id: 06426602
dt: j
an: 2015c.00498
au: Davis, Jon D.
ti: Reasoning and proving within Ireland’s reform-oriented national syllabi.
so: Math. Enthus. 11, No. 3, 665-706 (2014).
py: 2014
pu: Information Age Publishing (IAP), Charlotte, NC; University of Montana,
Department of Mathematical Sciences, Missoula, MT
la: EN
cc: E50 D30
ut: didactics of mathematics; foundations of mathematics; proving; standards;
curriculum development; syllabus; goals of mathematics education;
educational research; lower secondary; upper secondary; reasoning;
justifying; pattern identification; conjecture formulation; argument
construction; proofs; reform of mathematics education; innovation;
textbooks; proof purposes; explanation; verification; falsification;
generation; learning outcomes
ci:
li: http://www.math.umt.edu/tmme/vol11no3/Davis_11.pdf
ab: Summary: As educational systems around the world attempt to reform their
mathematics programs to increase students’ opportunities to engage in
processes central to the practice of mathematics such as proof, it is
important to understand how this mathematical act is portrayed in
national curriculum documents that drive that change. This study
examined the presence of reasoning-and-proving (RP) in Ireland’s
national reform-oriented secondary syllabi for junior cycle (ages
12‒15) and senior cycle (ages 15‒18) students. The analyses reveal
that there were no differences among direct and indirect RP learning
outcomes within each syllabus, but statistically significant
differences did exist across syllabi in these categories. Students were
provided with statistically different opportunities to engage in
pattern identification, conjecture formulation, and argument
construction in both syllabi. There were significantly fewer
opportunities to engage in conjecture formulation for junior cycle
students and significantly more opportunities to construct arguments
for senior cycle students. There were no instances of proof as
falsification across both syllabi, but students were given similar
opportunities to experience proof as explanation, verification, and
generation of new knowledge. Across both syllabi there were
statistically significantly more RP learning outcomes that were
divorced from content than those that were connected to content. The
results as well as the implications of these results for the design of
national curriculum documents are discussed.
rv: