مهدی آژینی

This study aimed at investigating the effectiveness of brain-compatible teaching model with mathematics reading comprehension strategy on correcting third grade students’ computational errors in solving verbal problems. In this study, quasi-experimental research method was used. A verbal question test was used as the research instrument in the study. The sample included 65 third grade female students from non-public schools that were assigned into two groups of control and experimental. The results obtained from Wilcoxon test indicated that the brain-compatible teaching model with mathematics reading comprehension strategy was effective on the third grade students’ correction of computational errors in solving verbal problems. Therefore, it can be concluded that considering and using the brain-compatible learning activities can enhance students’ educational success and motivate them to learn Mathematics. This was abstrac of this article whit Investigating the Effectiveness of Brain-compatible Teaching model with Mathematics Reading Comprehension Strategy (SQRQCQ) on Correcting Students’ Computational Errors in Solving Verbal Problems title.

The purpose of the present study is to investigate the role of representations in the problem solving performance of seventh grade students in solving word problems including proportional reasoning. The statistical population of this study included 8425 seventh grade students and the sample size was 269 people who were selected by convenience sampling method. The research was conducted by a mixed method. Data were collected through two tests taken from Lobato (2010), which were exactly the same in both tests; With the difference that in the second test, next to each task, visual or verbal representation was used. The content and face validity of the questions of both tests were confirmed by experts. To check the reliability, the halving method was used. Guttman coefficient was 0.913 in questions without representation and 0.840 in questions without representation, which has good reliability. Students' performance in solving proportional verbal problems in the second and third grade comprehension was examined and the results showed that most students comparatively multiply values and understand the effect of changing a value on the measured ratio. Also, the data were analyzed using paired t-test. Therefore, the desired effect of using representations in responding to these tasks was confirmed.

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.

In this paper, we introduce the Lebesgue -Sobolev spaces critical points theory then we consider the boundary value problem involving an ordinary differential equation with p(x)-Laplacian operator, and nonhomogeneous Neumann conditions. Existence results for ordinary differential equations with elliptic Neumann problems that depending on two real parameters are investigated. Precisely, by using the critical point theory, we show the existence of three weak solutions for p(x)-Laplacian problems. Using the critical point theorems we have proved, we give some conclusionsIn this paper, we introduce the Lebesgue -Sobolev spaces critical points theory then we consider the boundary value problem involving an ordinary differential equation with p(x)-Laplacian operator, and nonhomogeneous Neumann conditions. Existence results for ordinary differential equations with elliptic Neumann problems that depending on two real parameters are investigated. Precisely, by using the critical point theory, we show the existence of three weak solutions for p(x)-Laplacian problems. Using the critical point theorems we have proved, we give some conclusions

The idea of probabilistic metric space was introduced by Menger and he showed that probabilistic metric spaces are generalizations of metric spaces. Thus, in this paper, we prove some of the important features and theorems and conclusions that are found in metric spaces. At the beginning of this paper, the distance distribution functions are proposed. These functions are essential in defining probabilistic metric spaces. Then the Dirac function is presented as an important example of distributions functions. We also, introduced Sibley’s metric or Levy metric on the set of distance distribution functions and so this space becomes a metric space. In the following, probabilistic metric spaces are defined from the Serstnev’s view, and some examples such as Menger probabilistic metric spaces, are introduced. In this paper, the strong topology induced by distance distribution functions is introduced, and then probabilistic diameter, probabilistic bounded, probabilistic semi-bounded, probabilistic unbounded and probabilistic totally bounded sets are introduced. Also, we prove that in every probabilistic metric, every probabilistic totally bounded set is probabilistic bounded set. We also present the cantor intersection theorem and a formulation of Bair’s Theorem in complete probabilistic metric spaces. In addition, we prove that the Heine-Borel property and the Bolzano-Wierestrass property are equivalent.

Next, we study the stability of this type of functional equation. Clearly, the function - holds in this type functional equation. Also, we prove Hyers-Ulam stability for this type functional equation in the β-Gaussian Banach space.