تطوير طرق تفكير رياضية متقدم من خلال بحث رسوم بيانية لدوال مركبة

Abstract

This article deals with the graphical display of a composite function created by
moving the function algebraically or graphically and the mutual influence between
the two representations. The article presents the effect of changing the parameters 

in the algebraic representation of the function on the shape of its graph, applies the
findings on the special case of the absolute value function and refers to the
discovery of graphical patterns that help in constructing an appropriate algebraic
representation for a displayed function.
The benefits of the article are certainly not limited only to the understanding of
the characteristics and properties of the absolute value function. The article goes
beyond that and emphasizes the significance of using technology in teaching
mathematics, especially in illustrating various mathematical representations in
order to identify patterns, phenomena and relations between them. This is done in
order to expand the mathematical vision, perception and comprehension of the
student. It is worthwhile noting that we can also draw the functions manually
without using technology, i.e., we can teach the subject without the use of
technology; however, technology comes to facilitate and clarify all the stages and
steps needed to carry out the required algebraic and graphic changes on the
function.
This article exposes the teacher to practices that can help in developing higher
level of creative mathematical thinking processes which assist in increasing the
level of mathematical thinking during mathematical discussions and dialogues with
his or her students.
The article attempts to apply and internalize the objectives of the new
mathematics curriculum, not only those related to the mathematical content, but
also those associated to mathematical pedagogical objectives and the thinking
processes that the curriculum concentrates on.