Home > Students’ Perceptions About the Symbols, Letters and Signs in Algebra and How Do These Affect Their Learning of Algebra: A Case Study in a Government Girls Secondary School, Karachi, Pakistan
Students’ Perceptions About the Symbols, Letters and Signs in Algebra and How Do These Affect Their Learning of Algebra: A Case Study in a Government Girls Secondary School, Karachi, Pakistan
Algebra uses symbols for generalizing Arithmetic. These symbols have different meanings and interpretations in different situations. Students have different perceptions about these symbols, letters and signs. Despite the vast research by researchers, namely Kuchemann (1981&1998,), Collis (1975), and Booth (1988 & 1984) on the students' difficulties in understanding letters in Algebra, the overall image that emerges from the literature is that students have misconceptions about the use of letters and signs in Algebra. Through my study, I have explored the perceptions of students about the use of symbols and signs in Algebra. Here, I have used the case study method within a qualitative research design. In order to get insights of students' perceptions of Algebra, I have interviewed students in groups and invited them to work on different tasks related to uncovering their perceptions of Algebra. My empirical done through this study has revealed that the students have many misconceptions in the use of symbols in Algebra, which have bearings on their learning of algebra. It appears that the problems encountered by the students appeared to have a connection with their lack of conceptual knowledge and might have been a result of teaching they experience in learning Algebra at the secondary schooling level. Some of the findings also suggest that teachers appeared to have difficulties with their own content knowledge. Here, one can also see that textbooks are also not presenting content in such an elaborate way that these could have provided sufficient room to students for developing their relational knowledge and conceptual understanding of Algebra. Furthermore, the interviews and observation of the classrooms highlighted that the students usually perceive letter and variables as a fixed numbers or value. Some of the students perceive letters as short forms and abbreviations of some objects. Students also have difficulties in interpreting and developing algebraic equations and expressions. Moreover, this study investigates students' difficulty in translating word problems in algebraic and symbolic form. They usually follow phrase-to-phrase strategy in translating word problem from English into Urdu. This process of translating the word problem from English in to their own language appears to have hindered the correct use of symbols in Algebra. Textbooks, mathematical pedagogy, students' prior experience of arithmetic and the students' and teachers' inadequency in algebraic thinking emerged from my study as some of the reasons of students' misconceptions and why they experienced difficulties in learning of Algebra. The findings have some
ظاہری طور پر یہودیوں کے پاس ایسا کوئی خاص نظام یا قاعدہ موجود نہیں ہے جس کی رو سے یہ کہا جا سکے کہ وہ کن مخصوص عقائد کی پیروی کرتے ہیں۔ الہامی مذاہب میں خدا پر ایمان لانا ایک بنیادی عقیدہ ہے تاہم "ملحد یہودی" جیسے تصور نے اس عقیدے کو بھی متاثر کیا ہے۔ یہودی خود بھی اس معاملے میں اختلاف کا شکار ہیں کہ کیا رسمی عقیدے جیسی کوئی چیز مذہب میں موجود بھی ہے یا نہیں؟ اس معاملے میں ایک فریق یہ کہتا ہے کہ یہودیت میں عقائد جیسی کوئی چیز نہیں؛ صنہادرین تک نے ایسی کوئی وضاحت پیش نہیں کی جس کی رو سے یہودیت کے بنیادی عقائد کی فہرست مرتب کی جا سکے۔ موسی ابن میمون نے بھی جو تیرہ اساسی اصول مرتب کیے ہیں ان کو تمام یہودی قبول نہیں کرتے۔ اکثر و بیشتر راسخ العقیدہ یہودی ان پر اعتراضات اٹھاتے رہتے ہیں۔ بعض یہ خیال کرتے ہیں کہ وہ اپنے عقائد کی کوئی فہرست مہیا نہیں کر سکتے کیونکہ ان میں عقائد کے معاملات میں کبھی اتفاق رائے نہیں ہو سکا ہے۔ یہاں تک کہ عبرانی بائیبل کے فراہم کردہ مذہب کو بھی وہ متنوع سمجھتے ہیں۔[1] جو فریق یہ سمجھتا ہے کہ یہودیت میں کچھ بنیادی عقائد موجود ہیں وہ یہ دلیل دیتا ہے کہ اگر یہ مان لیا جائے کہ یہودیت میں عقائد کا وجود ہی نہیں...
The objective of this study was to empirically determine whether there is a correlation between the proportion of the board of commissioners, audit committee, information asymmetry, and company size with earnings management in the consumer goods manufacturing companies sector listed on the Indonesia Stock Exchange during the years 2010-2012. The study aims to clarify any potential links between the identified variables. Data was extracted from the financial statements of each sample company, which were publicly available on the websites www.idx.co.id and ICMD. The study employed purposive sampling, gathering data from 15 companies over a period of three years, resulting in a total of 45 observations. The independent variables include the proportion of the board of commissioners, audit committee, information asymmetry, and company size, while earnings management serves as the dependent variable. The findings from our study utilizing panel data and regression models demonstrate that neither the proportion of the board of commissioners, audit committee, information asymmetry, nor company size have any impact on earnings management either partially or concurrently.
Theoretical Investigations on Enhancement of Nonlinear Optical Properties of Alkali and Alkaline Earth Metal Doped X12Y12 Nanocages Materials with nonlinear optical response find applications in laser physics, optical fibers, optical computing, optical data handling, optical wave guides and gyroscopes, optical limiters, sensors and scanners. A number of strategies have appeared in the literature to design high performance nonlinear optical materials. A few well studied strategies are bond length alternation (BLA), synthesis of octupolar molecules, molecules with diradical character electrides, and alkalides. A relatively less explored strategy is doping of organic and inorganic systems with alkali metals. Doping with alkali metal generates diffuse excess electrons which reduce the transition energies for crucial excitations. The present research aims at exploring the potential of alkali and alkaline earth metal doping on the nonlinear optical response of X12Y12 nanocages. The objective of this study is not only to find the best nano-cage for doping but also to compare alkali metal with alkaline earth metal doping (substitutional and exohedral). Prior to this study, the literature illustrated only exohedral doping of alkali metal on Al12N12 nano-cage. In this study, Al12N12, B12N12, Al12P12 and B12P12 nanocages were studied. The stabilities of exohedral and substitutional doped nanocages are evaluated through adsorption and cohesive energies, respectively. The exohedral complexes of alkali metal are quite stable as reflected from their adsorption energies; however, certain alkaline earth metal doped systems have negligible adsorption energies. Cohesive energies of substitutional doped nanocages were less than the undoped system. Regardless of the doping mode, the HOMO-LUMO gaps are reduced significantly. The H-L gaps are reduced up to 74% of the original value. The maximum change in H-L gap is observed for Ca@PtopAl12P12 where the gap is reduced to 74.4% of the pristine AlP nanocage. The decrease in H-L gap also reduced the energies for crucial excitation which leads to significantly higher hyperpolarizabilities. The hyperpolarizabilities of the doped nanocages generally range from 1.3×102 au to 7.9×105 au which are several orders of magnitude higher than the values for pristine nanocages. Two level model is also applied to rationalize the obtained hyperpolarizabilities of certain doped systems. The trends of xi hyperpolarizabilities from two level method agree with the hyperpolarizability values from DFT calculations. 2nd hyperpolarizability values, which are real measure of practical application of a system are evaluated through βvec, are also remarkably high and in the same order as first hyperpolarizabilities. The participation of diffuse excess electrons in boosting nonlinear optical response of these doped systems is confirmed through analysis of partial densities of states. The results offer new insight into structure property relationship of inorganic fullerenes in designing new high performance nonlinear optical materials.