id: 06270968
dt: j
an: 2014b.00557
au: Stupel, Moshe
ti: A special application of absolute value techniques in authentic problem
solving.
so: Int. J. Math. Educ. Sci. Technol. 44, No. 4, 587-595 (2013).
py: 2013
pu: Taylor \& Francis, Abingdon, Oxfordshire
la: EN
cc: H30 I20 U70
ut: absolute value definition; absolute value techniques; authentic problems;
dynamic geometry software
ci:
li: doi:10.1080/0020739X.2012.729685
ab: Summary: There are at least five different equivalent definitions of the
absolute value concept. In instances where the task is an equation or
inequality with only one or two absolute value expressions, it is a
worthy educational experience for learners to solve the task using each
one of the definitions. On the other hand, if more than two absolute
value expressions are involved, the definition that is most helpful is
the one involving solving by intervals and evaluating critical points.
In point of fact, application of this technique is one reason that the
topic of absolute value is important in mathematics in general and in
mathematics teaching in particular. We present here an authentic
practical problem that is solved using absolute values and the
‘intervals’ method, after which the solution is generalized with
surprising results. This authentic problem also lends itself to
investigation using educational technological tools such as GeoGebra
dynamic geometry software: mathematics teachers can allow their
students to initially cope with the problem by working in an inductive
environment in which they conduct virtual experiments until a solid
conjecture has been reached, after which they should prove the
conjecture deductively, using classic theoretical mathematical tools.
rv: