Ioannis Papadopoulos

Modelling Problem-Solving Situations into Number Theory Tasks: The Route towards Generalisation

This paper examines the way two 10th graders cope with a non-standard generalisation problem that involves elementary concepts of number theory (more specifically linear Diophantine equations) in the geometrical context of a rectangle’s area. Emphasis is given on how the students’ past experience of problem solving (expressed through interplay among different modes of thinking and actions that show executive control and decision-making skills) supported them in their route towards generalisation.

Didactic Scenarios and ICT: A Good Practice Guide

In this paper a ‘good practice guide’ is presented for creating Didactic Scenarios (D.S.) with the support of ICT. This guide is based on: a) empirical data collected during longitudinal training programs addressed to secondary education teachers, b) observation of the way ICT is used in both levels of education and c) modern didactical theories.

Beliefs and Mathematical Reasoning during Problem Solving across Educational Levels

In this paper the status of empirical mathematical reasoning during problem solving across primary, secondary and tertiary education is studied. The main aim is to see whether the very same beliefs influence the students’ performance in the same way across educational levels. The results show that despite sharing the same beliefs, the way these beliefs affect students’ performance (positively or negatively) is different for different ages. More precisely, as we move from primary grades to college, the students’ ability to employ empirical mathematical reasoning is inclined as they persist to ask for connections with more formal ways of working. Even though the students solved the same task and shared the same beliefs, the negative effects of these beliefs were stronger for older students.

Using calculators for assessing pupils’ conceptualization on place-value

In this paper a two-stage research study is described focused on problem solving relevant to place-value and on the use of the operations within the calculator environment. The findings show that in this specific environment and via appropriate tasks teachers are provided with a context to better understand what year 5 or 6 pupils know or do not know about place-value and how they are able to apply their understanding of place-value and the use of operations in this particular context.

ICT in the Classroom Microworld - Some Reservations

Despite the promising perspective of the usage of ICT in education, contrasting opinions state that education has been barely influenced. In this paper we present a critical confrontation of aspects relevant to the usage of ICT in the classroom and categorize main difficulties that arise when ICT is applied in education.