University of Isfahan Mathematics and Society 2345-6493 4 2 2019 08 23 The role of computer games in mathematics education The role of computer games in mathematics education 1 9 24225 10.22108/msci.2019.115545.1316 FA Fatemeh Golfarshchi Tabriz, Tabriz Islamic Art University, Multimedia Faculty Journal Article 2019 02 10 Research indicates that the use of appropriate and content-rich games can play a significant role in education and learning for all individuals, especially children. Because games involve recreation and recreational activities play a significant role in acquiring various skills for understanding and learning different subjects and solving related problems, they can be used in education. Given the importance of mathematics at all educational levels and the existing problems in teaching and learning mathematics, the decrease in interest in mathematics, and the impact of computer games in addressing these issues, and the possibility of using new techniques and methods in teaching mathematics with the help of games, this article discusses the importance of educational computer games and their impact on the quality of teaching and learning mathematics, and examines studies conducted in this area. Research indicates that the use of appropriate and content-rich games can play a significant role in education and learning for all individuals, especially children. Because games involve recreation and recreational activities play a significant role in acquiring various skills for understanding and learning different subjects and solving related problems, they can be used in education. Given the importance of mathematics at all educational levels and the existing problems in teaching and learning mathematics, the decrease in interest in mathematics, and the impact of computer games in addressing these issues, and the possibility of using new techniques and methods in teaching mathematics with the help of games, this article discusses the importance of educational computer games and their impact on the quality of teaching and learning mathematics, and examines studies conducted in this area.

https://math-sci.ui.ac.ir/article_24225_14511f1e7df4cb48ee39c0644298cfdf.pdf

University of Isfahan Mathematics and Society 2345-6493 4 2 2019 08 23 How ancillary statistics can be Informative How ancillary statistics can be Informative 11 23 24233 10.22108/msci.2019.105827.1235 FA Mehdi Shams Isfahan, Kashan University, Department of Statistics Journal Article 2017 08 07 Ancillary statistics apparently do not provide any information about the unknown parameter, as their distribution does not depend on the unknown parameter. If a sufficient statistic is also complete, unnecessary information about the sample regarding the unknown parameter is eliminated, and in this case, the completeness of a sufficient statics leads to the greatest compression in the data. In fact, the complete sufficient statistic is independent of any desired ancillary statistic. In this article, it is shown that although ancillary statistics apparently do not provide any information about the parameter, when their joint distribution with a maximum likelihood estimator is considered, a minimal sufficient statistic is obtained. With this approach, lost information in the ancillary statistic is recovered, and ultimately, the ancillary statistic, combined with a maximum likelihood estimator, provides insightful information. It is also demonstrated that by conditioning on the ancillary statistics, there is a guarantee that no information about the parameter will be lost. In this case as well, conditioning on the ancillary statistics will be informative. Ancillary statistics apparently do not provide any information about the unknown parameter, as their distribution does not depend on the unknown parameter. If a sufficient statistic is also complete, unnecessary information about the sample regarding the unknown parameter is eliminated, and in this case, the completeness of a sufficient statics leads to the greatest compression in the data. In fact, the complete sufficient statistic is independent of any desired ancillary statistic. In this article, it is shown that although ancillary statistics apparently do not provide any information about the parameter, when their joint distribution with a maximum likelihood estimator is considered, a minimal sufficient statistic is obtained. With this approach, lost information in the ancillary statistic is recovered, and ultimately, the ancillary statistic, combined with a maximum likelihood estimator, provides insightful information. It is also demonstrated that by conditioning on the ancillary statistics, there is a guarantee that no information about the parameter will be lost. In this case as well, conditioning on the ancillary statistics will be informative.

https://math-sci.ui.ac.ir/article_24233_f55af2d94a2ea7d138a81086e7d69778.pdf

University of Isfahan Mathematics and Society 2345-6493 4 2 2019 08 23 On proofs of the lrrationality of the square root of 2 On proofs of the lrrationality of the square root of 2 25 45 24279 10.22108/msci.2019.119712.1345 FA Seyed Mohammad Amin Khatami Department of Computer Science, Birjand University of Technology, Birjand, Iran Ghasem Khakshoor Department of Basic Sciences, Birjand Girls' Technical and Vocational School, Technical and Vocational University, Birjand, Iran Journal Article 2019 10 18 This article reviews some of the most famous proofs of the irrationality of the square root of 2. Given the nature of defining irrational numbers, we will see that most proofs (except Proof No. 23) have been done either directly or indirectly using proof by contradiction. We have tried to mention cases that have the potential to be generalized to a proof for the irrationality of the square root of other numbers as well. Some proofs have been slightly modified to ensure clarity of the resulting text. Additionally, some new results have been obtained in certain cases. This article reviews some of the most famous proofs of the irrationality of the square root of 2. Given the nature of defining irrational numbers, we will see that most proofs (except Proof No. 23) have been done either directly or indirectly using proof by contradiction. We have tried to mention cases that have the potential to be generalized to a proof for the irrationality of the square root of other numbers as well. Some proofs have been slightly modified to ensure clarity of the resulting text. Additionally, some new results have been obtained in certain cases.

