id: 06439878
dt: a
an: 2015c.00514
au: Miyazaki, Mikio; Fujita, Taro; Jones, Keith
ti: Functions of open flow-chart proving in introductory lessons of formal
proving.
so: Liljedahl, Peter (ed.) et al., Proceedings of the 38th conference of the
International Group for the Psychology of Mathematics Education
“Mathematics education at the edge", PME 38 held jointly with the
36th conference of PME-NA, Vancouver, Canada, July 15‒20, 2014, Vol.
4. [s. l.]: International Group for the Psychology of Mathematics
Education (ISBN 978-0-86491-360-9/set; 978-0-86491-364-7/v.4). 225-232
(2014).
py: 2014
pu: [s. l.]: International Group for the Psychology of Mathematics Education
la: EN
cc: E53
ut: proof; understanding of proofs; flow-chart proofs; open problems; proving
ci:
li:
ab: Summary: Amongst important and under-researched questions are how
introductory lessons can be designed for teaching initial proofs to
junior high school students, and how such lessons enrich students’
understanding of proofs. With a view to improving the learning
situation in the classroom, in this paper we report on the various
functions of introductory flow-chart proofs that use ‘open
problems’ that have multiple possible solutions. Through an analysis
of a teaching experiment in Grade 8, and by using a model of levels of
understanding of proof structure, we identify the functions as
enhancing the transition towards a relational understanding of the
structure of formal proof, and encouraging forms of forward/backward
thinking interactively that accompany such a relational understanding
of the structure of proofs in mathematics.
rv: