
06580971
j
2016c.00585
Bostic, Jonathan D.
Fostering justification: a case study of preservice teachers, proofrelated tasks, and manipulatives.
J. Math. Educ. Teach. Coll. 7, No. 1, 3543 (2016).
2016
Teachers College (TC), Columbia University, New York, NY
EN
E59
D39
preservice teacher education
lower secondary
proving
justifying
argumentation
reasoning
proofs
modes of representation
educational media
teaching aids
manipulative materials
research
case studies
Summary: Instruction promoting reasoning and proof should be a part of K12 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 proofrelated tasks and manipulatives for middlegrades 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 middlegrades teacher might use manipulatives to engage students in justifying mathematical statements in proofrelated 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 middlegrades classroom instruction they might enact, and identified the role of struggle while engaging in proofrelated 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 K12 students in proofrelated tasks.