فهرست مطالب ابراهیم ریحانی

This study is investigating the performance of junior high school students in solving proportional problems .gender, and school type on their performance in solving proportional problems. This study is applied and descriptive (survey type) in nature by considering purpose and implementation consecutively. The sample of this study was 442 of Qazvin city’s junior high school students who were chosen based on Randomized cluster sampling. The measurement tool was a questionnaire with five tasks related to proportional reasoning witch its content and face validity were examined by some of the mathematics professors and mathematics education professors. The Cronbach's alpha coefficient for the questionnaire proved to be 0.865 which shows an acceptable level of reliability. Data analysis was done using Spss 26 software and descriptive and inferential statistics methods. The analysis of the results showed that the students had a fairly good performance in solving proportional problems and their performance was evaluated in general at the level of proportional reasoning. Also, the analysis of data showed that there is a significant difference between the performance of students in 7th, 8th, and 9th grades in solving proportional problems, and with the increasing educational grade, their problem-solving performance will be increased.

In this paper, we investigate the Einsteinian manifolds with parallel null distribution. For this purpose, we first obtain the equations, which are known as Einstein's equations, that lead to finding the mentioned manifolds and then, we reduce Einstein's equations by using Lie symmetry method. In this method, we first obtain the generators of the symmetry algebra and then calculate the differential Invariants for each of the generators and calculate the group invariant solutions of this equation. We also obtain the optimal system of the one-dimensional sub-algebras of these equations which helps us to have a classification on group invariant solutions by using conjugate mapping.

The main goal of this research is to analyze changes in the dimensions of educational pragmatism in the function chapter of mathematics textbooks using a mixed (quantitative-qualitative) method. The study focuses on the "function" chapter of two textbooks: "Mathematics (1) 10th grade of the second high school Period" published in 2020 and "Mathematics (3) and (4) of the second year of the New secondary education system" published in 1997. The statistical population of the research consists of mathematics teachers who have taught the two mentioned textbooks, and the sample was selected non-randomly from available mathematics teachers and educational leaders. To begin, the content of the textbooks was analyzed using a quantitative method based on John Dewey's "educational pragmatism" theory. A total of 87 completed questionnaires designed as a Likert scale were analyzed and the questionnaire was adapted from Jarrah et al.'s research and localized. The reliability of the questionnaire was verified using Cronbach's alpha coefficient of 0.86. Following this, a qualitative method was used, in which a five-person expert group analyzed the contents of the chapters of the two textbooks under the four dimensions of pragmatism: usefulness, interest, experience, and integration. The expert group coded the results. The joint analysis of the questionnaire and coding showed that the textbook published in 2020 had a more favorable situation in terms of the components and dimensions of pragmatism compared to the textbook published in 1997. Finally, suggestions for future editions of the textbook are presented, with an emphasis on the experience dimension.

The training process has several stages, one of the most important of which is the evaluation of training programs. One of the new evaluation models that can be used as a qualitative tool in assessing students' level of learning is the solo evaluation model. The purpose of this study is to investigate the structure of learners' observable learning outcomes in physics by solving a test and evaluating their answers using the solo model. The method of this research is descriptive, survey type. The statistical population of this study is female high school students in Fardis city, from which 251 students of 10th, 11th, and 12th grade have been selected by multi-stage random cluster sampling. The results show that on average 82% of tenth-grade students, 65% of eleventh-grade students and 86% of twelfth-grade students of theoretical schools in Fardis city are at the Unistructural level and almost none which did not reach the high levels of solo, that is, the levels of relational and extended abstract.

Today, the concept of probability is not only used in different fields of science and daily life but also included in the school curricula of various countries, including Iran. However, teaching and learning the concept of probability is fraught with challenges, of which some are unique to probability itself such as the multifaceted nature of probability, which lends itself to different interpretations and meanings. Currently, the three basic interpretations of probability included in the school mathematics curriculum are classical, frequentist, and subjective interpretations. Despite the continued attention paid to different interpretations of probability in different studies worldwide, few studies have focused on this issue within the context of Iranian school curriculum. Therefore, considering the importance of textbooks in the Iranian centralized education system and the need to deal with different interpretations of probability in these books, this research aimed to analyze national mathematics textbooks taught in junior high schools in Iran based on classical, frequentist, and subjective interpretations of probability. The results are hoped to shed light on how much attention is given to each of the three aforementioned approaches in the mentioned textbooks.

