147 Copyright © 2015, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. Chapter 7 DOI: 10.4018/978-1-4666-8714-1.ch007 ABSTRACT The chapter focuses on of-line communication using (not only) mobile devices where absence of direct communication increases the risk of misunderstanding and loss of time. Two principles that can lower this danger, the principle of charity and the principle of scafolding, are presented frst separately, and then in mutual relationship. The aim of this chapter is to show that charity and scafolding are two (connected) stages of help to pupils. If the teacher applies the principle of charity, it enables him/her to understand pupils and/or discover their problems. Having detected the learners’ misconceptions or problematic parts, he/she will be able to follow the pupils’ thinking process and with the help of scafolding advance the pupils’ knowledge to a higher level. All the presented theoretical constructs are illustrated by ex- amples from an on-line mathematical course for secondary pupils. The role of technological devices in developing the quality of pupils’ participation in the course is documented. INTRODUCTION Without any doubt, the teacher-pupil communication is of central importance in any educational process. The very fast expansion of the use of technological devices (in all forms, especially of those connected to the Internet) in education brings about the need to focus on and study communication in this new environment. Classical communication models do not always reflect the dynamics of communication Off-Line Communication in Mathematics Using Mobile Devices Pierre Clanché Université Bordeaux, LACES, France Antonín Jančařík Charles University in Prague, Czech Republic Jarmila Novotná Charles University in Prague, Czech Republic