1.2 Literature review

Historical context and basic Principles

Even if nowadays the majority of our population is familiar with the terms digital (or online) software and tools, there is still a sample of people (or teachers) who are quite uncertain of what is available in mathematics teaching. According to Drijvers et al (2010; cited in Ruthven, 2013) a “Digital Mathematics Environment (DME)” can help teachers and students with various materials and tools of technology. Some of them can be: Games, GeoGebra and Cabri software, Spreadsheets, Web (Internet) and online software/applications (also known as Mathematical Applets), found in Monaghan (2014).

What has been improved in Mathematics education, especially with the Internet’s
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In other words, the teacher has to organize and use artefacts (i.e. tools, objects) in a DME, with specific mathematical tasks, so as to guide his/her students’ instrumental genesis with i.e. selection, decisions, teaching strategies (Trouche, 2004; cited in Drijvers et al., 2010). However, students’ skills, such as thinking, explaining or discussing (Borba et al, 2013) can be established with or without the use of online material; it depends on teacher’s abilities and efforts.

What is an instrumental genesis though? It is a well-known term, which describes the process of “learning [or] problem solving” (Guin & Trouche, 1999) of a student, who accomplishes to “master” and get knowledge of and from the use and experimentation of an artifact/tool; i.e. online material, MAs, Interactive White Board, etc. (See Figure below).

Instruments, can relate to digital tools, in different forms and for different purposes, so the teacher may make the appropriate selection and evaluation. Therefore, technology could be used through “six major opportunities” in teaching/learning mathematics: learning from feedback; observing patterns; seeing connections; exploring data; teaching the computer; developing visual imagery” (National Strategies, 2009; cited in Pope, 2013), through “interactive software on CD, or online” techniques.

In view of the above, we can conclude that teachers can nowadays

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