فهرست مطالب منصوره موسی پور

Problem posing is one of the most important topics in mathematics education. Researches show that teachers' use of problem situations in classrooms and students' ability in this field are not desirable. Considering the important role of textbooks in mathematics education, the aim of the present research is to investigate and analyze the content of mathematics textbooks of the second secondary school in terms of problem posing.
This research is of a qualitative type and its statistical population is all mathematics textbooks of the second year of high school theoretical fields in the academic year 2023-2024. Content analysis was done by the Krippendorff method. First, the keywords that support the design of the problem were determined and then identified in the textbooks. The theoretical framework of Stoyanova and Ellerton, which divides the problem setting situations into three categories, free, semi-structured and structured, was used in this research. Based on this framework, the entire content of the books was examined. Then the situations of the problem were identified and separated based on the three stated situations. The frequency of each situation was calculated and data analysis was done.
The results of the research showed that in the 13 reviewed books, there are 75 situations of problem posing, of which 90.6% are semi-structured situations. The twelfth grade math and physics math book had the most problems with 16 positions. Also, in all the books, the semi-structured problem design had the highest percentage of problem posing.
The result of the analysis showed that little attention has been paid to the activities of problem posing by the authors. Considering the importance of these activities, increasing them quantitatively and qualitatively by the authors can help to solve this deficiency.

In this paper, we prove that these C0-semigroups exist on every infinite-dimensional Banach space. It is shown that C0-semigroups can be constructed on finite-dimensional Banach spaces and with respect to finite-dimensional subspaces. We define subspace-recurrent vectors for C0-semigroups and state that any C0-semigroup that has a dense set of subspace-recurrent vectors is subspace-recurrent. Moreover, we prove that any recurrent C0-semigroup is subspace-recurrent. Also, some sufficient conditions for subspace-recurrency are proved that are based on dense sets and open sets.

In this article, the new concept of disk-recurrent operators is introduced. We prove that an operator is disk-recurrent if and only if it has a dense set of diskrecurrent vectors. We prove that these operators can be found in infinite dimensional and also finite dimensional Banach spaces. In addition, we show that the operator T is disk-recurrent if and only if T n is disk-recurrent. We also observe that if the diskrecurrence of the direct sum of two operators is disk-recurrent, then any of them is disk-recurrent and we express some results about this.

A palpable example for a one-to-one Thomae-type popcorn continuous function of the real line is constructed.

In this article, we state some sufficient conditions for an operator to be subspace-chaotic. The properties of the direct sum of operators are interesting topics in operator theory. In this paper, we show that the direct sum of the two subspace-chaotic operators is subspace-chaotic with respect to at least two subspaces, and the same is true for the subspace-transitive and subspace-hypercyclic operators. We also make interesting examples of these operators with the help of the stated theorems. In addition, we prove that if the direct sum of two operators is subspace-chaotic or subspace-transitive, then each of those two operators is subspace-chaotic or subspace-transitive, respectively. We also generalize these results to the direct sum of a finite number of these operators.

Trigonometry is one of the basic and widely used concepts in mathematics, other sciences, and life. Students may be face misconceptions in learning trigonometry that prevent them from fully learning the lesson. Identifying these misconceptions and avoiding them is essential. Teachers have an important and critical role in addressing and preventing them and can be efficient to help students to improve their learning. In this article, we explore some of the misconceptions that arise for high school students when learning trigonometry and related topics. The article also offers solutions to this misconception, including the use of appropriate teaching methods, the use of tools such as calculators and mathematical software such as GeoGebra. We explain that how teachers can use these methods. In addition, the use of concept maps is recommended as another way of resolving misconceptions. We explain that concept maps can be used both in teaching and in assessing students.

Misconceptions in mathematics make it difficult for students to learn. Identifying these misunderstandings and finding ways to solve them can help teachers take constructive steps to improve student learning And it helps students learn better from math lessons and become more interested in learning math. Fractions are one of the most widely used concepts in elementary mathematics. Students deal with fractions and related operations at almost all elementary school math levels. In this article, we examine the misconceptions that elementary school students encounter in learning fractions. We also offer two solutions to deal with misconceptions. Multiple representations are introduced as one of the solutions to eliminate the misunderstandings of the fractions and some examples are provided in this regard. Also, Bybee teaching method, which is one of the learner-centered teaching methods, is suggested as another solution to eliminate misunderstandings in the field of fractions, and it is explained by giving examples.

