Alternative teaching of algebraic problems with multiple approaches in computting environment

Aim of this research is to determine terms and conditions that allow the design ofdidactic interventions, helpful in overcoming obstacles and difficulties anddeveloping cognitive flexibility for movement between concepts and objectsrevealing their interconnections specifically in the field of Systems of LinearEquations. The target population is of tertiary education, specifically students fromTEI of Piraeus. The main prerequisites were the imprint of the related learningobstacles and common difficulties and the design of interventions directly aiming inovercoming them. The research was largely qualitative and results more registeredunder a properly modified APOS typology. The theoretical framework of design ofthe intervention comprised of Tall’s Three Worlds of Mathematics categorization ofthe representations of mathematical knowledge and the pedagogic aspect of Kolb’scycles of experiential learning. Pedagogic use the accommodations that digitaltechnologies offer was investigated through the use of the use of MATHEMATICAand its multirepresentational CDFs and also through code study. Conceptualchange, procedural understanding, object knowledge were observed in importantlevels. Instrumental genesis was reported in advanced stages of the didacticalintervention along with improved cognitive flexibility among the students. Thecontribution of the multirepresentational environment and, to some extend, codestudy was found important although not altogether without problems. Overcomingcommon mistakes and difficulties at the time of toolset introduction seemed to alsohelp