Abstract: The article describes the theoretical concept of teaching secondary school students proof demonstration skills in mathematics. It describes in detail different levels of mastery of the concept of proof-which correspond to Piaget’s idea of there being three distinct and progressively more complex stages in the development of human reflection. Lessons for each level contain a specific combination of the visual-figurative components and deductive reasoning. It is vital at the transition point between levels to carefully and rigorously recalibrate teaching to reflect the development of more complex reflective understanding. This can apply even within the same age range, since students will develop at different speeds and to different potential. The authors argue that this requires an aware and adaptive approach to lessons to reflect this complexity and variation. The authors also contend that effective teaching which enables students to properly understand the implementation of proof arguments must develop specific competences. These are: understanding of the importance of completeness and generality in making a valid argument; being task focused; having an internalised locus of control and being flexible in approach and evaluation. These criteria must be correlated with the systematic application of corresponding methodologies which are best likely to achieve success. The particular pedagogical decisions which are made to deliver this objective are illustrated by concrete examples from the existing secondary school mathematics courses. The proposed theoretical concept formed the basis of the development of methodological materials which have been tested in 47 secondary schools.
Abstract: Deconstruction is an approach that is entirely incompatible with the traditional prevalent architecture. Considering the fact that this approach attempts to put architecture in sharp contrast with its opposite events and transpires with attending to the neglected and missing aspects of architecture and deconstructing its stable structures. It also recklessly proceeds beyond the existing frameworks and intends to create a different and more efficient prospect for space. The aim of deconstruction architecture is to satisfy both the prospective and retrospective visions as well as takes into account all tastes of the present in order to transcend time. Likewise, it ventures to fragment the facts and symbols of the past and extract new concepts from within their heart, which coincide with today’s circumstances. Since this approach is an attempt to surpass the limits of the prevalent architecture, it can be employed to design places in which creative events occur and imagination and ambition flourish. Thought-provoking artistic events can grow and mature in such places and be represented in the best way possible to all people. The concept of event proposed in the plan grows out of the interaction between space and creation. In addition to triggering surprise and high impressions, it is also considered as a bold journey into the suspended realms of the traditional conflicts in architecture such as architecture-landscape, interior-exterior, center-margin, product-process, and stability-instability. In this project, at first, through interpretive-historical research method and examining the inputs and data collection, recognition and organizing takes place. After evaluating the obtained data using deductive reasoning, the data is eventually interpreted. Given the fact that the research topic is in its infancy and there is not a similar case in Iran with limited number of corresponding instances across the world, the selected topic helps to shed lights on the unrevealed and neglected parts in architecture. Similarly, criticizing, investigating and comparing specific and highly prized cases in other countries with the project under study can serve as an introduction into this architecture style.