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The analysis presented in this article tries to obtain a global view of the field of interactive learning environments (ILE)
dedicated to arithmetic and algebra. As preliminaries, a brief overview of evaluation methods focusing on educational software
is given and a short description of ten ILEs concerned by the study is provided as a kind of a sta...
Citations
... Interactive Learning Environments (ILEs) are simply integrated mathematical exploration tools. Similar to GeoGebra, they provide exploration of mathematical concepts in a manner that may be tedious compared to pen and paper calculations [17]. ...
... The fact that E-slate is based on the Logo programming language illustrates that this solution is an obvious extension of constructionist pedagogy principles as outlined by Seymour Papert [3]. In this manner, while it is an incomplete environment, it is a prime example of the desire to produce mathematical tools based upon constructionism principles [17]. "Half-Baked" modules are available out-of-the-box in order to promote the creation of open ended translations of algebraic principles into other domains. ...
... Cognitive Tutor and various ILEs (ActiveMath, MathTeacher, MathXpert) allow for a solution pathway. It has been empirically demonstrated that guided selfexploration can contribute to student comprehension [1,2,5,13,17]. These techniques have been employed in nonmathematical fields, such as written English teaching (R-WISE). ...
This paper is inspired by M. Hohenwarter's analysis of GeoGebra. Hohenwarter makes very strong claims regarding the synthesis of geometry and algebra. This literature review paper attempts to redress fundamental flaws in Hohenwarter's understanding of algebra pedagogy in the formation of a seemingly effective human computer interaction model. In an analysis of the weak first principals of Hohenwarter's paper, it will be shown that his human computer interaction model may actually be detrimental to student comprehension. It is hoped that this exploration will serve as a warning to HCI developers' domain analysis. Hohenwarter's inability to appreciate first principals of his target domain has arguably led to a potentially harmful pedagogical tool. This human computer interface – incorporating the synthesis of algebra and geometry – will be examined in light of established pedagogical practice. Apart from GeoGebra, variant geometry and algebra visualization software will be documented and analyzed, as possible, in regards to its benefit to student learning. These alternatives will be reviewed in terms of their ability to adhere to established pedagogical standards. Finally an analysis of effective and tested geometric and algebraic visualization software will lead to an effective proposed model of human computer interaction.
... Such an environment needs to contain objects about which generalizations can be made. A recent review of software currently used for teaching algebra [19] shows that the objects commonly provided are algebraic objects such as functions, represented symbolically and graphically. Most current IGS programs also have the functionality to represent and explore functions (see [10] for some of the possibilities for exploration in an IGS). ...
... c.Enable the manipulation of generalizations. This includes traditional algebraic manipulation such as rearranging formulae, solving equations, etc. and, along with graphical representation, is the focus of much of the available algebra teaching software [19]. Of the IGS listed, currently only Casyopée and TI-Nspire have the capability for direct algebraic manipulation. ...
In order to consider the ways in which interactive geometry software might facilitate the expression of generality, an exploratory inspection using a series of tasks related to finding a connection between the radius and area of a circle was performed using Cabri II Plus, Casyopée, Cinderella, GeoGebra, Geometer's Sketchpad and TI-Nspire (CAS). It was found that the programs specifically designed to include algebraic functionality had less potential for enabling students to develop the concept of variable and to generate symbolic representations between variables than did the programs with less overt algebraic functionality. An implication is that more attention needs to be paid to the needs of learners in the early stages of algebraic thinking when incorporating algebra within IGS.
