for middle-grades PSTs that draws
on developmentally appropriate modes of argument representation. The
purpose of the instruction was for PSTs to explore mathematics content
through a lens of how a middle-grades teacher might use manipulatives
to engage students in justifying mathematical statements in
proof-related tasks. Results indicate that this instruction supported
PSTs to justify mathematical ideas and that PSTs characterized their
experiences positively. PSTs perceived proof in ways echoed in past
literature, saw connections between the PSTs’ instruction and future
middle-grades classroom instruction they might enact, and identified
the role of struggle while engaging in proof-related tasks. This case
study provides ideas for mathematics content instructors to develop
PSTs’ understanding of mathematics through instruction that prepares
them to engage their future K‒12 students in proof-related tasks.
rv: