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1 |
Population versus sampling procedures: implications from epidemiological studiesMatias Noll, Cláudia Tarragô Candotti, Bruna Nichele da Rosa, Flávio Antônio de Souza Castro, Jefferson Fagundes Loss
pp. 1-10 | Article Number: ijese.2018.001
Abstract Since sampling procedures are closely related to scientific validity, it is necessary to understand the influence of sampling procedures on obtained research results to ensure that epidemiological studies provide reliable information for planning actions designed to ensure quality in promoting health. Therefore, we verified whether the results regarding postural habits provided by diverse sampling procedures are consistent with those obtained from an entire population. A data bank obtained from a population epidemiological study involving 1,597 elementary school children from all the schools in the municipality of Teutônia, Rio Grande do Sul, Brazil (N = 11) was used. A question referring to postural habits contained in the Back Pain and Body Posture Evaluation Instrument questionnaire was analyzed. The data from the entire population were analyzed and compared with the results obtained from data collected using four distinct sampling procedures (simple random, stratified, clustered, and intentional sampling). The postural habits data from both the population and the four sampling procedures were analyzed using descriptive statistics and a calculated 95% confidence interval. The stratified sampling procedure, followed by the random and clustered procedures, presented the best distribution of school children, most closely approximating the distribution in the entire population. Therefore, the necessity of research about posture, both in the planning and execution stage, is vital. Researchers must pay attention to factors such as sampling method and utilizing an effective sample size. Keywords: posture, epidemiology, biostatistics, method, population, sample size References Altman, D. G. (1980). Statistics and ethics in medical research: III How large a sample? BMJ, 281(6251), 1336–1338. https://doi.org/10.1136/bmj.281.6251.1336 Christensen, E. (2007). Methodology of superiority vs. equivalence trials and non-inferiority trials. Journal of Hepatology, 46(5), 947–954. https://doi.org/10.1016/j.jhep.2007.02.015 Clark, T., Berger, U., & Mansmann, U. (2013). Sample size determinations in original research protocols for randomised clinical trials submitted to UK research ethics committees: review. BMJ, 346(mar21 1), f1135–f1135. https://doi.org/10.1136/bmj.f1135 Dupont, W. D., & Plummer, W. D. (1998). Power and sample size calculations for studies involving linear regression. Controlled Clinical Trials, 19(6), 589–601. https://doi.org/9875838 Gabriel, S. E., & Michaud, K. (2009). Epidemiological studies in incidence, prevalence, mortality, and comorbidity of the rheumatic diseases. Arthritis Research & Therapy, 11(3), 229. https://doi.org/10.1186/ar2669 Hayat, M. J. (2013). Understanding Sample Size Determination in Nursing Research. Western Journal of Nursing Research, 35(7), 943–956. https://doi.org/10.1177/0193945913482052 Kasten, A. P., Rosa, B. N. da, Schmit, E. F. D., Noll, M., & Candotti, C. T. (2017). Prevalence of postural deviations in the spine in schoolchildren: a systematic review with meta-analysis. Journal of Human Growth and Development, 27(1), 99. https://doi.org/10.7322/jhgd.127684 Noll, M., Candotti, C. T., Rosa, B. N. da, & Loss, J. F. (2016). Back pain prevalence and associated factors in children and adolescents: an epidemiological population study. Revista de Saúde Pública, 50(31), 1–10. https://doi.org/10.1590/S1518-8787.2016050006175 Noll, M., Tarragô Candotti, C., Vieira, A., & Fagundes Loss, J. (2013). Back Pain and Body Posture Evaluation Instrument (BackPEI): Development, content validation and reproducibility. International Journal of Public Health, 58(4), 565–572. https://doi.org/10.1007/s00038-012-0434-1 Noordzij, M., Tripepi, G., Dekker, F. W., Zoccali, C., Tanck, M. W., & Jager, K. J. (2010). Sample size calculations: basic principles and common pitfalls. Nephrology, Dialysis, Transplantation : Official Publication of the European Dialysis and Transplant Association - European Renal Association, 25(5), 1388–93. https://doi.org/10.1093/ndt/gfp732 Snedecor, G., & Cochran, W. (1967). Statistical Methods. Ames: Iowa State University Press. |
