Acquiring Abstract Geometrical Concepts: the Interaction between the Formal and the Intuitive
نویسنده
چکیده
The acquiring of formal, abstract mathematical concepts by students may be said to be one of the major goals of mathematics teaching. How are such abstract concepts acquired? How does this formal knowledge interact with the students' intuitive knowledge of mathematics? How does the transition from informal mathematical knowledge to formal mathematical knowledge take place? This paper reports on a research project which is examining the nature of the interaction and possible conflict between the formal and the intuitive components of mathematical activity. Details are presented of an initial study in which mathematics graduates, who could be considered to have acquired formal mathematical concepts, tackled a series of geometrical problems. The study indicates the complex nature of the interaction between formal and intuitive concepts of mathematics. The plans for the next stage in the research project are outlined.
منابع مشابه
Formal-comparative analysis of the spatial organization of student residence halls based on their spatial threshold patterns
Functional quality of the student residence halls has a great deal of importance due to their collective nature and the fact that they are considered as housing units, identifying and defining the role of intermediary spaces on the spatial organization and and spatial consociation of student residence halls which is a compound system of masses and spatial borderlines can bring order to its syst...
متن کاملThe role of intuition in managerial decision-making: Islamic approach
Current theories argue that decision making is largely based on quick and intuitive processes.The results of study on topping organizations show that successful decision-makings are intuitive rather than rational. Therefore in recent years the issue of intuition and intuitive decision making as an effective management has attracted increasing attention in scientific circles and world-class rese...
متن کاملIntuitive and logical way of thinking in the education of architectural design courses
Different approaches and methods are used in the architecture design process that logical and intuitional methods are the most common ones. The role of knowledge in each method is different. Investigating aspects of knowledge demonstrated the hierarchy from data to wisdom and the interaction of explicit and tacit types, subjective and objective sources, and analytical and exploratory ways of p...
متن کامل?Logic and Formal Ontology: Is the Final Formal Ontology Possible
Musa Akrami AbstractMany philosophers and logicians have contemplated the relationship between ontology and logic. The author of this paper, working within a Bolzanoan-Husserlian tradition of studying both ontology and logic, considers ontology as the science of the most general features of beings and the most general relations among them. He considers logic as the science concernin...
متن کاملAnalysis of the Interaction between the Formal Types of Traditional Houses and Spatial Configurations using Space Syntax Case Study: Traditional Houses of Kashan
Kashan is a city in Iran with a host of traditional houses that date to the Qajar period. Sociocultural and climatic factors have had the greatest impact on their spatial configurations. In this study, focusing on entrances, the spatial configuration of houses in Kashan is analyzed. Houses are first categorized in terms of physical form in four categories: single-courtyard houses with massing ...
متن کامل