Research Questions:

The research questions were as follows:1- How and to what extent is each of the classical, frequentist, and subjective interpretations of probability addressed in the seventh-grade high school math textbook?
2- How and to what extent is each of the classical, frequentist, and subjective interpretations of probability addressed in the eighth-grade high school math textbook?
3- How and to what extent is each of the classical, frequentist, and subjective interpretations of probability addressed in the ninth-grade high school math textbook?
4- How and to what extent do the mathematics textbooks designed to be taught in Iranian junior high schools deal with each of the classical, frequentist, and subjective interpretations of probability as well as the interaction between them?

This applied research utilized a quantitative approach. The data were analyzed through content analysis. The statistical population included seventh-, eighth-, and ninth-grade math textbooks (2021 edition), and the sample was selected purposefully and proportionately to the statistical population. A researcher-developed rubric was used to analyze the content of selected textbooks regarding the three interpretations of probability. The content and face validity of the research tool were confirmed by the authors of mathematics textbooks and several university faculty members in the fields of mathematics, statistics, and curriculum planning. To ensure the reliability of coding, the degree of agreement between the coders was assessed, and the results showed high a level of intercoder agreement.

The findings showed that 76% of the tasks in the probability section of mathematics textbooks taught in junior high schools were designed according to the classical interpretation, and the other two interpretations accounted for only 24% of the tasks, of which only 5% were related to the frequentist interpretation. This scant attention paid to the frequentist interpretation does not seem to be sufficient compared to the dominant presence of classical interpretation used in mathematical tasks. Additional analysis of the data showed that in the three above-mentioned books, only one task was designed with the aim of communicating the definition of probability.
Based on the findings, it was found that more than three-quarters of the tasks pertinent to the concept of probability in junior high school mathematics textbooks were designed according to the classical interpretation. The other two interpretations, namely, frequentist and subjective, were utilized in less than a quarter of all tasks. These results are in line with those reported by Gandhi (2022) in India and Martin et al. (2022) in Canada.

In explaining the results of this study, it can be said that no reliable scientific research has been done in Iran to introduce and examine different approaches and interpretations of probability and the relationship between them. Therefore, it can be concluded that the lack of in-depth research is one of the main reasons that has caused the imbalance in the presentation of different interpretations of probability in Iranian mathematics textbooks in junior high schools. Another main reason that can be cited for the above results is that content standards related to mathematical concepts, including probability, are not met in Iran. Accordingly, it is suggested that the authors of mathematics textbooks in Iran introduce all three interpretations of probability to students and ensure that all these three interpretations are reflected equally in tasks. Moreover, mathematics textbook writers are recommended to explain not only the importance and application of these approaches to probability but also how they are connected with each other. This is a crucial point because when students reach the next stages of their academic lives, i.e., senior high schools and university, the importance and application of frequentist and subjective interpretations increase in some cases. Finally, due to the fact that only few studies have been conducted on the concept of probability in Iran, it is suggested that more studies focus on how different approaches to and practical uses of probability can be included in high school mathematics textbooks.

The concept map becomes meaningful with the connection between the new concepts and the existing concepts in the cognitive structure. Using the concept map, the learners combine the contents and realize the internal connection between the concepts. In this sense, statistics is important as they help people interpret important information. The purpose of the effectiveness of the concept map is to identify misconceptions in the field of mathematics education from graphic literacy. The current research method is an interpretation of two quantitative and qualitative methods. The statistical population was all preservice mathematics teachers (PMT), 18 undergraduate PMTs and 15 master's PMTs were selected as the purposive sample. The PMTs of each level were divided into three groups. The PMTs of the first group completed the concept map and then answer the questions of the written exam and the second group first answer the questions of the written exam and then completed the concept map and the third group only answer the questions of the written exam. The PMTs of group 1 and 2 did not have the opportunity to return to the exam questions they did first and correct their answers. In order to evaluate the effect of using concept maps on PMTs' learning, all PMTs of the three groups answered one question called the total exam. To analyze the data, the one-way analysis of variance test was used for each group and as an average for all groups, as well as comparing the difference of the average scores of the groups in the written exam with Tukey’s post-test method. In the end, with the help of the concept map tool, PMTs' misconceptions were identified and classified into 4 categories, failure to correctly recognize the names of graphs, incorrect drawing of statistical graphs, failure to correctly recognize the type of variable and recognition of the appropriate graph for a data set. The research findings showed that the concept map identified the misconceptions of preservice teachers with better results than the results of the written exam. PMTs can use this method to teach different subjects, especially statistics in school, and improve the teaching-learning process and strengthen meaningful learning.