https://math-sci.ui.ac.ir/article_24279_55ca45e00515bb75d7cd8c94db25109b.pdf

University of Isfahan Mathematics and Society 2345-6493 4 2 2019 08 23 Montessori method as a basis for integrated mathematics learning Montessori method as a basis for integrated mathematics learning 47 56 24343 10.22108/msci.2020.114965.1313 FA Mahsa Mirzargar Faculty of Science, Mahalat Higher Education Center, Mahalat, Iran Mohammad Sajjad Reshadati Faculty of Science, Mahalat Higher Education Center, Mahalat, Iran Journal Article 2019 01 31 This paper is a translation of the the following paper into Persian: [J. Milinkovic and D. Bogavac, Montessori method as a basis for integrated mathematics learning, Metodicki obzori, 11 (2011) 135-142.] This research offers a theoretical comparative analysis of the Montessori Method and integrative teaching. Current trends call for incorporation of an integrative approach into educational practice. From the constructivists’ cognitive perspective knowledge is constantly changing, and results from acting and thinking. Maria Montessori developed an approach which is intellectually challenging and motivating. It develops a creative, flexible, authentic and constructive personality. In this paper we focus on theoretical aspects of both Montessori Method and integrative approach and look for compatible elements. We pay special attention to effects of the Montessori Method on development of mathematical aspects of reasoning. Our argument is that preschool Montessori Method has the capacity to become the basis for an integrative school approach. This provides a smooth move from early childhood learning to school learning. We point to the similarity of learning goals. Also, we pay attention to features of productive environments created within these two Methods for mathematics learning. In the light of the analysis, we suggest common features of the Montessori Method and integrated curriculum approach which have positive effects on mathematics learning. Finally, we draw some educational and curricular research questions. Our argument is that the Montessori Method presents natural prerequisites for integrated learning. We conclude that together they fulfil the social need for functional knowledge and holistic approach to a child’s development. This paper is a translation of the the following paper into Persian: [J. Milinkovic and D. Bogavac, Montessori method as a basis for integrated mathematics learning, Metodicki obzori, 11 (2011) 135-142.] This research offers a theoretical comparative analysis of the Montessori Method and integrative teaching. Current trends call for incorporation of an integrative approach into educational practice. From the constructivists’ cognitive perspective knowledge is constantly changing, and results from acting and thinking. Maria Montessori developed an approach which is intellectually challenging and motivating. It develops a creative, flexible, authentic and constructive personality. In this paper we focus on theoretical aspects of both Montessori Method and integrative approach and look for compatible elements. We pay special attention to effects of the Montessori Method on development of mathematical aspects of reasoning. Our argument is that preschool Montessori Method has the capacity to become the basis for an integrative school approach. This provides a smooth move from early childhood learning to school learning. We point to the similarity of learning goals. Also, we pay attention to features of productive environments created within these two Methods for mathematics learning. In the light of the analysis, we suggest common features of the Montessori Method and integrated curriculum approach which have positive effects on mathematics learning. Finally, we draw some educational and curricular research questions. Our argument is that the Montessori Method presents natural prerequisites for integrated learning. We conclude that together they fulfil the social need for functional knowledge and holistic approach to a child’s development.

