A CHARACTERIZATION OF U4(2) BY NSE

‎Let $G$ be a finite group and $\omega(G)$ be the set of element orders of $G$‎. ‎Let $k\in\omega(G)$ and $m_k$ be the number of elements of order $k$ in $G$‎. ‎Let $nse(G)=\{m_k|k\in \omega(G)\}$‎. ‎The aim of this paper is to prove that‎, ‎if $G$ is a finite group such that nse($G$)=nse($U_4(2)$)‎, ‎then $G\cong U_4(2)$

DOMINATION NUMBER OF TOTAL GRAPH OF MODULE

Abstract. Let R be a commutative ring and M be an R-module with T (M ) as subset, the set of torsion elements. The total graph of the module denoted by T (Γ(M )), is th

Some classes of perfect strongly annihilating-ideal graphs associated with commutative rings

summary:Let $R$ be a commutative ring with identity and $A(R)$ be the set of ideals with nonzero annihilator. The strongly annihilating-ideal graph of $R$ is defined as the graph ${\rm SAG}(R)$ with the vertex set $A(R)^*=A(R)\setminus\{0\}$ and two distinct vertices $I$ and $J$ are adjacent if and only if $I\cap {\rm Ann}(J)\neq (0)$ and $J\cap {\rm Ann}(I)\neq (0)$. In this paper, the perfectness of ${\rm SAG}(R)$ for some classes of rings $R$ is investigated

Un estudio de los cambios en el conocimiento y creencias de docentes, después de un taller con software educativo matemático, analizado mediante el método Fuzzy

In this paper, the effect of holding a math training workshop using GeoGebra software has been studied on the changes on teachers' knowledge and beliefs . The selected sample is 40 male and female teachers in Iran. Before and after the intervention were administered a pre and post questionnaire with two components: TPACK knowledge and teachers’ beliefs. Fuzzy logic and Fuzzy TOPSIS methods were used to analyze the data. The results of this method showed a significant difference between the results before and after the workshop.El estudio contempla el efecto de un taller de matemáticas con GeoGebra sobre los cambios en el conocimiento y las creencias de los docentes. La muestra seleccionada considera 40 docentes en Irán. Se administró un cuestionario, antes y después de la intervención, enfocado en dos componentes: el TPACK y las creencias. Los datos se analizaron aplicando herramientas del método Fuzzy mediante el cual se evidencia una diferencia significativa entre los resultados antes y después del taller

ON THE GRUNDY BONDAGE NUMBERS OF GRAPHS

For a graph $G=(V,E)$, a sequence $S=(v_1,\ldots,v_k)$ of distinct vertices of $G$ it is called a \emph{dominating sequence} if $N_G[v_i]\setminus \bigcup_{j=1}^{i-1}N[v_j]\neq\varnothing$. The maximum length of dominating sequences is denoted by $\gamma_{gr}(G)$. We define the Grundy bondage numbers $b_{gr}(G)$ of a graph $G$ to be the cardinality of a smallest set $E$ of edges for which $\gamma_{gr}(G-E)>\gamma_{gr}(G).$ In this paper the exact values of $b_{gr}(G)$ are determined for several classes of graphs

Funciones ejecutables de las representaciones en el aprendizaje de los conceptos algebraicos

This study aimed to examine the role of multiple representations in learning algebraic concepts for high school students. Using the semiexperimental research method for teaching of numerical, symbolic, and graphical representations, and traditional teaching, 83 female students were selected from the tenth grade of a high school in Tehran. We concluded that there is a significant difference between the mean scores of mathematics in the control and experimental groups. Using the method based on different representations helped the students to become creative and provide similar Algebra examples; thereby analysis power will be increased.Este estudio tiene como objetivo examinar el papel de las representaciones múltiples en el aprendizaje de los conceptos algebraicos en estudiantes de educación secundaria. Se desarrolló una investigación semiexperimental para la enseñanza de representaciones numéricas, simbólicas y gráficas y la enseñanza tradicional, en este estudio participaron 83 estudiantes femeninas del décimo grado de una escuela secundaria en Teherán. Se concluyó que hay una diferencia significativa entre los puntajes promedio de matemáticas en el grupo control y los grupos experimentales. El uso del método basado en diferentes representaciones ayudó a las estudiantes a ser creativas y proporcionar ejemplos de álgebra similares; por lo tanto, la capacidad de análisis aumentará

