
06528356
j
2016a.00451
Miyazaki, Mikio
Fujita, Taro
Jones, Keith
Flowchart proofs with open problems as scaffolds for learning about geometrical proofs.
ZDM, Math. Educ. 47, No. 7, 12111224 (2015).
2015
Springer, Berlin/Heidelberg
EN
E53
G43
D43
scaffolding
flowchart proof
open problem
geometry
doi:10.1007/s1185801507125
Summary: Recent research on the scaffolding of instruction has widened the use of the term to include forms of support for learners provided by, amongst other things, artefacts and computerbased learning environments. This paper tackles the important and underresearched issue of how mathematics lessons in junior high schools can be designed to scaffold students' initial understanding of geometrical proofs. In order to scaffold the process of understanding the structure of introductory proofs, we show how flowchart proofs with multiple solutions in `open problem' situations are a useful form of scaffold. We do this by identifying the `scaffolding functions' of flowchart proofs with open problems through the analysis of classroombased data from a class of Grade 8 students (aged 1314 years old) and quantitative data from three classes. We find that using flowchart proofs with open problems support students' development of a structural understanding of proofs by giving them a range of opportunities to connect proof assumptions with conclusions. The implication is that such scaffolds are useful to enrich students' understanding of introductory mathematical proofs.