https://math-sci.ui.ac.ir/article_24343_d387056ca59dc196575ef85d6072a78a.pdf

University of Isfahan Mathematics and Society 2345-6493 4 2 2019 08 23 How high school mathematics teachers use the history of functions into their teaching How high school mathematics teachers use the history of functions into their teaching 57 66 24411 10.22108/msci.2020.118430.1333 FA Abolfazl Rafiepour Department of Mathematics, Education Faculty of Mathematics and Computer Shahid Bahonar University of Kerman, Maryam Mohseni Kerman - Zarand - Zarand Education Department Journal Article 2019 07 27 The concept of a function is one of the fundamental concepts in school mathematics, serving as a unifying idea throughout mathematics. Functions are the primary tools for describing the real world in mathematical language. Almost all students who go through units of mathematics in their academic curriculum become familiar with the concept of a function. However, various research studies indicate that many students have a weak understanding of the concept of a function. The main objective of this article is to depict the historical development of the concept of a function over time and then examine how a group of mathematics teachers in Kerman province teaches it. In other words, this article seeks to address the question of how high school mathematics teachers teach the concept of a function and whether their teaching approach aligns with any historical perspective. The participants in this study are 20 high school mathematics teachers in Kerman province who were selected purposively. The results obtained from classroom observations showed that the participating teachers mostly did not incorporate the historical development and formation of the concept of a function into their teaching. They typically began teaching functions with a formal definition and after presenting a few examples, enumerated the properties of functions. Additionally, the analysis of the study's data indicated that the concept of a function was presented based on the latest recognized representation of functions, namely based on the correspondence approach between sets (ordered pairs). The concept of a function is one of the fundamental concepts in school mathematics, serving as a unifying idea throughout mathematics. Functions are the primary tools for describing the real world in mathematical language. Almost all students who go through units of mathematics in their academic curriculum become familiar with the concept of a function. However, various research studies indicate that many students have a weak understanding of the concept of a function. The main objective of this article is to depict the historical development of the concept of a function over time and then examine how a group of mathematics teachers in Kerman province teaches it. In other words, this article seeks to address the question of how high school mathematics teachers teach the concept of a function and whether their teaching approach aligns with any historical perspective. The participants in this study are 20 high school mathematics teachers in Kerman province who were selected purposively. The results obtained from classroom observations showed that the participating teachers mostly did not incorporate the historical development and formation of the concept of a function into their teaching. They typically began teaching functions with a formal definition and after presenting a few examples, enumerated the properties of functions. Additionally, the analysis of the study's data indicated that the concept of a function was presented based on the latest recognized representation of functions, namely based on the correspondence approach between sets (ordered pairs). https://math-sci.ui.ac.ir/article_24411_9e751e2f18404a6ee7f19e187a837b2c.pdf

University of Isfahan Mathematics and Society 2345-6493 4 2 2019 08 23 Ranking methods in sports teams Ranking methods in sports teams 67 81 24363 10.22108/msci.2020.118609.1334 FA Efat Golpar Raboky Qom, University of Qom, Department of Mathematics Maryam Nedaee Qom, Qom University, Department of Physical Education and Sport Sciences Journal Article 2019 08 05 Ranking is a general order relation, a relationship between elements of a set in which one element has a higher rank than another. Ranking establishes an ordering of scores in such a way that the first element has the highest score and the last element has the lowest score. A sports scoring system is a system that analyzes the results of sports competitions to assign scores to each team or player. Various ranking methods have been proposed, their performance based on the points teams earn in different games. Some of these methods rank teams based solely on the number of wins and losses, while in some ranking methods, the situation of the rival team is also considered in scoring. In these methods, wins and losses against weak and strong teams are not valued equally. If a team's victories are only against weak teams, it cannot be confidently said that this team is strong, and necessarily, the number of wins cannot demonstrate a team's superiority. There are various methods for ranking teams, using statistics, graph theory, and linear algebra. In this article, we discuss some ranking methods that mostly utilize linear algebra concepts. In this regard, we examine methods such as percentage of wins, ranking percentage index, Massey method, Colley method, Keener method, defense-offense method, and the page-rank method. We illustrate the results of ranking with these methods through an example. Ranking is a general order relation, a relationship between elements of a set in which one element has a higher rank than another. Ranking establishes an ordering of scores in such a way that the first element has the highest score and the last element has the lowest score. A sports scoring system is a system that analyzes the results of sports competitions to assign scores to each team or player. Various ranking methods have been proposed, their performance based on the points teams earn in different games. Some of these methods rank teams based solely on the number of wins and losses, while in some ranking methods, the situation of the rival team is also considered in scoring. In these methods, wins and losses against weak and strong teams are not valued equally. If a team's victories are only against weak teams, it cannot be confidently said that this team is strong, and necessarily, the number of wins cannot demonstrate a team's superiority. There are various methods for ranking teams, using statistics, graph theory, and linear algebra. In this article, we discuss some ranking methods that mostly utilize linear algebra concepts. In this regard, we examine methods such as percentage of wins, ranking percentage index, Massey method, Colley method, Keener method, defense-offense method, and the page-rank method. We illustrate the results of ranking with these methods through an example.

https://math-sci.ui.ac.ir/article_24363_813293d9194c2ac94a0d2f93a9268169.pdf