id: 06469958
dt: j
an: 2015e.00552
au: Karakok, Gulden; Soto-Johnson, Hortensia; Anderson Dyben, Stephenie
ti: Secondary teachersâ€™ conception of various forms of complex numbers.
so: J. Math. Teach. Educ. 18, No. 4, 327-351 (2015).
py: 2015
pu: Springer Netherlands, Dordrecht
la: EN
cc: F59 C39
ut: complex numbers; mathematical content knowledge; operational conception;
process/object duality; representations; structural conception
ci:
li: doi:10.1007/s10857-014-9288-1
ab: Summary: This study explores in-service high school mathematics teachersâ€™
conception of various forms of complex numbers and ways in which they
transition between different representations of these forms. One 90-min
interview was conducted with three high school mathematics teachers
after they completed three professional development sessions, each 4 h,
on complex numbers. Results indicate that, in general, these teachers
did not necessarily have a dual conception of complex numbers. However,
they demonstrated varying conceptions with different forms of complex
numbers. Teachers worked at an operational level with the exponential
form of complex numbers, but there was no evidence to indicate that
they had a structural conception of this form. On the other hand, two
teachers were very comfortable with the Cartesian form and exhibited a
process/object duality by translating between different representations
of this form. These results indicate that high school teachers need
more opportunities to help them develop a dual conception of each form
(multiple duals), which in turn can result in developing a dual
conception of complex numbers. An interesting phenomenon that we found
was that teachers who taught courses such as geometry and international
baccalaureate were able to draw from their teaching experiences as they
attempted the interview tasks. This particular observation may suggest
that teachersâ€™ teaching assignments coupled with appropriate
professional development activities could facilitate their
understanding of these concepts.
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