Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Master
SUBJECT

Code	Subject	
MME1016	Special Topics in Modern Didactics I	

Section	Semester	Hours: C+S+L	Category	Type	
Didactic Mathematics - in Hungarian	1	2+2+0	speciality	compulsory	

Teaching Staff in Charge	Lect. ANDRAS Szilard Karoly, andrasz@math.ubbcluj.ro	
Aims	The modell of heuristical thinking and problem solving, elaborated by George Polya and the model of corresponding affective states (Lenard). The eficienty of teaching heuristical thinking.	
Content	I. The principles of heuristical thinking (George Polya)
II. The affective states in he modell of Polya (the Lenard modell) 
III. Induction and analogy
IV. Induction in geometry
V. Triangle-tetrahedron analogies
VI. Generalizations in the process of problem solving (colorful Helly and Caratheodory type theorems)
VII. Examples and counterexamples
VIII. Proofs without words
IX. Geometrical models for algebraic problems
X. Geometrical models for analysis problems
XI. Algebraic models for geometric problems
XII. Algorithms in the school
XIII. Developing heuristical thinking in the school

Bibliography	&#8226;	George Pólya: Mathematical Discovery. On understanding, Learning, and Teaching Problem Solving, John Wiley and Sons, 1962. (A problémamegoldás iskolája, Tankönyvkiadó. 1985)
&#8226;	George Pólya: Mathematics and Plausible Reasoning, Princeton University Press, 1954. (Indukció és analógia, A plauzibilis következtetés 1988,. Gondolat Kiadó)
&#8226;	Lakatos Imre: Bizonyítások és cáfolatok, Typotex, 1998
&#8226;	Cofman Judit: What to solve? Oxford University Press,1997
&#8226;	Kosztolányi József: A problémamegoldási stratégiák tanításáról, teză de doctorat, Univ. Debrecen, 2005

	
Assessment	Didactical project: 50%
Final exam 50%

If a student&#8217;s absentees is greater than 50% from the number of all activities, the student has to prepare a special presentation (paper) in a subject specified by the professor.