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2 |
Effectiveness of Counselling on Academic Achievement of Low AchieversA. Rajkamal, N.Prema
pp. 11-16 | Article Number: ijese.2018.002
Abstract Low achievers are the students who are not at satisfactory level in their academics due to several reasons. Proper counselling may help them to achieve to the extent possible. The prime aim of this study is to know whether all the low achievers are slow learners by testing their intelligence level and provide counselling for the low achievers and to make out the impact of counselling on academic achievement of such students. Out of Forty six students, Twenty six of them were identified as low achievers from 7th standard as sample for this experimental research process. Intelligence level of all the low achievers have been measured and noted that 13 out of 26 were not slow learners and they have I.Q ranged between 90 and 105 can be categorized as low achievers with normal level of I.Q. The remaining 13 students were falls under slow learners (backward children) having I.Q ranged between 80 and 89 (below normal-I.Q) can be categorized as slow learners. Counselling had been given by the investigator separately for both the group, and also individually to all the low achievers for a period of 3 months. Pre-test and post-test scores have been analysed and found out that there was a remarkable improvement among low achievers with normal level of I.Q in their academic achievement and comparatively little lesser improvement have also been noted among students with below normal level of I.Q in their academic achievement. Keywords: Counselling, Low achievers, Slow learners, Intelligence, Academic achievement and I.Q test References Jose I. Navarro, Manuel Aguilar, Esperanza Marchena, Gonzalo Ruiz, Inmaculada Menacho, Johannes E. H. Van Luit (2011) Longitudinal study of low and high achievers in early mathematicsBritish Journal of Educational Psychology9 August Kelly anne vanauker-ergle (2003) Barriers to low achievers’ success in the elementary classroom as perceived by teachers: a qualitative study The University of Florida Digital Collections (UFDC)http://ufdc.ufl.edu/UFE0002340/00001 Mangal.S.K (2011) Advanced Educational Psychology PHI Learning Private Limite, New Delhi Mary Wong Siew Lian (1998) An investigation into High-Achiever and Low-Achiever Knowledge Organisation and Knowledge Processing in Concept mapping, A Case Study Research in Science Education 28(3), 337-352. https://educationposter.blogspot.in/2013/01/guidance-and-counselling-educational.html http://dictionary.reverso.net/english-cobuild/low%20achiever |
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3 |
The relevance Knowledge management and Social Capital with Staff EmpowermentNaser Seifollahi, Hossein Rahimi Koloor
pp. 17-29 | Article Number: ijese.2018.003
Abstract The aim of this study was to investigate the relationships between Knowledge management and social capital and staff empowerment among education personnel in the city of Kohgiluyeh (Iran). The population in the present descriptive-correlational study consisted of all male education personnel in the city of Kohgiluyeh (n=270) in 2014. Using Jersey-Morgan table and stratified random sampling method, 152 people were selected as the study’s samples. The data were collected through the Staff Empowerment the Knowledge management Questionnaire and the Social Capital Questionnaire. The data were analyzed using Pearson Correlation and Multiple Regression Analysis. The results showed significant relationships between Knowledge management and staff empowerment and between social capital and staff empowerment. Among the components of Knowledge management, externalization and understanding legal and economic issues related to the use of information had respectively the highest (0.575) and the lowest (0.490) predictive power in predicting staff empowerment. Keywords: Knowledge management, Social Capital, Empowerment References Abdollahi, B., Nave Ibrahim, A. (2006). Empowering staffs: the golden key to human resources management. Virayesh Publication, Tehran. Ali Ahmadi, A. R., Ahmadi, A. A., Hatami Naghani, F. (2010). The relationship between organizational learning and empowering Iran’s oil industry pension funds staffs. Journal of