id: 05834557
dt: a
an: 2011a.00887
au: Amit, Miriam; Jan, Irma
ti: Model eliciting environments as “nurseries" for modeling probabilistic
situations.
so: Lesh, Richard (ed.) et al., Modeling students’ mathematical modeling
competencies. ICTMA 13. Proceedings of the 13th international
conference on the teaching of mathematical modelling and applications,
July 22‒26, 2007. London: Springer (ISBN 978-1-4419-0560-4/hbk;
978-1-4419-0561-1/ebook). 155-166 (2010).
py: 2010
pu: London: Springer
la: EN
cc: M13 C33
ut: mathematical modeling; lower secondary; probability; realistic mathematics;
model eliciting activities
ci:
li: doi:10.1007/978-1-4419-0561-1_13
ab: Summary: This study presents an extension of model-eliciting problems into
model eliciting environments which are designed to optimize the chances
that significant modeling activities will occur. Our experiment,
conducted in such an environment, resulted in the modeling of a
probabilistic situation. Students in grades 6‒9 participated in
competitive games involving rolling dice. These tasks dealt with the
concept of fairness, and the desire to win connected students naturally
to familiar “real life" situations. During a “meta-argumentation"
process, results were generalized, and a model was formed. In this
case, it was a model describing a “fair game" created by the
differential compensation of different events to “even the odds." The
strength of this model can be seen in its ability to first reject
preexisting knowledge which is partial or incorrect, and second to
verify the knowledge that survives the updating and refining process.
Thus, a two-directional process is created ‒ the knowledge
development cycles lead to a model, and the model helps to
retroactively examine the knowledge in previous stages of development.
rv: