This paper inspired by simulation by Artificial Neural Networks (ANNs) applied recently for evaluation of phonics methodology to teach children "how to read". A novel approach for teaching a mathematical topic using a computer aided learning (CAL) package applied at educational field (a children classroom). Interesting practical results obtained after field application of suggested CAL package with and without associated teacher's voice. Presented study highly recommends application of a novel teaching trend based on behaviorism and individuals' learning styles. That is to improve quality of children mathematical learning performance.

What knowledge do teachers need for integrating appropriate digital technologies in teaching mathematics? An overarching construct called TPACK is proposed as the interconnection and intersection of knowledge among technology, pedagogy, and content and is referred to as the total knowledge package for teaching mathematics with technology. Five stages in the process of developing TPACK - recognizing, accepting, adapting, exploring, and adapting – describe the process of teachers’ learning to integrate technology. Teachers learn to teach mathematics from their own learning – K-12 mathematics - collegiate mathematics coursework, teacher preparation program, field experiences and professional development as they teach mathematics. The challenge is to identify appropriate experiences to guide this integration of technology in teaching mathematics in ways that develop TPACK. A framework for these experiences directs attention to emergent social and psychological perspectives.

Central to this article is networking in math lessons, whereby concentration is placed on the construction of a student-focused teaching method for the networking of mathematical knowledge in the lower secondary. Firstly, normative standards and descriptive results will be compared. Secondly, several already existing teaching methods for networking in math lessons will be added to the method of „chapter-spanning task variation“. Using this method, attention is be placed on the integration of mathematical content and specific social netowrk-form (e.g. teacher led classes, group-work etc.). This paper will be concluded with the presentation of the testing of the method in the school context).

On the basis of experiences and studies developed in the last ten years, the contribution aims to discuss some different peculiarities between Cooperative Learning and Peer Tutoring models in Mathematics lesson. These models are specific interpretations of a way of conducting Mathematics lessons which requires the activity of students, their personal participation in the construction of knowledge. In the description of the two teaching-learning models, the analysis will deal in particular with the social aspects these models involve. Describing these two modalities of cooperation, also the importance of the care for the choice of suitable mathematical tasks and for different pedagogical setting they require will appear clearly. The issues described, together with the analogies and differences between the two models, could contribute to suggest more adequate didactical projects for teachers and deeper studies about students’ collaboration based models for researchers.

In the teaching of the subject of Mathematics and in particular, in the teaching of the linear function f(x) = ax + b, the use of Microsoft Office Excel programme ( 1st grade of Eniaio Lykeio/ Unified upper-secondary school) equally facilitates both participants of the learning process, as the particular programme is incorporated in the context of the learner-centered educational procedure. Within the framework of this point of view and with the aim of effectively compiling the syllabus, the application of twelve (12) basic principles hinging on the active participation of learners in mutual cooperation, is considered necessary. Selfevaluation and the need to establish specific incentives and set concrete aims and objectives constitute indicative examples of basic principles. Within the frame of the afore-mentioned educational principles, it is suggested that the class is divided in groups of 2-3 students and new technologies are implemented, with the ultimate goal to clarify and comprehend concepts and applications relevant to the subject. Criteria for the design of such an activity are the exploitation of learners’ background knowledge and experience as well as the experimental involvement in new teaching practices. As prerequisites, we pose the formulation of conjectures and conclusions and the ‘depenalization’ of errors in the mind of learners.

A Markov chain is introduced to the major steps of the process of learning a subject matter by a group of students in the classroom, in order to obtain a mathematical representation of the above process. A classroom experiment for learning mathematics is also presented illustrating the applicability of our results in practice.

Certainly one of the most powerful and important modeling languages of our time is the Calculus. But research consistently shows that students do not understand how the variables in calculus-based mathematical models relate to aspects of the systems that those models are supposed to represent. Because of this, students never access the true power of calculus: its suitability to model a wide variety of real-world systems across domains. In this paper, we describe the motivation and theoretical foundations for the DeltaTick and HotLink Replay applications, an effort to address these difficulties by a) enabling students to model a wide variety of systems in the world that change over time by defining the behaviors of that system, and b) making explicit how a system\'s behavior relates to the mathematical trends that behavior creates. These applications employ the visualization and codification of behavior rules within the NetLogo agent-based modeling environment (Wilensky, 1999), rather than mathematical symbols, as their primary building blocks. As such, they provide an alternative to traditional mathematical techniques for exploring and solving advanced modeling problems, as well as exploring the major underlying concepts of calculus.

Algebraic thinking is a crucial and fundamental element of mathematical thinking and reasoning. It initially involves recognising patterns and general mathematical relationships among numbers, objects and geometric shapes. Using historical evidence, this paper will highlight how the ability to think algebraically might support a deeper and more useful knowledge, not only of algebra, but the thinking required to successfully use mathematics. It will also provide a framework for educators of primary and middle years’ students to develop the necessary thinking strategies required to understand algebra.

Physical experiments have a great potential in mathematics lessons. Students can actively discover how mathematical concepts are used. This paper shows results of research done how students got to know the different aspects of the concept of variable by doing simple physical experiments. Further it will be shown what other concepts could be touched by the same treatment.

The concept of the limit of a function is undoubtedly the key to higher mathematics. With a view to very fine mathematical essence of the notion mathematics educators permanently deliberate what didactic method to take in order to reach relatively satisfactory level of its understanding. The paper presents an approach based on the aid of hypothesis that is put forward by means of calculator support.