id: 06619297
dt: j
an: 2016e.00438
au: Kosyvas, Georgios
ti: Levels of arithmetic reasoning in solving an open-ended problem.
so: Int. J. Math. Educ. Sci. Technol. 47, No. 3, 356-372 (2016).
py: 2016
pu: Taylor \& Francis, Abingdon, Oxfordshire
la: EN
cc: D50 F30 H30
ut: arithmetic; reasoning; solving simultaneous equations with arithmetic;
problem solving; multiple solution strategies; whole-class discussion;
justification
ci:
li: doi:10.1080/0020739X.2015.1072880
ab: Summary: This paper presents the results of an experimental teaching
carried out on 12-year-old students. An open-ended task was given to
them and they had not been taught the algorithmic process leading to
the solution. The formal solution to the problem refers to a system of
two linear equations with two unknown quantities. In this mathematical
activity, students worked cooperatively. They discussed their
discoveries in groups of four and then presented their answers to the
whole class developing a rich communication. This study describes the
characteristic arguments that represent certain different forms of
reasoning that emerged during the process of justifying the solutions
of the problem. The findings of this research show that within an
environment conducive to creativity, which encourages collaboration,
exploration and sharing ideas, students can be engaged in developing
multiple mathematical strategies, posing new questions, creating
informal proofs, showing beauty and elegance and bringing out that
problem solving is a powerful way of learning mathematics.
rv: