International Teacher Education Conference 2014 1

International Teacher Education Conference 2014
group replied to the instruction “Test whether the model you have elicited is correct or not by using real data.” as
such:
Operations carried out by Group 4 during the model validation process
As in the case of groups 3 and 6, group 4 elicited a linear model by using the data of 2009 and 2010 and tried
to validate the model by considering the year 2011. The analysis of the video records of this process shows that
there were such conversations among students in the group:
G4-A: Sooo...It’s 3766.
….G4-B is checking the real data….
G4-B: But it should be 3835????
G4-A: So it is wrong.
G4-C: Professor. But our model is wrong. What is going to happen now?
As seen here, the pre-service teachers in this group think their model is wrong since it does not yield the real
result. These students have the misconception that the model that does not yield the exact result is wrong.
CONCLUSIONS
In terms of the importance of validation for the model eliciting process, it is crucial for pre-service math
teachers, who will raise students that have modeling competences, to have this competence. But as a result, it
was determined that pre-service math teachers have “ model can be validated by data which elicited the model”,
“it is enough to validate a model with a single data", “model which does not yield the exact result is wrong“
misconceptions. In this context, when these misconceptions are considered, discussions are made at the end of
validation processes, it can be attempted to make students capable of validation is “determining the degree to
which a model is an accurate representation of the real world from the perspective of the intended uses of the
model (AIAA, 1998)”
Also, competencies to validate the solution is include sub-competencies as following; competency• to
critically check and reflect on found solutions; • to review some parts of the model or again go through the
modelling process if solutions do not fit the situation; • to reflect on other ways of solving the problem or if
solutions can be developed differently; • to generally question the model (Blum & Kaiser 1997, p.9). In this
context, designing learning environments to equip pre-service teachers with sub-competence expected to arise in
the validation process can be recommended.
In addition, this study focuses on the validation process, which is a part of the modelling process. Studies on
processes that arise during the modelling process such as simplifying, mathematizing, working with
mathematics, interpreting can be carried out. Considering outcome this studies, effective teacher training
courses need to be developed which are connected to teachers’ needs and add to their knowledge as well as
support the necessary competencies and understandings.
REFERENCES
AIAA, (1998). Guide for the Verification and Validation of Computational Fluid Dynamics Simulations, G-077-
1998.
Berry, J. & Houston, K. (1995). Mathematical modeling. London: Edward Arnold.
Blomhøj, M. & Jensen T.H. (2006). What’s all the fuss about competencies? Experiences with using a
competence perspective on mathematics education to develop the teaching of mathematical modelling. In W.
Blum, P.L. Galbraith and M. Niss: Modelling and Applications in Mathematics Education. New York: Springer,
2(2), 45-56.
Blum, W. & Leiß, D. (2007). How do students and teachers deal with modelling problems? In C. Haines et al.
(Eds), Mathematical Modelling. Education, Engineering and Economics. Chichester: Horwood. 222-231.
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