احمد شاهورانی

Fallibility and Certainty of mathematics in the perspective of DeductivismAbstractThis research shows that fallibility, with all the transformations it has created, is flexible to some extent, and it is possible to establish a relationship between it and the certainty of mathematical concepts. This possibility is done through the revival of analogy. The distinction between pure and applied mathematics leads to an indisputable form of mathematical fallibility, especially in pure mathematics. Moreover, this distinction fits well with analogicalism. Because according to Einstein's attitude, although it is not possible to prove mathematical certainty in reality, it is possible in pure mathematics. As a result, analogism with the aim of proving theorems and mathematical concepts can eliminate some possible errors in mathematics, and corrections are integrated into analogism, and fallibility claims are recounted in their non-controversial forms. 

Ability to relate all the essential features of a situation in the form of zooming in or out represents thought in a relative form. The emergence of relative thinking, is the prognosis for the beginning of building a bridge to fill the gap between collective and multiplicative structures. Relative thinking is a cognitive function that describes the ability to analyze the change in relative conditions. The ability to lead and work with qualitative aspects leads to the strengthening of quantitative proportional thinking. Studying the quality of teachers’ perception is a perspective of how learners create and develop conceptual structures. With the aim of determinning the qualitative characteristics of knowledge of content pedagogy of qualitative proportional reasoning, this study examined the knowledge of related representations among the research participants. It was a descriptive study with survey design. The research sample consisted of 180 primary school teachers, first cycle high school math teachers and student-teachers. The research tool was the researcher-made test and the evaluation was done under the framework of the theories of this field through a mixed-methods analysis. Based on the results, the closeness of the performance of student-teachers and the primary school teachers could be pointed out, i.e., almost half of each of these two groups had a successful performance. The most correct interpretations were presented by high school teachers, student-teachers and primary school teachers, respectively.Paying attention to the preliminaries and necessities of the process of developing proportional reasoning by teachers, deepening its investigation by researchers and demanding it in the educational designs of teacher training centers were emphasized by the researchers of this study.Regarding the training of future teachers, developing sensitivity to the consequences of the delay in the emergence of students' proportional thinking is necessary.

Metaphors are powerful tools, which are used to present teachers' attitudes about mathematics and reflect their experiences. Teachers' metaphorical perception can make many educational events more tangible in order to examine the current status of education. Previous studies asked provident teachers to provide metaphors for teaching mathematics and to use these metaphors to understand their attitudes about mathematics. On the other hand, these days, educational technologies have rapidly created new opportunities for meaningful education of mathematics. Therefore, the role of teachers in integrating education and technology is getting more and more important. Frequent use of technology, in almost every aspect of our lives, requires a change in the content and nature of school math programs, and it is important for students to use computers to increase their understanding of math concepts as they change. The use of computers in educational programs should be supported. Since the interpretation and explanation of teachers' attitudes toward the field of technology is important in teaching-learning, metaphors are used to compare mere and common interpretation. The National Council of Teachers of Mathematicshas stated that the use of technology is an appropriate method in mathematical reasoning, expression, problem solving, and effective communication. Moreover, the use of computers in educational programs should also be supported. Therefore, the main purpose of the current study based on the instrumentation method was to standardize the metaphorical perception scale of the effectiveness of mathematics education software in the teaching-learning process from the perspective of mathematics teachers.

The research method was descriptive and the method entailed instrumentation and standardization. Using two-stage cluster sampling method and Morgan table, 198 male and female math teachers working in all primary and secondary state and non-state secondary schools in 1, 2, 3, 4 education districts of Tehranwere selected as the participants. Researchers prepared and designed a questionnaire with 44 items based on theoretical basics and related technologies in the field of mathematics education. In the first stage, CVI and CVR content validity indices were examined.

After two stages of distributing questionnaires among eight experts in the field of education and technology of mathematics, the results showed that some items were removed due to not reaching the standard level. Finally, 28 items according to the components in the questionnaire were approved.The questionnaire was then distributed among math teachers in virtual networks.The results of reliability and exploratory factor analysis confirmed four factors with 26 items and the reliability value of each factor was proved and recordedbetween 0.78 and 0.94.Four main factors were identifiedincluding a metaphorical understanding of access and acquaintance, skill and mastery, interest, attitude, impact and application in the use of mathematical software.

The results of this survey and tooling based on the views of math teachers showed that the four mentioned factors were very important in the efficiency and application of math education technologies and software in middle school teaching. Determining and explaining such factors can lead to a more detailed examination of the challenges and resources available in the preparation and distribution of mathematics education technologies in schools.