MODELLING THEORY OF MIND, DIVERGENT THINKING AND MATHEMATICAL PROBLEM POSING OF FIRST GRADERS

Objetivo: A colocação de problemas tem uma importância central na disciplina de matemática e na natureza do pensamento matemático. O objetivo deste estudo foi investigar as relações explicativas e preditivas entre as variáveis da teoria da mente, pensamento divergente e problema que se apresentam nos alunos da primeira série do ensino fundamental, utilizando a abordagem de modelagem de equações estruturais. Método: Os sujeitos são 345 alunos (176 meninas e 169 meninos) da primeira série da escola primária de Zahedan, usando o modelo de amostragem disponível. Eles viviam e eram educados nas áreas urbanas médias da cidade. Os alunos responderam à teoria da mente, pensamento divergente e problemas matemáticos que colocam testes. A modelagem de equações estruturais foi utilizada para analisar os dados coletados no instrumento de pesquisa. Resultados: A análise dos dados revelou um impacto significativo (P <0,05) da variável de pensamento divergente no resultado das habilidades de colocação de problemas. Curiosamente, um impacto indireto da variável teoria da mente, via pensamento divergente, sobre a variável que coloca o problema foi observado neste estudo. Essas descobertas demonstraram claramente os impactos positivos dos componentes do pensamento e da teoria da mente divergentes sobre o problema matemático. Implicações para pesquisa e prática: continua a ser necessário explorar ainda mais o papel da mente noproblema que coloca a capacidade em relação à educação matemática.Propósito: La presentación de problemas tiene una importancia central en la disciplina de las matemáticas y en la naturaleza del pensamiento matemático. El propósito de este estudio fue investigar las relaciones explicativas y predictivas entre las variables de la teoría de la mente, el pensamiento divergente y la presentación de problemas en los estudiantes de primer grado de la escuela primaria, utilizando el enfoque de modelado de ecuaciones estructurales. Método: Los sujetos son 345 estudiantes (176 niñas y 169 niños) de los alumnos de primer grado de la escuela primaria de Zahedan, utilizando el modelo de muestreo disponible. Vivieron y fueron educados en las áreas urbanas promedio de la ciudad. Los estudiantes respondieron a la teoría de la mente, el pensamiento divergente y las pruebas de planteamiento de problemas matemáticos. El modelado de ecuaciones estructurales se utilizó para analizar los datos recopilados en el instrumento de encuesta.Resultados: El análisis de datos reveló un impacto significativo (P <0.05) de la variable de pensamientoen el resultado de las habilidades para plantear problemas. Curiosamente, en este estudio se observó un impacto indirecto de la variable de la teoría de la mente a través del pensamiento divergente sobre la variable de planteamiento del problema. Estos hallazgos demostraron claramente los impactos positivos de los componentes del pensamiento divergente y la teoría de la mente sobre el problema matemático que plantea. Implicaciones para la investigación y la práctica: sigue siendo necesario explorar más a fondo el papel de la mente en la capacidad de plantear problemas con respecto a la educación matemática.Purpose: Problem posing has a central importance in the discipline of mathematics and in the nature of mathematical thinking. The purpose of this study was to investigate the explanatory and predictive relationships among the variables of the theory of mind, divergent thinking, and problem posing in the first grade students of elementary school, using structural equation modeling approach. Method: The subjects are 345 students (176 girls and 169 boys) of the first graders of elementary school of Zahedan, using available sampling model. They lived and were educated in the average, urban areasof the city. Students responded to the theory of mind, divergent thinking, and mathematical problem posing tests. Structural Equation Modeling was used to analyze the data gathered survey instrument. Findings: The data analysis revealed a significant (P<0.05) impact of divergent thinking variable on the outcome of problem posing skills. Interestingly, an indirect impact of theory of mind variable via divergent thinking on the problem posing variable were observed in this study. These findings clearly demonstrated the positive impacts of the components of divergent thinking and theory of mind on the mathematical problem posing. Implications for Research and Practice: remains necessary to further explore the role of mind on the problem posing ability with regard to mathematical education

A study on the changes on teachers' knowledge and beliefs after a workshop based on mathematics education software, by relying on Fuzzy analysis

In this paper, the effect of holding a math training workshop using GeoGebra software has been studied on the changes on teachers' knowledge and beliefs. The selected sample is 40 male and female teachers in Iran. Before and after the intervention were administered a pre and post questionnaire with two components: TPACK knowledge and teachers’ beliefs. Fuzzy logic and Fuzzy TOPSIS methods were used to analyze the data. The results of this method showed a significant difference between the results before and after the workshop