Problem-solving is one of the most important pillars of mathematics education and as one of the most important goals of mathematics education at school, it is of great interest to teachers and practitioners. Problem-solving skills in mathematics are among the most important skills of learners. Some learners become frustrated with math problems due to their lack of familiarity with problem-solving skills, but teaching students problem-solving strategies can help students with problem-solving skills. , Improve and give them more motivation to learn math and make them more empowered in this lesson. Therefore, strategies that enhance students' problem-solving ability in mathematics should be taken into consideration by educators, and this Teach them strategies. This article describes some of these strategies and discusses five strategies: brainstorming, concept mapping, meta-cognition, and KWDL strategies that are effective strategies to improve problem-solving ability, and the benefits of each. We explain the strategies and how they are implemented in the classroom.

Argumentation and proof are important and valuable aspects of mathematics. Without realizing the arguments and proofs, the full understanding and understanding of the students of mathematics will not be realized. Understanding the methods of reasoning makes students more aware of mathematics and its beauties and develops their rational thinking and makes students do not look at mathematics as a mere procedural knowledge. Mathematicians have proven worthwhile arguments and arguments that are not worthy of consideration. In this article, the views of some mathematicians and mathematicians on the reasoning and the proof of its importance and necessity are expressed. Arguments are also described along with examples. Among the methods of reasoning that we are discussing in this article are: intuitive understanding, allegorical reasoning, inductive reasoning, mathematical induction, deductive reasoning, and the method of posterior argument. In this paper, each of them is defined and described, and the strengths of each one are expressed.

The purpose of study is to analyze the content of the mathematical books of the 12th students in Mathematical and Physical branch published in 1397, which includes Geometry (3), Discrete Mathematics and Calculus (2). In this research, the problems in exercises and work in the classes and activities in these books, according to the five categories of modeling and application areas, namely "without background", "unreasonable circuit background", "background field" Independent of the field "," Standard application "and" Modeling "were reviewed and coded. The results of the study showed that uncontrolled issues constitute a high percentage of the studied issues. So that 99% of the issues in the book of geometry (3), 75.18% of the discrete mathematical questions and 92.22% of the book of calculus (2) were unconditional, and after them, the questions " Independent of the field "and" standard application ". In Geometric books (3) and discrete mathematics, there were no questions "unreasonable circuit background", but 68.6% of the questions examined in the of Calculus (2) were in this category. Also, none of the surveyed questions was in three books on "modeling", which is indicative of the lack of consideration of the modeling approach and applications in these three books.

The purpose of this study is to analyze the content of the new book of calculus (1), the eleventh-grade of the secondary school, published in 1396. Using the William Rummy technique to examine the activity-centered nature of the text and pictures of the book, the analysis of activities, work in classes and exercises, based on the Bloom's cognitive domain, has been done. The statistical population of this research is the book of calculus (1) published in 1396. The results of the study showed that the students' conflict ratio is 1.27. This means that the text of the book is active according to William Rummy technique. The conflict factor was obtained with images 3 that shows that images are not suitable based on the William Rummy technique and is actually over-active. In the analysis section of activities, work in classes and exercises, based on Bloom's cognitive domain, it was determined that the level of perception and understanding with 47.89% had the highest percentage of attention. The level of knowledge, application, and analysis has also been well received, but very low attention has been paid to two levels of cognitive domains, the combination, and evaluation.

Textbooks play an important role in shaping the national identity of students. The purpose of this research is to examine and analyze the national identity in the mathematical book (1) of the 10th grade of the secondary school. The method of research is quantitative and qualitative content analysis. The information gathering tool includes a checklist in content analysis, and the analytical unit is themed. The dimensions of national identity in this research are the symbol, value, cultural heritage, celebrities and characters, events and happenings. The statistical population of the mathematical library (1) is the 10th grade of the secondary school (mathematics and physics and experimental sciences) in 1396-1395. The results of the qualitative analysis show the emphasis on national values, attention to places and buildings in the cultural heritage, and the low use of hadiths, verses, literary order, and the lack of attention to economic values and contemporary celebrities. According to the results of the quantitative analysis, 132 references to the concept of national identity are mentioned in this book. Among the dimensions of national identity, the dimension of national values with 42.31% of the highest frequency of events and happenings with 0/76% have the lowest frequency.