The purpose of this research is to investigate the statistical thinking of undergraduate student teachers in the field of mathematics education in the topic of diagrammatic literacy based on the framework of Wilde and Pfannkuch. For this purpose, a questionnaire including 9 diagram literacy questions (box diagram) was designed. The questions were classified based on the components of the Wilde and Pfannkuch framework. Questionnaire was completed by 50 student teachers of math education of Farhangian University of Education and Training of the director of Shahid Darjaei (boys and girls). The responses were leveled based on Watson's framework, which is a modification of Solow's model. The significance of the gender differences of student teachers was not confirmed statistically. The findings showed that most of the student teachers' answers in all statistical components are at the relational level, but the results showed the average performance of the student teachers in the components of statistical thinking in the topic of graph literacy.

The purpose of this study is to investigate the use of researcher-made examples by GeoGebra software as an educational tool to increase the learning skills of geometric theorems and assess the attitude of 11th-grade math students towards geometry and provide a practical model for teaching geometry.

 This research is a quasi-experimental type with an experimental group and a control group. It uses pre-test and post-test and is applied in terms of purpose. The statistical population of the present study included all-female high school students in the eleventh grade of mathematics in the districts three and four of Isfahan in the academic year 2021-2022. The statistical sample consisting of 120 students was purposefully selected using the available sample method. A pre-test of geometry course 1 as well as a three-scale Cattell intelligence test were administered to all groups in the same manner. A researcher-created questionnaire on a five-point Likert scale was given to all groups to assess the students' attitudes towards geometry before and after the research. The opinions of experienced education consultants and teachers were used to assess the validity of the questionnaire, and after correction, it was made available to students. The Cronbach's alpha coefficient was used to determine the reliability of the questions. Reliability was 0.93 indicating the high reliability of the questionnaire. The experimental group was taught how to use, construct simple shapes, and measure the components of shapes in GeoGebra via cyberspace, and their problems were solved by the researcher in five one-hour sessions.A researcher- created nine practical examples related to the sections of the circle and transformation sections in Geometry 2 using the opinions of five experienced professors and teachers, their answers were designed using GeoGebra software, and they were provided to the experimental group. Using this software, they guessed the components and checked their accuracy. The correct answers were then given to them. They also deduced the original form of the relevant theorems and demonstrated them. During this time, the control groups were given the contents of this section of the book in the traditional manner. The post-test was administered equally for all groups at the end of this period. The inferential part of SPSS 25 software, which included MANCOVA analysis, Kolmogorov-Smirnov test, Levin test, and M box test, was used to analyze the obtained data.

The results of MANCOVA analysis show that the use of examples made by GeoGebra software compared to traditional teaching has a statistically significant effect on students' ability to guess and learn geometric theorems. In addition, the questionnaire given to the students show that they value the use of GeoGebra to solve these examples and guess and prove the theorems related to them and have more motivation to participate in the geometry class.

According to the findings, the teaching method of proving a geometric theorem by using examples made by GeoGebra software increases the amount of learning in the classroom and increases students' motivation to learn geometry, and makes the classroom more attractive to them. This method increases students' creativity and causes them to be more involved in the learning process and becomes more active in the classroom, and these skills enable students and facilitate learning in the geometry classroom. There were some issues with the research. Some school principals, for example, refused to allow this method of teaching geometry. Some geometry teachers were also unfamiliar with GeoGebra software. In-service courses in this area are ideal for math teachers who want to help their students learn geometry more effectively and enthusiastically.

The purpose of this study was to investigate the mathematical creativity of tenth grade students using open ended problem posing in structured situations. The research method is descriptive of survey type. The participants in this study were 158 tenth grade gifted students in three cities in the south-east of Tehran province in the academic year 1399-1400. To collect the data, a researcher-made test was used, consisting of two open ended problem posing in structured situations (Stoyanova and Elrton). The validity of the test was confirmed by mathematics educators and experienced mathematics teachers. By using the criterion of Cronbach's alpha, this approximate reliability coefficient (0.71 and 0.82) was obtained. The result showed the math creativity score of the 10th grade students was 0.2082. The results indicated that tenth grade students have a low level of mathematical creativity. In fact, there was no sufficient situations for these students to encounter activities and tasks that enhance mathematical creativity, including problem-solving and ended problem posing in the classroom.