Teachers 'beliefs and ideological structures are one of the main axes of educational research in order to achieve reforms in teachers' teaching methods. There have been several experimental studies on the beliefs of math teachers that have helped to conceptualize and define beliefs and convictions. In a study titled "Developing Teachers 'Beliefs Through Online Education: A One-Year Experience of Teachers' and Scientific Teachers 'Beliefs in Learning and Teaching" by Wong, Wong showed that teachers' beliefs in using online education are influenced by the years of teaching. Skemp, In his study introduced two types of beliefs about mathematics: instrumental mathematics and relational mathematics. Mohammadi and Mosalaei, in a study entitled "Assessing the Beliefs of Selected Math Teachers in the Country Based on Their Demographic-Cognitive Characteristics" showed that teachers' beliefs about the process of updating their professional competencies in teaching increased; Their responsibility for their professional behavior increases. With the advent of new technologies, math teachers have also turned their attention to using a new framework to integrate technology knowledge with pedagogical knowledge and content knowledge. The main aim of the current study was examining the effect of mathematical education on the basis of the content-pedagogical and technological model (TPACK) on changing the beliefs of high school teachers regarding the rate of application of mathematical education software in the teaching process.

The researcher used a semi-experimental two-way pre-test and post-test method to observe the changing beliefs of teachers before and after the implementation of a workshop training in software. The statistical population of this study is all high school math teachers of North Khorasan rovince. Based on Cochran's formula, 73 of them were selected by cluster sampling and were divided into two groups: control (n=33) and experiment (n=40). The standard questionnaire used in this research was made by Zambak (2014), based on the theoretical framework. Data were analyzed by SPSS software and covariance analysis was used to test the research hypothesis.

The results of statistical analysis of this study showed that the holding of a mathematical training workshop using GeoGebra in the form of a "content-pedagogical and technological model (TPACK)" has had a positive impact on the beliefs of high school math teachers about using modern technologies in education. The study's findings also show that some math teachers, while adopting technology as a useful teaching tool for classrooms; But they are concerned about misplaced technology interference in the understanding of a mathematical subject and, therefore, are not encouraged to use technology in their classroom, and allow it only as an informal educational activity.

According to the findings of this study, it can be concluded that the development of knowledge and change of math teachers' beliefs about using up-to-date technologies in mathematics teaching based on school facilities and limitations of educational organizations in different provinces of the country is very important. It is suggested that the decision makers in this field, by discovering and identifying talented teachers in different parts of the country, offer short-term and long-term training to enhance their ability to improve the overall level of mathematics teachers in the country.  

 

This paper describes two proposed strategies for involving families in mathematics education and forming a mathematical association for parents with the aim of involving parents in their children's mathematics education, implemented at one of the Tehran schools, describing the outcomes and performance of students before and after school. They were analyzed using Data Envelopment Analysis (DEA).Data Envelopment Analysis (DEA) is a linear programming method whose main purpose is to compare and evaluate the efficiency of a number of similar decision-making units, to compare and analyze them with different amounts of inputs and outputs.In this research, inputs on various aspects of cultural, social, and economic conditions (such as family income, physical and mental health of family members, parents' occupation, etc.) of families of sixth grade elementary school boy students in TALAYEDARAN school, district 4 of Tehran, and outputs The success of the math test is the interest of the students in these math activities in math lessons and ethical discipline

Students with math disorders have problems with cognitive functions in addition to educational problems. Today, math skills are one of the basic skills that helps a person to succeed in many daily routines. Children usually learn basic math skills in the first years of primary school. Some of these children despite their natural intelligence have difficulty in acquiring these basic skills and are often identified as children with malfunction. According to some researches, roughly 6% of primary school students suffer from math disorders. Their mathematical score is constantly lower than 80 percent of their classmates while their IQs are often within the natural range. In order to provide educational methods and appropriate treatment processes for students with math disorders, some researchers want to recognize the defective cognitive function in these children. Probably, cultural–social and hereditary differences, as well as differences in the educational practices of Iran impact on the disorder in our country. Regarding the existing history, poor performance in general cognitive skills can be cause of motility disorders especially in elementary students. Therefore, the present study aimed to investigate general cognitive functions in Iranian students with math disorder and compare them with their normal peers.

The research method was causal–comparative. The statistical population of this research was all students of the first elementary school of high population and governmental schools (about 1500–2000 students) in the Kerman city (Kerman province, Southeast of Iran). The primary sampling method was to select the two schools with the highest population among the elementary schools and then select the research sample by referring to them. Since this research was a comparative study, in order to determine the number of suitable samples in each group, a researcher–made mathematical test was performed for all students. Then, students who achieved score less than 80% of all students were separated, and video subjective tests and vocabulary of Wechsler adult intelligence test were applied to them. Among these students, those who showed normal and proportional scores to their age in these sub–tests were selected (40 of them were selected by simple random sampling method). These students were considered as the sample group of students with math disorders (with normal IQ) for the next steps. Other students who achieved score more than 50% of all students in the math test researcher, 40 students were randomly selected as normal students. In order to ensure the intelligence status of this group and to make it proportionate to the group of people with mental disorders in terms of intelligence, video arts subtasks and Wechsler vocabulary were also conducted on this group. The research instruments were Wexler's intelligence test for children and active acoustic memory tests, visual–spatial memory and long–term memory. Data were analyzed using mean, standard deviation, ANOVA and independent t–test.

