
06647415
j
2016f.00930
Caglayan, Gunhan
Mathematics teachers' visualization of complex number multiplication and the roots of unity in a dynamic geometry environment.
Comput. Sch. 33, No. 3, 187209 (2016).
2016
Taylor \& Francis, Philadelphia, PA
EN
F50
U70
complex number multiplication
dilation
dynamic geometry software
mathematics teacher education
representations
roots of unity
rotation
ME 1991f.01445
ME 1993g.00503
ME 2012a.00190
doi:10.1080/07380569.2016.1218217
Summary: This qualitative research, drawing on the theoretical frameworks by {\it R. Even} [Educ. Stud. Math. 21, No. 6, 521544 (1990; ME 1991f.01445); J. Res. Math. Educ. 24, No. 2, 94116 (1993; ME 1993g.00503)] and {\it A. Sfard} [J. Learn. Sci. 16, No. 4, 565613 (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.