AbstractThe derivative is one of the most important topics in calculus that is used in various sciences.  One of the topics in this field is the interpretation of the derivative function graph with the help of its antiderivative function and vice versa. Research shows that because students understanding of derivative graphs requires high-level thinking skills, students have difficulty in understanding the relationship. The present study investigates the methodology and content of these studies to determine their underlying theory. This study is a descriptive study and qualitative meta-analysis method to show an insight into the coherence of these studies. The research field included all related research that were done by regularly searching for keywords and also by searching among citations of articles in national and international databases based on PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses). Based on the inclusion criteria, 182 studies were identified between 1992 and 2022 and finally, based on the exclusion criteria, 26 studies were selected for final review and analysis. The qualitative meta-analytic findings identified 13 main frameworks among the research that focuses on the three Krutetskii thinkers (analytical, visual, and harmonic), Dubinsky APOS (action-process-object-schema) theory and the three layers of graph disclosure (objects-relationships- functional relationships) is Swidan. The new method used in the qualitative meta-analysis of the present study can be used by researchers in different fields of education. Also, the findings of this meta-analysis for teaching and learning the relationship between the graph of the derivative function and its antiderivative function for teachers, and professors; will be useful for authors of textbooks and researchers.

Problem-Posing is one of the most important topics in mathematics education research today. One of the challenges researchers faces after investigating problem-posing skills and thinking processes is how to evaluate them. The present study investigated the content and methodology of these studies to determine their structure. This study presents a qualitative meta-analysis of the major frameworks that researchers have used to evaluate the posed problems in order to provide a comprehensive picture of how these studies have turned out. To this purpose, 25 studies on evaluating Problem-Posing Skills were selected from 83 research studies between 1994 and 2020 and analyzed descriptively and instrumentally. Students presenting a solution, adaptability, mathematical expression, linguistic knowledge and expression, solvability, quantity, and quality of data, Open-Ended and generalizable problems, solution strategies, and multiple solutions are among the nine common criteria identified by the meta-analysis findings. In addition, after reviewing the research, a framework with 11 criteria was created, with an emphasis on mathematical problem-posing and problem-solving. With the aid of generalizability theory, this framework has been validated by experts in mathematics and mathematics education, as well as teachers from all three grades, and has been evaluated in two stages.

The purpose of this study is to investigate the effect of Open-Ended probloms on the problem solving ability of 7th grade female students. This research is a quasi-experimental of pre-test, post-test type having a control group. The statistical universe of the study includes all 7th grade female students of Baghbaderan in the 1392-93 academic year. The sample consisted of 62 female 7th grade students in two, experimental (32 students) and control (30 students) groups that were selected using random method. Measurement tool of this study is three exams that were designed by researchers of this syudy, and their reliablity were obtained 0.79,0.81 and 0.80. First, both experimental and control groups took pre-test, then experimental variable (Open-Ended problems) was implemented to experimental group during 11 sessions in. In control group, same topics were trained using traditional method. Then the post-test was taken for two groups. Data analysis was accomplished by using descriptive statistic method (mean, standard deviation) and inferential tests such as analysis of independent t-test and Mann-Whitney Test. Results of t-tests demonstrated that mathematical problem solving abilities of students in experimental group are more than the students of control group.

The aim of this research was investigating understanding of Tehran’s second ‎elementary school students of the fraction concept (part-whole subconstruct) based on APOS and ‎SOLO theories. This study’s method was descriptive-survey ‎method, its statistical population was Tehran’s second elementary school students in the academic ‎year 1397-1398 and its sample was 598 people of the statistical population that selected by multistage sampling method. A test with an unusual task used for collecting data. The content validity of the research tools were confirmed by experts and scholars of mathematics education, and the reliability of the research tools was obtained based on Cronbach's alpha of 0.7. Results of this ‎study showed that students have a limited understanding of fraction’s concept and they have common misconceptions. The most common misconceptions ‎found include: (1) Disregarding the requirement of ‎equal parts in part- whole ‎subconstruct; 2- Understanding fraction in part- whole subconstruct as ‎the part-to-part ratio & 3- ‎Using approximate partitioning ‎to determine the exact fraction of the specified part.‎ Analyzing the responses based on the APOS theory also revealed students did not have ability to use this concept in dealing with unusual situations. In analyzing ‎the responses based on the Solo model, more than 60% of the responses were ‎in the multistructural level. The suggestions of this research ‎are not to over-emphasize the part -whole subconstruct, creating ‎equal opportunities for developing other subconstruct‎s of fraction and emphasizing on ‎conceptual learning of procedures and algorithms relative to fraction ‎concept in content and ‎opportunities presented to students.‎

