Διερεύνηση του μετασχηματισμού της τεχνολογικής παιδαγωγικής γνώσης στα μαθηματικά φοιτητών/τριών στο πλαίσιο της προπτυχιακής τους εκπαίδευσης και της μετέπειτα σχολικής τους δράσης ως εκπαιδευτικών

Abstract

Η παρούσα μελέτη διερευνά το μετασχηματισμό της Τεχνολογικής Παιδαγωγικής Γνώσης προπτυχιακών φοιτητών/τριών στα Μαθηματικά, στο πλαίσιο ενός εξαμηνιαίου προγράμματος εκπαίδευσης - έρευνας δράσης σε συνεργατικά περιβάλλοντα. Επιπρόσθετα, διερευνά αν ο παραπάνω μετασχηματισμός συντελείται στη μετέπειτα σχολική τους δράση ως εκπαιδευτικών. Εικοσιπέντε φοιτητές (εννέα άντρες και δεκαέξι γυναίκες) συμμετείχαν στην έρευνα, ενώ ο ερευνητής με την επιβλέπουσα της διατριβής είχαν ταυτόχρονα αναλάβει το ρόλο των διδασκόντων.Στην παρούσα μελέτη αξιοποιήθηκε το πλαίσιο της Τεχνολογικής Παιδαγωγικής Γνώσης Περιεχομένου (ΤΠΓΠ) που έχουν αναπτύξει οι Mishra και Koehler (2006). Επίσης, υιοθετήθηκε η οπτική της διαλεκτικής φύσης των Μαθηματικών (Lakatos, 1976; Davis & Hersh, 1981), οι εκδοχές του κατασκευαστικού εποικοδομισμού (Papert, 1980) και της εγκαθιδρυμένης μάθησης (Lave, 1988) με σκοπό να διερευνηθεί ο μετασχηματισμός της ΤΠΓΠ των φοιτητών στους άξονες της εφαρμογής του Προγράμματος Σπουδών, της Αξιολόγησης των μαθητών/τριών, της Μάθησης, της Διδασκαλίας και της Πρόσβασης στις Ψηφιακές Τεχνολογίες (ΨΤ) με βάση τα στάδια ανάπτυξης που διέρχονται οι εκπαιδευτικοί (Αναγνώριση, Αποδοχή, Προσαρμογή, Διερεύνηση και Εξέλιξη), σύμφωνα με τους Niess et al. (2009). Ταυτόχρονα, επιχειρήθηκε η γνωστική ανάλυση της γεωμετρικής σκέψης των φοιτητών, σύμφωνα με τους τύπους της Αντιληπτικής, Σειριακής, Λεκτικής και Λειτουργικής κατανόησης γεωμετρικών σχημάτων (Duval, 1995) και η ανάλυση των αντιλήψεων των φοιτητών για τη φύση των Μαθηματικών σύμφωνα με τις κατηγορίες: Εργαλειακή οπτική, Πλατωνική οπτική και οπτική Επίλυσης Προβλήματος (Ernest, 1989).Οι φοιτητές μέσω μιας σπειροειδούς διαδικασίας ανατροφοδότησης, αναστοχασμού και σταδιακών τροποποιήσεων μέσα σε ένα διαλεκτικό πλαίσιο συνεργασίας εργάστηκαν σε μαθηματικές δραστηριότητες (με ή χωρίς την τεχνολογία) και σχεδίασαν εκπαιδευτικά-διδακτικά σενάρια (Κυνηγός, 2006) ενσωματώνοντας στο σχεδιασμό της διδασκαλίας τους εκπαιδευτικά λογισμικά Μαθηματικών που προτείνονται από το Υπουργείο Παιδείας, ώστε να διδάξουν γεωμετρικές έννοιες σε μαθητές/τριες Στ΄ Δημοτικού και Β΄ Γυμνασίου. Ταυτόχρονα, με σκοπό να διευκολυνθεί η ενδυνάμωση της μαθηματικής, παιδαγωγικής και τεχνολογικής γνώσης των φοιτητών χρησιμοποιήθηκαν συνεργατικά εργαλεία του διαδικτύου (web 2.0).Ως προς την μεθοδολογική ερευνητική προσέγγιση έγινε προσπάθεια τριγωνοποίησης ποιοτικών και ποσοτικών μεθόδων και αξιοποιήθηκαν οι ατομικές μελέτες περίπτωσης, η παρατήρηση, τα τεκμήρια, οι ποιοτικές ημιδομημένες συνεντεύξεις και ερωτηματολόγια. Τα ποιοτικά δεδομένα καταχωρήθηκαν και επεξεργάστηκαν με το λογισμικό Nvivo 8, ενώ τα ποσοτικά με το SPSS 15.0. Η ποιοτική μελέτη εστίασε σε επτά φοιτητές (δύο άντρες και πέντε γυναίκες), οι οποίοι μετά το πέρας των σπουδών τους εργάστηκαν ως εκπαιδευτικοί.Τα ευρήματα αναδεικνύουν ότι οι τελειόφοιτοι φοιτητές της έρευνας έχοντας αποκτήσει εμπειρίες και έχοντας αναπτύξει την προσωπική τους οπτική για τα Μαθηματικά....

