How Archimedes Helped Students to Unravel the Mystery of the Magical Number Pi     

Ioannis Papadopoulos 《Science & Education》2014,23(1):61-77

This paper describes a classroom experiment where students use techniques found in the history of mathematics to learn about an important mathematical idea. More precisely, sixth graders in a primary school follow Archimedes’s method of exhaustion in order to compute the number π. Working in a computer environment, students inscribe and circumscribe regular polygons inside and around a circle in order to find the approximate area of the circle. They then compute the ratio of that approximation to the area of a square with side-length equal to the radius of the circle. This ratio indicates how many times larger the area of the circle is than the area of the square. Mirroring Archimedes’s findings, students discover that as they increase the number of sides in their polygons, the numerical results they obtain convince them that this number is almost equal to 3.14.  相似文献   

Phonological and cognitive correlates of word-reading acquisition under two different instructional approaches in Greek     

Timothy C. Papadopoulos 《European Journal of Psychology of Education - EJPE》2001,16(4):549-568

This study examined whether phonological and cognitive tasks correlate with beginning reading acquisition in Hellenic populations under two different instructional approaches: a whole language approach supplemented by implicit coding instruction through incidental learning, as used in Cyprus, versus the syllable-splitting approach characterised by explicit decoding instruction, as used in Greece. Planning, attention, simultaneous, and successive processing tasks together with three phonological coding tasks (Oddity task, Phoneme Elision, and Sound Isolation) were administered to 50 Greek and 50 Cypriot Grade 1 students. Word Attack and Word Identification were also administered to measure early reading competency. The main findings of the study were as follows: (a) significant group differences were revealed in word-decoding accuracy but not in realword reading accuracy, an expected finding in a system characterised by high grapheme-phoneme consistency; (b) successive processing and phonological coding consisted of the fundamental abilities that differentiated the Greek from the Cypriot first-graders; and (c) the Greek group exhibited a higher linguistic ability than the Cypriot group. This was facilitated by the use of the distal cognitive processes to reading, that is, successive and simultaneous processing. The discussion focuses on the need to reconsider the nature of early reading instruction in languages such as Greek with high grapheme-phoneme consistency.  相似文献   

Correction to: Teaching and learning in a multilingual Europe: findings from a cross-European study     

Dockrell  J. E.  Papadopoulos  T. C.  Mifsud  C. L.  Bourke  L.  Vilageliu  O.  Bešić  E.  Seifert  S.  Gasteiger-Klicpera  B.  Ralli  A.  Dimakos  I.  Karpava  S.  Martins  M.  Sousa  O.  Castro  S.  Knudsen  H. B. Søndergaard  Donau  P.  Haznedar  B.  Mikulajová  M.  Gerdzhikova  N. 《European Journal of Psychology of Education - EJPE》2022,37(2):321-323

European Journal of Psychology of Education - A Correction to this paper has been published: https://doi.org/10.1007/s10212-021-00539-z  相似文献