In the turn of present century, dramatic changes have taken place in education and society. Among these changes, the change from an industrial to a knowledge-based society, the change from information technology and new information in various scientific fields, and the change in occupations can be mentioned. As a result, education has faced many shortcomings based on the level of the expectations of the society and its outputs. Due to the changes in the objective of the educational systems and the changes in the dimensions of people's lives, the teacher researcher paradigm has been considered by most teacher training systems in recent years, and that is why, it has led to some reforms in teacher training programs. The main and most important components of teacher training, curriculum, consists of goals, content, teaching method and evaluation. The present study explains the goals of the curriculum based on a teacher-researcher training at Farhangian University. The goals of the study are comprised of three areas of knowledge, competence, and attitude. According to the objectives of the study a mixed research method of the exploratory type was used which consists of two qualitative and quantitative stages. In the qualitative stage interpretive phenomenological method of data collection tool was used and In the quantitative stage, a descriptive survey method was utilized.

Inthe qualitative section, the research population comprised of the experts in the field of teacher training among which the appropriate instances were selected through targeted sampling and the required information was collected through a semi-structured interview. Theoretical saturation was achieved from interviews with 15 experts. In the analysis of the text of the interview the interpretive content analysis was used. To validate the data, credibility, transferability, reliability and validation were used. In the quantitative stage, the research population were the faculty members of different campuses of Farhangian University, among which four provinces were selected as the sample. The multi-stage cluster sampling method was used to select the sample and using Cochran's formula 274 people were selected among the faculty members of campuses and provincial centers. Data collection was done through a researcher-made questionnaire which was extracted from the qualitative part of the research. The data were analyzed by using a single sample T-test and Friedman test.

In this study, the goals of the curriculum were explained in terms of knowledge, ability and attitude. The results showed that the area of knowledge includes reflection, critical thinking, scientific expertise and research knowledge. The area of ability is comprised of the ability to perform research, to write, to be creative, to act systematically, to be independent and self-sufficient; and the area of the attitude includes interest in research and having no prejudice and stereotypes. The quantitative results of the study also showed that the components of attention and accuracy in relation to the issues of education in the field of knowledge, students' ability to self-assess; in the area of ability, and avoidance of prejudice and black and white thinking, and in the area of attitude received the most attention by the faculty members. There is clear evidence of a gap between the goals of the Farhangian University at the executive level in terms of knowledge, ability and attitude.

This study showed that the goals of the teacher taining curriculum need a general reformation at the executive level. It is important to pay attention to all areas of goals including knowledge, ability, and attitude and It is necessary to pay equal attention to all areas and to combine theoretical courses with the required practical work in teacher training programs. 

The main purpose of present study was to investigate the effect of teaching problem solving using drawing strategy on word problem Solving performance of seventh grade students. This study was fundamental in terms of purpose and in terms of implementation a quasi-experimental method using pre-test and post-test design with the control group. The number of students in the experimental group and the control group was 207 and 216, respectively. To determine reliability, in a implementation, the questions of both tests were performed on a sample of 30 students, and Cronbach's alpha of the pre-test questions was 0.81 and the post-test questions was 0.77, which was desired. Results showed that students usually use non-formal strategies to solve word problems. However, after learning the drawing strategy, they prefer to use this strategy rather  than problem-solving strategies. They also draw various shapes to solve problems. This means that the shapes are not unique, and students draw the shape according to their personal and previous experiences. In addition, using parametric t-test, the difference between the problem-solving performance of the experimental and control group students in the pre-test and post-test was significant, meaning that the experimental group students performed better in solving word problems.

The aim of this paper is to study the relationship between algebra content formation in mathematics textbooks and the mathematics teachers’ current knowledge. Based on this aim, we have considered three subjects: 1. mathematics teachers’ current knowledge of algebra, 2. the beginning and presentation methods of algebra content on the number of selected previous textbooks and 3.the role of previous textbooks content in teacher knowledge forming. Research Methodology had been a survey, content analysis, and historical and documentary analysis. This study showed that the teacherschr('39') knowledge and teaching methods do not coincide with the algebra content of the current seventh-grade mathematics textbook, and about 30% of teachers’ knowledge is based on the experiences of the previous textbooks.

