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This thesis is an exploratory study of teachers' and children's understandings of the National Numeracy Strategy, and of interactive whole class teaching in particular. It starts by identifying aspects of the Strategy that are of significance to teachers and develops these by detailing the challenges that face them in teaching in this way. Data are collected by means of interviews and classroom observations, progressively focusing the study. In particular, the way in which teachers and children understand the role of discourse in whole class discussion is examined. This understanding illuminates a tension between the rhetoric of the Strategy, which appears to promote a view of learning that is based firmly on negotiation of meaning through discourse, and its practice, which is seen to be little different from forms of pedagogy that have preceded it. The contribution to knowledge made by the thesis is represented by several features. First, it lies in the detail of the exploration of the interaction between teacher and children, illuminating new ideas about the nature of such interaction in the context of whole class teaching. Though discursive interaction has been examined in some depth through previous studies, few have done so in this context. Second the study's findings relate specifically to the National Numeracy Strategy and again, in complementing other recent (mainly quantitative) studies, it therefore relates previous theory to this particular contemporary initiative. Third, in addition to new knowledge in the field of class interaction and mathematics pedagogy, it develops a novel method of data collection from children, making use of video of children's own involvement in mathematics lessons to stimulate reflection in interviews.

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Η παρούσα διπλωματική εργασία αφορά στη μελέτη της ανάπτυξης της πολλαπλασιαστικής σκέψης των μαθητών του Δημοτικού Σχολείου. Σκοπός της έρευνας ήταν η αξιολόγηση της επίδοσης των μαθητών των δύο τελευταίων τάξεων του Δημοτικού Σχολείου σε προβλήματα αναλογίας, ως χαρακτηριστικό παράδειγμα προβλημάτων πολλαπλασιαστικής σκέψης, όσο και η διερεύνηση των μαθηματικών στρατηγικών που χρησιμοποιούν για την επίλυση αυτών. Η πολλαπλασιαστική σκέψη αποτελεί μία ιδιαίτερα σημαντική ικανότητα που παρέχει τη δυνατότητα στους μαθητές να σχεδιάζουν εύστοχες στρατηγικές λύσης σε κατηγορίες προβλημάτων που έχουν αυξημένες δυσκολίες δομής και περιεχομένου. Τα δεδομένα που συλλέχθηκαν συγκρίθηκαν μεταξύ των μαθητών των δύο τάξεων και διαπιστώθηκαν οι διαφορές μεταξύ αυτών. Με τον τρόπο αυτό, ερμηνεύθηκε ο ρόλος της ηλικίας των μαθητών, ως παράγοντας που συνδέεται με την ανάπτυξη της πολλαπλασιαστικής σκέψης. Η έρευνα έδειξε ότι οι μαθητές και των δύο τάξεων παρουσιάζουν ιδιαίτερα σημαντικές δυσκολίες στην επίλυση προβλημάτων αναλογίας. Ταυτόχρονα, φαίνεται ότι οι μεγαλύτεροι σε ηλικία μαθητές έχουν μεγαλύτερη ικανότητα στη λύση των προβλημάτων. Τέλος, η έρευνα δείχνει ότι η δομή και το περιεχόμενο των προβλημάτων αυτών αποτελούν παράγοντες που επηρεάζουν τους μαθητές στη διαδικασία επίλυσης που επιλέγουν να εφαρμόσουν. / This thesis concerns the study of the development of multiplicative thinking of primary school students. The purpose of this study was to evaluate the performance of grade 5 and grade 6 students on proportional problems, as an example of multiplicative thinking problems, and exploring mathematical strategies used to solve them. The multiplicative thinking is a very important skill that enables students to design targeted strategies in different categories of proportional problems which have increased difficulties in structure and content. The collected data were compared between students of the two grades and found the differences between them. In this way interpreted the role of students’ age, as a factor associated with the development of multiplicative thinking. The survey shows that the students of both grades have substantial difficulties in solving proportional problems. At the same time, the survey appears that the older students have greater ability in problem solving. Finally, research shows that the structure and the content of these problems are factors that affect students in the process of resolving which they choose to apply.