Mathematics Education
F.Z. Heidari; N. Asghary
Abstract
Background and Objective:Many international studies have been done in order to trace the intellectual path of students in manipulation with the concept of variables and algebraic expressions, as well as to examine and specify their functional problems. However, despite the importance of these two concepts, ...
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Background and Objective:Many international studies have been done in order to trace the intellectual path of students in manipulation with the concept of variables and algebraic expressions, as well as to examine and specify their functional problems. However, despite the importance of these two concepts, comprehensive research has not been conducted in the seventh, eighth and ninth grades in Iran, and research has often focused on how to manipulate and write algebraic expressions. Due to the change in Iran's mathematics curriculum in 2009 and the consequent change in mathematics textbooks, the need for a clear picture of students' understanding of these two concepts is doubled.Algebraic expressions are the important part of Algebra and its deep understanding is necessory for solving algebraic problems. The purpose of this study was to investigate grade 7th, 8th and 9th students' understanding of algebraic expressions. Methods: 400 students were selected by multistage cluster sampling from 7th , 8th and 9th grade students in Tehran. A researcher-made test was designed and implemented. Out of 400 students, 15 students were selected and semi-structured interviews were conducted in order to clarify and interpret students' perceptions. Findings:The results of the test and interviews showed that most students have a poor structural understanding of algebraic expressions and they have understood them merely procedurally. Increasing academic bases did not almost improve structural understanding, but procedural understanding improves with increasing levels. Conclusion:The results of this study showed that most students in algebraic expressions (simple and complex) have a purely procedural understanding, which means that they have understood algebraic expressions as a set of algorithms and processes. As it turned out from the interviews, these people, when it is necessary to perform an operation on the algebraic expression and consider the algebraic expression as a whole, only memorize the steps as a parrot because they have no understanding of the whole structure of the algebraic expression; and they focus only on the steps within an algebraic expression. In complex algebraic expressions, compared to simple algebraic expressions, the percentage of students who had a purely procedural understanding was reduced. The results of interviews with a number of students showed that this decrease was not due to an increase in students' structural understanding, but for reasons such as ignoring the distributive action, not understanding algebraic expressions, not understanding the process in complex algebraic expressions.
Mathematics Education
E. Mohammadzadeh Chineh; H. Soltanzadeh
Abstract
Background and Objectives:Architecture training is to enable students to create three-dimensional spaces for human activities or to provide a better environment for human societies. Today, a wide range of different activities in the fields of skills, industry, creativity, knowledge, wisdom, are under ...
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Background and Objectives:Architecture training is to enable students to create three-dimensional spaces for human activities or to provide a better environment for human societies. Today, a wide range of different activities in the fields of skills, industry, creativity, knowledge, wisdom, are under the general title of "architectural education" in the schools of architecture. Typically, the curriculum in contemporary architecture schools is a set of basic courses that develop design knowledge, technology courses that develop the scientific formation of architecture; art courses to express architecture and finally design courses, which is a combination of the previous three and is the defining part of design education. The necessity of mathematics education and application of its concepts in architectural design is among major concerns of educational programs in universities and contemporary educational institutions. In architectural education in Iran, mathematics is delivered through traditional methods and independent from design practical courses. Moreover, mathematics is considered as a secondary course or sometimes an intricate problem in education. Professors of architecture always point to difficulties of students in understanding mathematical concepts and their application in structural design process. Methods and Materials: Therefore, the present study tries to compare the degree of attention to mathematics in architectural curricula in selected universities abroad and in Iran in order to provide a comprehensive knowledge regarding the place of mathematics in the curricula of these countries and prepare the ground for the development of an appropriate educational program incorporating mathematics in architectural education curriculum in our country. Findings: Comparative analysis of mathematics role in curricula of different universities and its targets via applied analytical-descriptive research method suggests that average mathematical courses provided in US architectural schools during the training course is 3%, in Asian countries 2.2% and in Iran 1.7%. The results emphasize the coordination of mathematical teaching methods with modern developments in design process and show that it entails mathematical knowledge delivered in the format of combined independent courses as preliminary, applied, technological and design. Conclusion: Mathematics courses and their teaching in architecture must be in line with new developments in the design process. This issue requires the definition of new courses in the field of mathematical application in architecture, mathematical history in architecture, as well as combined courses to transfer mathematical knowledge to design workshops. The subject of mathematics courses as independent preparation and basic courses for engineering students with the content of calculus, mathematics or their combination should be revised. This will give a new definition to the nature of the relationship between architecture and mathematics, as the role of mathematics in design was a priority in the Middle Ages. Considering the design workshop as the core of the architecture education program in the first and second academic year with an average of 40-36 credits per year, it is necessary to apply and new meaning of mathematics in introductory design workshops in two analytical-logical and structural concepts. Pay attention.