This research was conducted with the aim of ‎investigating ‎Mathematical-Task Knowledge and Common Content Knowledge ‎of ‎elementary School teachers of fraction concept in Tehran province. The method of this study was ‎descriptive-survey method, its ‎statistical ‎population included the elementary School teachers in Tehran province ‎in the academic year 1397-‎‎1398 and its sample were 137 ‎people ‎selected by multi-stage cluster sampling method. In this study, a researcher-made test consisting of an unusual two-part task was used to examine the Mathematical-Task Knowledge and Common Content Knowledge ‎of ‎elementary teachers regarding the fraction concept.‎ The results of the study revealed that teachers do not have ‎suitable Mathematical-Task Knowledge and Common Content Knowledge of the fraction concept (part-whole sub-construct). ‎The overemphasis on part-whole sub-construct, lack of attention ‎to all aspects of part-whole sub-construct of fraction, and lack of ‎balanced attention to other sub-constructs of fraction concept in the ‎educational content of teachers and students can be part of the ‎possible causes of this weakness. Therefore, balancing the various ‎sub-constructs of fraction concept and disengagement from the part-whole approach in the educational content of teachers and students and improving elementary teachers' Common Content Knowledge and Mathematical-Task Knowledge through courses and workshops are the suggestions of this study.

Teachers need a variety of knowledge and competencies to teach mathematics well, and examining teachers' status of these skills and competencies can be a good area of research. One of the competencies needed by teachers is the competence of designing mathematical tasks. Mathematics task plays a key role in students' mathematics learning, and " what students learn is largely defined by the tasks they are given." There are various definitions of mathematics task in research literature. Watson and Sullivan (2008) define mathematics task as information that serves as the prompt for student work, presented to them as questions, situations, and instructions that are both the starting point and context for their learning. Various classifications for mathematics tasks have been presented so far. One of them is the classification of tasks according to the type of their function in the teaching process. In this type of classification, tasks are classified to 1- Warm up task; 2- learning task; 3- review task; 4- Practice task; 5. Assessment tasks. Assessment tasks are tasks that teachers use to evaluate students' performance, and because of the role and importance of assessment in the mathematics teaching and learning process, can play an important role in teaching and learning process. With considering the importance of the ability to design task, one of the appropriate situations that can study teachers' ability in this case by that, is the mathematical problem posing situation. Silver (1994) defines the mathematical problem posing as producing of a new problem from a situation or experience, new formulating of problems. Stoyanova and Ellerton (1996) classified problem-posing situations according to their structure into three categories: 1) free; 2) semi-structured; and 3) structured. A review of research literature revealed that one of areas deceived by researchers is examining relationship between teachers' task design ability and teacher' problem posing ability, and evaluating teachers' task design ability using problem posing situations. Accordingly, the present study aimed to investigate task design ability of new elementary Mathematics books’ provincial instructors based on ‎problem posing situations about addition and subtraction operations. The reason for this study of the two operations of addition and subtraction is the role and importance of these two operations in individuals' mathematical learning. Addition and subtraction is the foundation of school mathematics and has an impact on mathematical content across different grades. A descriptive survey method was used to conduct this study. The statistical population of the study consisted of the new elementary Mathematics books’ provincial instructors. 151 of whom participated in one of State Mathematics Supply Courses New Mathematics Textbooks for Elementary School were selected by convenience sampling. To collect the data. A researcher-made test was used in which their' assessment task design ability for two addition and subtraction operations was evaluated through the free problem posing situation. The posed problems by the participants were analyzed on two basis: 1) addition and subtraction and 2) task design. For the analysis of problems based on addition and subtraction operation axis, closed-ended symbolic problems were analyzed using Van de Walle et al. (2016) model and closed-ended verbal problems were analyzed using Riley et al. (1983) model. To analyze problems based on task design axis, symbolic problems analyzed regarding their open-ended and closed-ended responses and verbal issues analyzed based on 1- open-ended and closed-ended questions, 2- Shao (2018) model and 3- Shimizu et al. (2010) model. The results of the posed problems based on the addition and subtraction operations axis showed the problems that the teachers posed symbolically were more limited to the two forms of "unknown result (addition)" and "unknown result (subtraction)" and the problems presented in others formats were low (less than 10% each). The analysis of the verbal problems revealed that the problems were mostly in two modes of change and composition and percentage of problems in comparison form was very low (7%). It was also found that the verbal problems wasn’t not in the form of "Compare 6". The problems analysis base on the task design axis also revealed that very few of the posed problems (4% symbolic and almost 0% of verbal ones) were open-ended and most of them were closed-ended. The results of the verbal problems analysis revealed that although most of them had real-life contexts (89%) but there was no task designed to engage students in solving practical problems. The results also revealed that among the designed tasks, there was no task that was completely "authentic", "rich" and "complex", and although most of them involved students at the “application” level, they were tasks that link them With real life and application limited to mentioning an object or an event from the real world and not really contextual. On this basis, it can be concluded that most of them were low-level tasks. Given the impact of mathematics textbooks’ content on teachers' task design ability, it is suggested to improve the mathematics textbooks design capability so that the content of them can be modified to have necessary diversity generally in all topics and  specifically in both addition and subtraction operations. Another suggestion is enhancing teachers' task design ability, provide appropriate instructional content on mathematics tasks, and conduct empowerment courses and workshops based in these content. This study was conducted using convenient sampling method, so the results cannot be generalized to the statistical population. Accordingly, it is recommended that a similar study be conducted with appropriate sampling methods that can be generalized to the whole population. Another limitation of this study was that teachers were asked to design tasks for assessment. This can lead to limiting them in design of diverse tasks with regard to teachers' perception of assessment as final assessment. Accordingly, different studies are suggested to investigate ability of teachers to design task based on different tasks in mathematics teaching process.