The present study examines undergraduate students’ transformation of Technological Pedagogical Content Knowledge (TPACK) in Mathematics during a six-month cooperative action research programme. Furthermore, it examines whether the above-mentioned transformation is transferred to their subsequent activity as schoolteachers. Twenty-five undergraduate primary students (nine men and sixteen women) took part in this educational intervention while the researcher, as well as the supervisor of this research, were teachers of the participant students group.Mishra and Koehler (2006) Technological Pedagogical Content Knowledge (TPACK) framework was used in this study. Furthermore, the dialectical nature of Mathematics (Lakatos, 1976; Davis & Hersh, 1981), the tenets of constructionism (Papert, 1980) and of situated learning (Lave, 1988) were also adopted so as to investigate students’ TPACK transformation in regard to Curriculum implementation, pupil Assessment, Learning, Teaching and Access to digital technologies at Niess et al. (2009) developmental stages (Recognizing, Accepting, Adapting, Exploring, and Advancing). Moreover, this study examines students’ cognitive analysis of geometrical thinking according to four apprehensions of geometrical figures: Perceptual, Sequential, Discursive and Operative (Duval, 1995) and also researches students’ perceptions about the nature of mathematics according to Ernest’s (1989) categories: Instrumentalist, Platonist and Problem-Solving.Through a learning process of action, feedback, reflection and gradual task modifications in a dialectical context, students involved in a variety of mathematical activities (using technology or otherwise) and designed educational-teaching scenarios (Kynigos, 2006) in which the instructional use of some educational mathematics software (recommended by the Ministry of Education for assisting instruction of geometrical concepts 6 and 8 grades pupils) had been integrated. At the same time, in order to facilitate students’ enhancement of mathematical, pedagogical and technological knowledge, web 2.0 tools were also used.The adopted methodological approach is both qualitative and quantitative while research questions have been investigated through triangulation methods. Furthermore, as an action research study, the following methods were used for data collection: individual case studies, observation, students’ documents, qualitative, semi-structured interviews and questionnaires. Nvivo 8 software was used for the analysis of the qualitative data and SPSS 15.0 for the analysis of the quantitative data. The qualitative analysis focused on seven students’ case studies (two men and five women) who at the end of their undergraduate studies worked as teachers.The findings show that, in last semester of their studies, students transformed in varying degrees their Technological Pedagogical Content Knowledge (TPACK), as a result of their already formulated personal experience and idiosyncratic views. So, it seems that very few of the students reach the last Niess’s et al. stages: exploring and advancing concerning Curriculum implementation, pupil Assessment, Learning, Teaching and technological Access. Regarding of cognitive analysis of students’ geometrical thinking it seemed that some students’ deficient cognitive apprehension which exceeded in some cases, using the learning framework. Moreover some students had adequate procedural knowledge, but inadequate conceptual knowledge. In addition, some students succeeded to change their perceptions about the nature of mathematics by passing the instrumentalist perspective in problem solving.A significant role in students’ TPACK transformation was played by the mediation of the particular learning tools that had been employed in this educational action research, such as educational-teaching scenarios, educational software and web 2.0 tools, as well as various processing and communication tools. Furthermore, students’ TPACK transformation was found to be facilitated –according to the student’s own view– by the interactions experienced within their groups which acted as learning communities, by the teachers/researchers’ pedagogical mediation, as well as by the characteristics of the particular educational intervention as a whole.Moreover, the actual instructional practice of the former students, who were subsequently found to be working as teachers in various schools, was shown to be affected by some differing situational factors within schools concerning matters of our study. This kind of personal pragmatic experience, in return, contributed to their further self-reflection and critical thinking concerning the manner in which they would use digital technology within school reality and, finally, to the relative transformation of their approach to the issue of the pedagogical integration of digital tools in mathematics education.Additionally, the findings showed that students’ TPACK transformation: a) Depended on the degree of their engagement in the training programme; b) was related to students’ previous cognitive constructs concerning learning and teaching as well as the dialectical nature of Mathematics, and, finally, c) was associated with some favorable or unfavorable conditions which they were encountered with at school.However, it is worth noting that the most significant factor for the inclusion of digital technology in the instructional practice by the participant teachers had to do with their personal dynamic, creative and critical approach to their role as teachers as well as to their views concerning potential benefits of the different kinds of digital technology when used as learning tools. This is why, although the participant teachers encountered similar problematic situations in their schools, they actually differed in their behavioural mode of handling those situations as well as in their ability to use technology for the advancement of their pupil’s learning environment. Those teachers who took advantage of digital technology claimed that its inclusion in their instructional practice improved their relationships with pupils and contributed to their pupils’ development of mathematical thinking as well as to the improvement of schools’ functioning.Finally, new questions have been raised concerning: the characteristics and timing of the implementation of similar experiential programmes for the empowerment of future teachers’ educational development and initial training; the ways in which student’s learning within such programmes could be supported and facilitated during their undergraduate studies and the impact of all the above on actual teachers’ school practice.