Didaktiske situationer for fuldstændiggørelse af kvadratet i andengradsligningen
Didaktiske situationer for fuldstændiggørelse af kvadratet i andengradsligningen [pdf, 8MB]
IND's studenterserie nr. 28. Specialerapport. Matematik.
Niven Adel Atie, januar 2013
Vejleder: Carl Winsløw.
This Master’s thesis enlightens, that the essence of the derivation of the general solution formula for the quadratic equation is based on completing the square. The proof in the standard course in stx is based on algebra and mathematical operations. The algebra is often the most difficult tool for students in stx to work with. Therefore the hypothesis about the completing the square, being a trick of mystery in the standard course for stx students, is tested. The hypothesis is confirmed as I observe a standard course in the subject quadratic equations. TDS, the theory of didactical situations is used as a tool of analysis. The result in the standard course is unsatisfying and I therefore chose to design a course using TDS which is based on the algebraic and geometric completing the square. I observed the completion of the designed course. It showed that the geometric tool is a support to the algebra. The geometry makes the algebra make sense, as one can visualize “the trick”, completing the square.