The aim of this study, that was carried out in descriptive of the survey, is to assess the understanding and misunderstanding of the concept of probability eighth grade students. The samples of this study are, all eighth grade boy and girl students of Tehran province. The study sample,1330 eighth grade students in Tehran who were selected randomly. A random sample of 1330 students, from different public school. intelligence school, Shahed and perspicacious school randomly classified. and they were given 15 questions. which their validity has been studied by the number of math professors and teachers of mathematics and experienced math teachers. The reliability tests with Cronbach's alpha coefficien. 961 Was confirmed.After analyzing descriptive statistics, misunderstanding of the students were identified in seven groups as follow: lack of understanding rational numbers and its relationship to fractions, lack of understanding some of the concepts prerequisite, language problems, using their own methods to calculate the probability, inability to count all possible states, inappropiate generalization and the inability of the undrestanding of prerequisite problems.

Recent research by Rivera and Sinclair et al. Shows the impact of spatial abilities on achieving different goals in different fields of study and real life, and suggests the need to extend its learning to all levels of education. Traditional approaches to teaching geometry based on the classification of shapes and objects and their properties have been intuitively focused on ultimately formal proof. Currently, more emphasis is placed on spatial abilities such as mental rotation, representation of three-dimensional objects, and coordination of motion and position. Incorporating such abilities into textbooks plays an important role in students' understanding of the concepts of geometry. Structure of Observed Learning Outcome (SOLO) is one of the most practical theories that falls into the general and local frameworks of cognitive development. The importance of this theory is that it can assess students' understanding of a subject at all ages. The aim of this study was to investigate the ability of students' spatial skills in solving one task and to analyze their responses based on SOLO taxonomy. Solo theory is one of the theories of mathematical education, which has a great application in our cognition of mathematical understanding and math learning of students.

The research method is descriptive of survey type .A question of the Purdue standard questionnaire on spatial visualization has been selected which  its formal and content validity has been confirmed by 3 math education professors and 4 teachers of geometry. By using the criterion of Cronbach's alpha, this approximate reliability coefficient(0.9) was obtained.The participants in this study were 498 students from the tenth , eleventh and twelfth grade students who were  selected randomly in a multi-stage cluster of theoretical and technical schools in Bushehr.

The results show that in the field of visualization 59% of students in ordinary schools are in a unistructural level. In this regard, none of the technical students reached multistructural and relational levels. While analyzing responses, their thinking patterns, multiple solutions, strategies and common misconceptions have been analyzed. The results of the study are very important for the planners, the authors of the textbooks and the researchers.

The SOLO model helps teachers assess student learning outcomes and assess students' understanding. In order to improve students' understanding of spatial visualization and increase spatial skills, it is suggested that such issues be used in curricula and textbooks. The use of dynamic geometry and software is effective in better understanding spatial visualization, as shown by research by Demir and Ildiz. The use of the solo model is also suggested to researchers and teachers to assess students' understanding of a subject.

