a powerful mathematical thinking and a basic
indicator of the investigating invariants component
of geometric habits of mind. In this study, balancing
exploration and reflection appeared explicitly in
the perimeter problem. The majority of candidates
intuitively constructed random triangles for the
desired triangle and tried familiar strategies. Only
two went beyond spontaneous thinking and trials,
and they engaged in holistic thinking by returning
to the big picture and visualizing the final state—
these strategies indicate geometric habits of mind.
Similarly, the component balancing exploration
and reflection was the least used habit among the
teacher candidates in Koç and Bozkurt’s (2012)
study. In addition, in their study about primary
school teacher candidates’ problem-posing skills
on semi-structured situations, Işık and Kar (2012)
found that participants could pose very few
problems regarding the desired situation, that most
of the problems they posed could be solved through
simple calculations, and that these were related to a
limited number of different mathematical concepts