Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Master
SUBJECT
| MME1016 | Special Topics in Modern Didactics I |
| Teaching Staff in Charge |
Lect. ANDRAS Szilard Karoly, andrasz math.ubbcluj.ro |
| Aims |
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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 |
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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 |
| References |
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• George Pólya: Mathematical Discovery. On understanding, Learning, and Teaching Problem Solving, John Wiley and Sons, 1962. (A problémamegoldás iskolája, Tankönyvkiadó. 1985)
• George Pólya: Mathematics and Plausible Reasoning, Princeton University Press, 1954. (Indukció és analógia, A plauzibilis következtetés 1988,. Gondolat Kiadó) • Lakatos Imre: Bizonyítások és cáfolatok, Typotex, 1998 • Cofman Judit: What to solve? Oxford University Press,1997 • Kosztolányi József: A problémamegoldási stratégiák tanításáról, teză de doctorat, Univ. Debrecen, 2005 |
| Assessment |
|
Didactical project: 50%
Final exam 50% If a student’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. |
| Links: | Syllabus for all subjects Romanian version for this subject Rtf format for this subject |