Recently, the National curriculum of Islamic Republic of Iran has been developed by the Ministry of Education to provide educational policies. In this document, an implicit emphasis on so called context base aspect of the program can be seen in the mathematics curriculum framework section. In this paper, I first, introduce the different aspects of context base Mathematics Education, and then this educational approach has been traced in the newly written mathematics textbooks in Iran.

The role of mathematics in various fields of science and technology and its usefulness in improving human life has been so effective and irreplaceable that it has been called the mother of sciences. Therefore, the development and improvement of mathematics curricula has always been on the agenda of curriculum planners. In such a way that these programs can provide more and more ground for the development of process, skills and attitudes of learners in mathematics and they lead to the growth and development of their understanding and logical reasoning. Therefore, achieving the goals of mathematics education should be monitored in different ways. International tests that are conducted for this purpose are designed and implemented to measure the mathematical literacy of students in participating countries and indicate the sensitivity of educational systems to the performance of students' mathematical performance. This paper evaluates the curriculum of 10th grade mathematics from the perspective of the respective teachers working in Tehran, Iran.

The research is based on Aker’s curriculum elements and it also has emphasis on the mathematics context-based approach. The method is descriptive background study. The tool for the research is a self-constructed questionnaire which has been validated with the content validation method. The Cornbach’s alpha test has been utilized to test the consistency of the questionnaire which resulted in value equal to 0.910. The statistics sample size is equal to people all of which has been working as teachers throughout the 2017 academic year. To attain samples, we utilized multistage cluster sampling that carried out on a sample of 111 respective teachers. One sample t-test was used to answer the research question.

The results reveal that the answer to the 6 research question were negative. That is, in curriculum of 10th grade mathematics have not been noticed to the context-based mathematical curriculum elements.

Evaluative studies are the bases of change and transformation of curricula. Changing math curricula to a performance-based approach and link of school mathematics to everyday life and students' experiences can reveal the usefulness of mathematics to them. In this way, the interest and motivation of learning in learners increases. Therefore, it is necessary to conduct other research in the theoretical dimension to formulate the theoretical foundations of this approach in accordance with the culture of the country, so that using these fundamentals, extract principles to design appropriate mathematics curriculum. Also, in practical aspect, it is suggested that the organization of the content of the tenth human mathematics textbook be changed so that the book begins with an issue of students' daily lives to help students recreate mathematical concepts. Changing the content organization requires taking the time to teach as well as educating teachers so that they can guide students during the modeling process. 

One of the most important concepts in mathematics, which has always been difficult for students to understand, is the concept of limit. Due to the connection of this concept to many other concepts such as infinitely large and infinitesimally small, continuity, derivative and integral, its correct understanding and comprehension is of particular importance and this has led to its teaching and learning by math educators. Although this concept has been explored many times in educational research by researchers, it is still difficult for students to understand. There are several ways to identify problems in understanding concepts, including the concept of limit. One of these methods is to study how concepts and structures are formed that students create to learn concepts in their minds. The aim of this study is to assess students, understanding of the concept of limit in the third year of secondary school based on the APOS theory. APOS theory is a theory of learning that is used in academic mathematics. The theory categories students’ understanding of concept across the levels, and is able to models mental structures that person to understand of the concept.

 Method and Materials: 

This research is a descriptive study using survey. The sample of this research is 234 students in third grade from Qarchak city who have been randomly selected. The instrument is a researcher-made questionnaire with six questions. The reliability of the test was estimated by Cronbach’s alpha and is approved in the amount of 0.82.

The results show that most students do not have a good understanding of the concept of limit and they mostly can do the limit problems correctly, if they have a routine way to solve them. The weak structures affect not only their understanding of the concept, but also depend on the understanding of the concepts such as continuity.

When introducing the concept of limit, the teacher can prevent the construction of correct schemas of the concept of limit by using slang and giving the initial idea. Because the role of the teacher in constructing a concept of limit is very important, if the teacher teaches in an inappropriate way, it may prevent the student from absorbing the concept of limit. Another reason for stopping the growth and development of the concept is the continuous evaluations in educational environments that do not emphasize the need for conceptual understanding of the concepts and are limited to routine methods to achieve better results. For this reason, doing research in the field of teaching and learning any concept in mathematics, such as the concept of limit, can lead to more effective teaching strategies.