Didactical Modeling, Vol. 7, pp. 30-36

COMPUTER SUPPORTED RECONSIDERATION OF CONICS

Borislav Lazarov1, Dimitar Dimitrov2
1 Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, lazarov@math.bas.bg
2 125th High School “Boyan Penev”, Sofia, dimitrov@netbg.com

Abstract  

Under consideration is a way to present the conics in a dual manner: as loci and envelopes.. A bunch of computer technologies is drawn to explore and investigate this duality of the conics. An example of how it is done for a particular conic is given. The target group includes secondary school students who are advanced in math and information technologies. The theoretical base is an original didactical model for designing individual educational trajectories that is adapted for the team-working mode. The educational goal includes developing synthetic competence of an entire team. The individual characteristics of the team members complement one another for resolving complex problems from the local behavioral environment, which were specifically formed for the purposes of the experimental teaching.

Keywords: synthetic competence, individual educational trajectory, conics, loci, envelopes.

REFERENCES

[1]     Akulenko, I. et al. Current Status and Prospects of Mathematical Education. Eds. prof. N. Tarasenkova, & L. Kyba. – Budapest, SCASPEE, 2018. Pages 37-53.

[2]     Dimitrov, M., Peeva, G., Stoyanov, B. Conic sections as loci of points and boundaries. Mathematics, Issue 1, 2019, 46-57.

[3]    Lazarov, B. Teaching envelopes in secondary school. The Teaching of Mathematics, vol. XIV, 1 (2011). Pages 45-55

[4]    Lazarov, B. Paper and Pencil versus ICT – Battlefield Geometry. Е-learning, distance education or … The education of 21st century international conference. Sofia, Bulgaria, 6-8 April 2011. Conference proceedings. Pages 123-130.

[5]    Lazarov, B. Application of some cybernetic models in building individual educational trajectory. Information Models and Analyses. Vol. 2, No1, 2013, Pages 90-99.

[6]    Paskaleva, Z., Paskalev, G. Mathematics 8. grade. Sofia, Arhimed, 2001, p. 253-256.

[7]    Paskaleva, Z., Paskalev, G., Alashka, M. Mathematics 8. grade. Sofia, Arhimed, 2013, p. 188-189.

[8]   Var der Waerden. Пробуждаща се наука. Science and Art, Sofia, 1968, p. 300, 330, 331.

FULL TEXT (In Bulgarian)