caa a22 4500 60618788X CHVBK 20210128100842.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s10857-014-9288-1 doi (NATIONALLICENCE)springer-10.1007/s10857-014-9288-1 Secondary teachers' conception of various forms of complex numbers [Elektronische Daten] [Gulden Karakok, Hortensia Soto-Johnson, Stephenie Dyben] This study explores in-service high school mathematics teachers' 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 4h, 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 teachers' teaching assignments coupled with appropriate professional development activities could facilitate their understanding of these concepts. Springer Science+Business Media Dordrecht, 2014 Complex numbers nationallicence Mathematical content knowledge nationallicence Operational conception nationallicence Process/object duality nationallicence Representations nationallicence Structural conception nationallicence Karakok Gulden University of Northern Colorado, Greeley, CO, USA aut Soto-Johnson Hortensia University of Northern Colorado, Greeley, CO, USA aut Dyben Stephenie University of Northern Colorado, Greeley, CO, USA aut Journal of Mathematics Teacher Education Springer Netherlands 18/4(2015-08-01), 327-351 1386-4416 18:4<327 2015 18 10857 https://doi.org/10.1007/s10857-014-9288-1 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10857-014-9288-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Karakok Gulden University of Northern Colorado, Greeley, CO, USA aut NATIONALLICENCE 700 1- Soto-Johnson Hortensia University of Northern Colorado, Greeley, CO, USA aut NATIONALLICENCE 700 1- Dyben Stephenie University of Northern Colorado, Greeley, CO, USA aut NATIONALLICENCE 773 0- Journal of Mathematics Teacher Education Springer Netherlands 18/4(2015-08-01), 327-351 1386-4416 18:4<327 2015 18 10857