\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2016f.00930}
\itemau{Caglayan, Gunhan}
\itemti{Mathematics teachers' visualization of complex number multiplication and the roots of unity in a dynamic geometry environment.}
\itemso{Comput. Sch. 33, No. 3, 187-209 (2016).}
\itemab
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.
\itemrv{~}
\itemcc{F50 U70}
\itemut{complex number multiplication; dilation; dynamic geometry software; mathematics teacher education; representations; roots of unity; rotation}
\itemli{doi:10.1080/07380569.2016.1218217}
\end