ɌEME, ɝ . XLI, ɛɪ. 3, ʁɭɥ ɫɟɩɬɟɦɛɚɪ 2017, ɫɬɪ. 623637
Ɉɪɢɝɢɧɚɥɧɢ ɧɚɭɱɧɢ ɪɚɞ DOI: 10.22190/TEME1703623D
ɉɪɢɦʂɟɧɨ: 23. 9. 2016. UDK 371.3:514
Ɋɟɜɢɞɢɪɚɧɚ ɜɟɪɡɢʁɚ: 3. 4. 2017.
Ɉɞɨɛɪɟɧɨ ɡɚ ɲɬɚɦɩɭ: 15. 6. 2017.
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Ⱥɩɫɬɪаɤɬ
ɍ ɪɚɞɭ ɫɭ ɪɚɡɦɚɬɪɚɧɢ ɬɟɨɪɢʁɫɤɨ-ɩɟɞɚɝɨɲɤɢ ɨɤɜɢɪɢ ɪɚɡɜɨʁɚ ɝɟɨɦɟɬɪɢʁɫɤɨɝ
ɦɢɲʂɟʃɚ ɭɱɟɧɢɤɚ ɭ ɪɚɡɥɢɱɢɬɢɦ ɮɨɪɦɚɦɚ, ɩɨɫɟɛɧɨ ɪɟɡɨɧɨɜɚʃɟɦ ɭɱɟɧɢɤɚ ɭ ɧɚɫɬɚɜɢ
ɝɟɨɦɟɬɪɢʁɟ: 1) ȼɚɧ ɏɢɥɨɜɨɦ ɬɟɨɪɢʁɨɦ ɨ ɧɢɜɨɢɦɚ ɪɚɡɭɦɟɜɚʃɚ ɝɟɨɦɟɬɪɢʁɟ, 2) Ɏɢɲɛɚʁ-
ɧɨɜɨɦ ɬɟɨɪɢʁɨɦ ɮɢɝɭɪɚɥɧɢɯ ɩɨʁɦɨɜɚ ɢ 3) ɍɞɟɦɨɧ-Ʉɭɡɧɢɚɤɨɜɢɦ ɩɚɪɚɞɢɝɦɚɦɚ ɪɚɡɜɨʁɚ
ɝɟɨɦɟɬɪɢʁɫɤɨɝ ɦɢɲʂɟʃɚ. ɐɢʂ ɪɚɞɚ ɛɢɨ ʁɟ ɞɚ ɚɧɚɥɢɡɢɪɚɦɨ ɬɪɢ ɧɚɜɟɞɟɧɚ ɬɟɨɪɢʁɫɤɚ
ɨɤɜɢɪɚ ɢ ɨɛɪɚɡɥɨɠɢɦɨ ɪɚɡɥɨɝɟ ʃɢɯɨɜɨɝ ɢɡɛɨɪɚ, ɚ ɞɚ ɢɡɥɨɠɟɧɟ ɬɟɨɪɢʁɟ ɫɚɝɥɟɞɚɦɨ ɭ
ɫɦɢɫɥɭ ɢɡɧɚɥɚɠɟʃɚ ɦɨɝɭʄɧɨɫɬɢ ɩɪɨɠɢɦɚʃɚ ɢ ɩɨɜɟɡɢɜɚʃɚ ɭ ɰɟɥɨɜɢɬɭ ɬɟɨɪɢʁɭ. ɍ
ɢɫɬɪɚɠɢɜɚʃɭ ʁɟ ɤɨɪɢɲʄɟɧɚ ɞɟɫɤɪɢɩɬɢɜɧɨ-ɚɧɚɥɢɬɢɱɤɚ ɢ ɚɧɚɥɢɬɢɱɤɨ-ɤɪɢɬɢɱɤɚ
ɦɟɬɨɞɚ ɬɟɨɪɢʁɫɤɟ ɚɧɚɥɢɡɟ. Ɋɟɡɭɥɬɚɬɢ ɢɫɬɪɚɠɢɜɚʃɚ ɩɨɤɚɡɭʁɭ ɞɚ ɢɡ ɫɜɚɤɨɝ ɨɞ ɬɪɢ
ɧɚɜɟɞɟɧɚ ɬɟɨɪɢʁɫɤɚ ɨɤɜɢɪɚ ɦɨɠɟɦɨ ʁɚɫɧɨ ɞɚ ɭɨɱɢɦɨ ɢ ɢɡɞɜɨʁɢɦɨ ɝɟɨɦɟɬɪɢʁɫɤɟ
ɨɛʁɟɤɬɟ, ɞɨɤ ɢɯ ɭɱɟɧɢɰɢ ɬɚɤɨ ɧɟ ɜɢɞɟ. Ɉɧɢ ɢɯ ɜɢɞɟ ɭɤɥɨɩʂɟɧɟ ɢ ɫɬɪɭɤɬɭɪɢɪɚɧɟ ɭ
ɧɢɡɭ ɩɪɨɰɟɞɭɪɚ, ɚ ɛɚɲ ɢɡ ɬɨɝ ɪɚɡɥɨɝɚ ɦɨɠɟɦɨ ɞɚ ɤɚɠɟɦɨ ɫɥɚɛɨ ɩɨɜɟɡɚɧɢɯ. ɍ ɬɨɦ
ɫɦɢɫɥɭ, ɨɬɜɨɪɢɥɢ ɫɦɨ ɢ ɩɢɬɚʃɚ ɡɚ ɞɚʂɚ ɢɫɬɪɚɠɢɜɚʃɚ ɨ ɝɟɨɦɟɬɪɢʁɫɤɨɦ ɨɛʁɟɤɬɭ ɤɚɨ
ɜɚɠɧɨɦ ɟɥɟɦɟɧɬɭ ɫɚɞɪɠɢɧɫɤɨɝ ɞɨɦɟɧɚ ɝɟɨɦɟɬɪɢʁɚ ɭ ɨɤɜɢɪɭ ɧɚɫɬɚɜɧɨɝ ɩɪɨɝɪɚɦɚ
Ɇɚɬɟɦɚɬɢɤɟ.
Ʉʂɭчɧе ɪечи: ɝɟɨɦɟɬɪɢʁК, ȼɚɧ ɏɢɥɨɜ ɦɨɞɟɥ, Ɏɢɲɛɚʁɧɨɜɚ ɬɟɨɪɢʁɚ,
ɍɞɟɦɨɧ-Ʉɭɡɧɢɚɤɨɜɟ ɩɚɪɚɞɢɝɦɟ, ɝɟɨɦɟɬɪɢʁɫɤɢ ɨɛʁɟɤɚɬ.
THEORETICAL FRAMEWORKS OF DEVELOPMENT
GEOMETRICAL THINKING ACCORDING TO VAN
HIELE, FISCHBEIN AND HOUDEMENT-KUZNIAK
Abstract
This research is a pedagogical study of theoretical frameworks of development of
stuНОЧts’ РОoЦОtrТМКХ tСТЧФТЧР ТЧ vКrТous ПorЦs, pКrtТМuХКrХв stuНОЧts’ РОoЦОtrТМ rОКsoЧТЧР
in teaching geometry: 1) ЦoНОХ oП vКЧ HТОХОs’ ХОvОХs oП uЧНОrstКЧНТЧР oП РОoЦОtrв,
2) theory of figural concepts of Fischbein and 3) paradigms of Houdement-Kuzniak
development of geometrical thinking. The aim of our research was to analyze the three
theoretical framework and explain the reasons for their choice and expose them in terms of