Main presenter			Co-presenter(s)
Name :	Dr. Harry Silfverberg		Name:
E-mail:	harry.silfverberg@uta.fi		E-mail:
Institution or Company:	University of Tampere		Name:
Department:	Dept. of Teacher Education		E-mail:
City:	Tampere		Name:
State/Province:			E-mail:
Country:	Finland		Name:
Type of presentation:	Lecture :  25 minutes.		E-mail:
Conference strand and number:	ACDCA ,    Number: A15		Schedule:   Room:	Thursday, 11h30   1422
Related website:	http://www.uta.fi/~tnhasi/Montreal/Tasks.doc
Title of presentation:	DGS and CAS as tools supplementing each other in an inquiry task
Abstract:
The presentation/paper deals with the project ”Locus curves” which was carried out as a part of the first university level geometry course for mathematics teacher students. The students were given the following task as a 4x3-table (rows R1-R4 refer to the rows and C1-C3 to the columns): “What kind of locus does the point P draw IF the distances d1 and d2 are interpreted in one of the following ways: (C1) d1 and d2 are the Euclidean distances of the point P from two fixed points P1 and P2, (C2) d1 is the Euclidean distance of the point P from a fixed point P1 and d2 is the Euclidean distance of the same point P from the line L, (C3) d1 and d2 are the Euclidean distances of the point P from two fixed intersecting lines L1 and L2, AND IF the type of the constancy is one of the following ones: (R1) the sum of the distances is constant, (R2) the difference of the distances is constant, (R3) the product of the distances is constant or (R4) the ratio of the distances is constant. “ Each group of two or three students was asked to solve two of the 12 different tasks from the table. The students were first asked to construct the curves geometrically as locus curves determined by the geometrical properties of the curves using the dynamic geometry programme GEONExT and then to present the solutions as applets locally or in net. In addition to this, the features of curves were asked to be examined analytically with the CAS-software QuickMath (http://www.quickmath.com/) which can be run freely through the net. In the presentation I will report what curves the students with these tools were able to find from this rich family of curves (including well known cone sections, Cassinian curves, lemniscate of Bernoulli, circle of Apollonius etc.) and give some examples of how they performed the tasks. In the presentation I will also discuss how the different points of view offered by DGS- and CAS-approach supplement each other in solving these kinds of inquiry tasks.