id: 06647415
dt: j
an: 2016f.00930
au: Caglayan, Gunhan
ti: Mathematics teachers’ visualization of complex number multiplication and
the roots of unity in a dynamic geometry environment.
so: Comput. Sch. 33, No. 3, 187-209 (2016).
py: 2016
pu: Taylor \& Francis, Philadelphia, PA
la: EN
cc: F50 U70
ut: complex number multiplication; dilation; dynamic geometry software;
mathematics teacher education; representations; roots of unity;
rotation
ci: ME 1991f.01445; ME 1993g.00503; ME 2012a.00190
li: doi:10.1080/07380569.2016.1218217
ab: Summary: This qualitative research, drawing on the theoretical frameworks
by {\it R. Even} [Educ. Stud. Math. 21, No. 6, 521‒544 (1990; ME
1991f.01445); J. Res. Math. Educ. 24, No. 2, 94‒116 (1993; ME
1993g.00503)] and {\it A. Sfard} [J. Learn. Sci. 16, No. 4, 565‒613
(2007; ME 2012a.00190)], investigated five high school mathematics
teachers’ geometric interpretations of complex number multiplication
along with the roots of unity. The main finding was that mathematics
teachers constructed the modulus, the argument, and the conjugate of a
complex number along with the roots of unity through a series of
discursive transformations without specifying the common terminology.
While teachers exhibited a variety of visualizations, each founded in a
diversity of approaches on the dynamic geometry software, writing
mathematical expressions and equations proved challenging. Construction
of roots of unity required teachers’ mathematical proficiency ‒ in
particular, strategic competence in simultaneously coordinating various
interpretations of complex numbers, and representational fluency in
analytic geometrical and transformational reasoning.
rv: