Aims to find out the (Extent of mathematics teachers' appreciation of the mathematical problem `multiple solutions) Research sample consisted of (100) mathematics teachers distributed on the General Directorates of Education in Baghdad (Rusafa 1/2/3) and (Karkh 1/2/ 3) There was two research approach which are: The first - two different answers of students to the same issue where teachers must assess each answer and explain which one the teacher will accept and why? The second - Different solutions of students' to the same issue, including wrong answers , Teachers should correct the answers and give them final grades (0-10). Descriptive and analytical Approch was used in this research methodology And zero hypotheses, which are as follows. 1-Mathematics teachers' assessment of mathematical problems with multiple solutions is statistically identical in terms of greater than (0.05) level. 2. Mathematics teachers estimate the level of achievement of their students through different solutions to mathematical problems is statistically identical in terms of greater than the level (0.05). Some of The search results are as follows: 1. The existence of a difference between mathematics teachers in the assessment of mathematical problems `multiple solutions 2. There is a difference in the assessment of mathematics teachers to the level of achievement of their students through various solutions to mathematical problems.
The behavior and shear strength of full-scale (T-section) reinforced concrete deep beams, designed according to the strut-and-tie approach of ACI Code-19 specifications, with various large web openings were investigated in this paper. A total of 7 deep beam specimens with identical shear span-to-depth ratios have been tested under mid-span concentrated load applied monotonically until beam failure. The main variables studied were the effects of width and depth of the web openings on deep beam performance. Experimental data results were calibrated with the strut-and-tie approach, adopted by ACI 318-19 code for the design of deep beams. The provided strut-and-tie design model in ACI 318-19 code provision was assessed and found to be u
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In this paper, Touchard polynomials (TPs) are presented for solving Linear Volterra integral equations of the second kind (LVIEs-2k) and the first kind (LVIEs-1k) besides, the singular kernel type of this equation. Illustrative examples show the efficiency of the presented method, and the approximate numerical (AN) solutions are compared with one another method in some examples. All calculations and graphs are performed by program MATLAB2018b.
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The present work aims to study forward osmosis process using different kinds of draw solutions and membranes. Three types of draw solutions (sodium chloride, sodium formate, and sodium acetate) were used in forward osmosis process to evaluate their effectiveness with respect to water flux and reverse salt flux. Experiments conducted in a laboratory-scale forward osmosis (FO) unit in cross flow flat sheet membrane cell. Three types of membranes (Thin film composite (TFC), Cellulose acetate (CA), and Cellulose triacetate (CTA)) were used to determine the water flux under osmotic pressure as a driving force. The effect of temperature, draw solution concentration, feed and draw solution flow rate, and membrane types, were studied with
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An efficient combination of Adomian Decomposition iterative technique coupled Elzaki transformation (ETADM) for solving Telegraph equation and Riccati non-linear differential equation (RNDE) is introduced in a novel way to get an accurate analytical solution. An elegant combination of the Elzaki transform, the series expansion method, and the Adomian polynomial. The suggested method will convert differential equations into iterative algebraic equations, thus reducing processing and analytical work. The technique solves the problem of calculating the Adomian polynomials. The method’s efficiency was investigated using some numerical instances, and the findings demonstrate that it is easier to use than many other numerical procedures. It has
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The logistic regression model is an important statistical model showing the relationship between the binary variable and the explanatory variables. The large number of explanations that are usually used to illustrate the response led to the emergence of the problem of linear multiplicity between the explanatory variables that make estimating the parameters of the model not accurate.
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n this paper, we formulate three mathematical models using spline functions, such as linear, quadratic and cubic functions to approximate the mathematical model for incoming water to some dams. We will implement this model on dams of both rivers; dams on the Tigris are Mosul and Amara while dams on the Euphrates are Hadetha and Al-Hindya.
When searching for an answer to the following question: What are the reasons for the reluctance of female physical education teachers in secondary schools to referee sports competitions according to the variable of years of service? It was found that the research aimed to reveal the differences between the opinions of the research sample of physical education teachers in secondary schools (girls) about refereeing sports competitions according to the variable of years of service. To achieve the research goal, it is assumed that there are significant differences between the average opinions of the research sample of female teachers and their reluctance and the reasons for the differences in the practice of refereeing sports competitions accor
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