There was a significant difference between the cognitive functions of students with math disorder and normal students in the first period of primary education at the level of (p<0.001). Cognitive functions were more common in math disorder students than in primary school normal students.

General cognitive skills are a prerequisite for math learning and authorities have to plan for these skills in order to prevent any learning problem in children. In addition, the results of this study show that general cognitive skills, especially active memory and information processing speed have a supporting role in the ability to learn numerical computing. Therefore, before the formal training of numerical calculus was begun. Student with the disorder should refer to the relevant specialists to undergo specific training.

In this paper, the importance of the mediator role of higher order mathematical thinking skills in financial affairs in relationship between lower order mathematical thinking skills in finance and empowering financial employees was investigated from employees' viewpoint in Iranian banks. After reviewing the skills, the employees’ attitudes were examined by a researcher-made questionnaire. The research method is descriptive-correlative. In order to data analysis and hypotheses testing, structural equation modeling was used. The results showed that from the perspective of participants, lower order mathematical thinking skills in finance, has directly a positive and nonsignificant effect, and indirectly a positive and significant effect on professional skills of financial staff in banking; while higher order mathematical thinking skills in financial affairs has a direct and significant effect on the skills. Due to higher order mathematical thinking skills in finance, overall effect of lower order mathematical thinking skills in finance has greatly increased. The results showed the participants believe that the higher order mathematical thinking skills in finance are more effective than the lower order mathematical thinking skills in finance. According to the importance of higher order math thinking, we suggest some recommendation to bankers and educators.

In this paper, mathematical applications in balance-sheet management were examined, based on mathematical word problems, to provide asset-liability management reporting in a developmental bank. After reviewing the importance of balance-sheet management in banks, introducing development bank, the literature ant theoretical basis about mathematics word problems and applications of mathematical modelling in assets and liabilities management, two case of word problems (arithmetic and algebraic) were examined in balance-sheet management in which mathematical representing and modelling were used to solve problems, respectively. Then the results were interpreted in financial field. The results revealed mathematical representing and modelling helps to interpret balance-sheet information for managing assets and liabilities in a developmental bank. Regarding the results, balance-sheet management can be observed from the perspective of mathematical word problems. Therefore, it can result a more accurate interpretation of balance-sheet data in banks, based on accurate expressing mathematics and analysing problems in the real world. This sheds light on the necessity of giving attention to mathematical applications in balance-sheet management. Finally, it is recommended that in future research, conceptual understanding mathematics examine in solving word problems as balance-sheet management among users in such a way that understanding those concepts led to an increase in applying mathematics in finance affairs and consequently, accurate analysis and evaluation of financial data.

Decimal numbers are one of the basic issue in school mathematics. After introducing Decimal numbers to students in elementary course, they are usually used as one of the important concept as generalizable tool in upper grades and they play important role in mathematics. In this research, inferential (contingency table) and descriptive statistics are used for analyzing data.The aim of this research is to study, categorization and comparing the students’ misconceptions in comparing decimal numbers. The sample in this research consists of 103 students in 6th, 7th and 8th grade, chosen from the available statistical population. The data were collected by using “Decimal comparison tests” and answers were analyzed in accordance with the assigned criteria. According to the achieved results relating to the misconceptions of Decimal numbers comparison, the 8th grade students had the most amount of misconception in comparison with the 6th and 7th grade students and statistically there was a meaningful deference between the results. Showed that most discovered misconceptions in other research works, also showed themselves in this research. Meanwhile, misconception expands as the student’s progression the course. In addition, a pattern is introduced for discovering misconceptions of Decimal numbers comparison by the help of previous research conducted by others mentioned in the literature.

The total purpose of this research was investigation of effective traits in interpersonal relationship of math teachers and students with math learning. Statistical sample of this research included 79 high school freshman students of Tehran city and 67 teachers in 2008-2009 academic year, selected by branch method through high schools of zones 3, 6,10,16 and 17. Correlation descriptive method was used to analyzed data. Measurement tool was a researcher designed questionnaire, based on effective traits of interpersonal relationship (openness, empathy, supportiveness, positivism and equality). The validity of the questionnaire based on Cronbach alpha was 0.959. Frequency table and the t-test were used by SPSS software for analyzing the data. The research results showed that there was no meaningful difference between math teachers and students effective traits of interpersonal relationship. Also female math teachers had a better interaction with students by using effective traits of interpersonal relation than male math teachers and in math learning girls were more successful than boys. There was a positive and meaningful correlation among effective traits of interpersonal relationship with math learning.