A prospective secondary mathematics teachers's development of the meaning of the cartesian form of complex numbers

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dc.contributorGraduate Program in Secondary School Science and Mathematics Education.
dc.contributor.advisorKaragöz Akar, Gülseren.
dc.contributor.authorSaraç, Merve.
dc.date.accessioned2023-03-16T11:30:43Z
dc.date.available2023-03-16T11:30:43Z
dc.date.issued2016.
dc.description.abstractIn thisstudy,Iarticulatehowaprospectivesecondarymathematicsteacher reconstructs complexnumbersuponthesetofrealnumbersinthecontextofthe solution setsofquadraticequations.Previousresearchhasindicatedthatonceasked the meaningof x and y in theCartesianformofacomplexnumberwhichisformally de ned as x + iy where x and y are realnumbers,bothstudentsandteacherswere able tostatethat x and y are realnumbers,yetconsideredthemseparatelyrather than beingcomponentsofasingleentity.Thus,thequestionarisesastowhat x and y refer toalgebraicallyandgeometrically;why x and y havetoberealnumbersand what itmeanstobeanelementofthesetofcomplexnumbers.Thisstudyexplicates a prospectivesecondarymathematicsteacher'sanswerstothesequestionsthroughthe articulation oftheparticipant'squantitativereasoningbyconsideringSfard's(1991) theory onthedualnatureofthemathematicalconceptions.Withthisaccount,Iintend to contributetomathematicseducationbyprovidingevidenceonhowthedevelopment of theelementsofcomplexnumbers,whichisthroughshrinking/stretchingofthe distance(s) betweentherootsandthex-coordinateofthevertexofanyquadratic functions' graph,a ordsconceptualizinganycomplexnumberasasingleentityina well-de nedsetratherthanonlyanalgebraicprescriptionofcertainoperations.As the resultoftheinstructionalsequenceinthisstudy,theparticipantpresentsthiswell- de ned setasthesetconsistingoftherootsofquadraticequationswithrealcoe cients.
dc.format.extent30 cm.
dc.format.pagesxviii, 151 leaves ;
dc.identifier.otherSCED 2016 S37
dc.identifier.urihttps://digitalarchive.library.bogazici.edu.tr/handle/123456789/15568
dc.publisherThesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2016.
dc.subject.lcshMathematics teachers.
dc.subject.lcshNumbers, Complex -- Study and teaching (Secondary)
dc.titleA prospective secondary mathematics teachers's development of the meaning of the cartesian form of complex numbers

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