Management Tomorrow, 9 (25), 67-82. Conger JA,Kanungo RN(1998). ”The Integrating theory and Empowerment process: practice”, Academy of Management Review, 13.471-482. Danchev, Alexi. (2006). Social capital and sustainable behavior of the firm” Industrial Management & Data Systems, Vol.106, No.7, pp.953-965. Denis, T. (2005). Top management skills: empowerment, a basis for strong management. Translated by, Ramezani, B. Nei Publication, Tehran. Ebrahimi, M. M. (2011). The role of new technologies in empowering staffs’ and cultural managers’ decision-making (case study: Art and Cultural Organization of Tehran Municipality). International Congress on Cultural Journalism. Foy.N(1997). ”Empowering people at work”. Published by Gower Publishing Ltd, 1997, England, Published(1). Hall, M. (2008, February-April). The effective of comprehensive performance measurement system on role clarity, psychological empowerment and managerial performance. Accounting,Organization, and Society, 33(2-3), 141-163. Hashemi, A., Pour Amin Zad, S. (2011). Challenges facing human resources development and ways to fix them. Journal of Work and Society (136). Iran Zadeh, M., Bahrami Nejad, Z. (2010). Empowering staffs in new organizations. Forouzesh Publication, Tabriz. Jami. Parsons,(2009), Reading/Language Arts: Extra! Extra! Read and Write All about It. School Library Media Activities Monthly. 25. 9; 12-3. Kamalian, A. R., Salar Zehi, H., Oliaei, K. (2013). The role of IT in empowering staffs of Technical and Professional Training Organization. Journal of Management and Accounting, University of Zahedan, 4(2), 39-48. Keshavarzi, A. H., Hoseini, A., Heidari Nasab, L., Amadeh, A. A. (2011). The relationship between social capital and psychological empowerment (case study: Qom Governor). Journal of Advanced Behavior and Management. Shahed University, 50 (1), 329-344. Kiamarsi, A., Momeni, S. (2013). The relationship between social capital, happiness and academic achievement of female high school students. Journal of School Psychology, 2 (1), 119-130. Lak, B., Javadian, R. (2011). The impact of IT infrastructures on police staffs’ empowerment. Journal of Human Resources Management and Support, (19), 31-60. Mirza Safi, A., Rajaei Pour, S., Jamshidian, A. (2011). The relationship between Knowledge management and entrepreneurial capabilities of graduate students of Isfahan University. Journal of Library and Knowledge Science, 14 (1), 241-268. Patterson, A.(2009). A need analsis for Knowledge management provision for research: a case study in university college Dublin. journal of Knowledge management, 3(1), 5-18. Pour Kiani, M., Bahrami Nejad, Z. (2012). The role of social capital in organizational entrepreneurship. National Conference on Entrepreneurship and Management of Knowledge management based Businesses. Mazandaran University, Mazandaran. Quinn, R. E. 2005. Moments of greatness: Entering the fundamental state of leadership. Harvard Business Review (July/August): 74-83 Raza, H., Mahmood, J., Owais, M., & Raza, A. (2015). Impact of employee empowerment on job satisfaction of employees in corporate banking sector employees of Pakistan. Journal of Applied Environmental and Biological Sciences, 5(2), 1-7. |
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4 |
Constructs and relationships in the study of entrepreneurial intentions in university studentsAlejandro Valencia-Arias, Ivan Montoya, Alexandra Montoya
pp. 31-52 | Article Number: ijese.2018.004
Abstract The purpose of this article is to examine the main research findings on entrepreneurial intention among university students. Secondary information sources from indexed international journals were utilized. Results show that the model of Entrepreneurial Event and Theory of Planned Behavior are the approaches more used to measure the entrepreneurial intention and the necessity of adequately incorporating entrepreneurial self-efficacy in the entrepreneurial intention analysis in emerging economies. Furthermore, it is recommended adopting and validating the entrepreneurial intention models according to economic, social and educational context in developing countries, allowing the structuring of coherent educational strategies with university students population environment. Keywords: entrepreneurs, students' attitudes, comparative study, higher education, education and business References Ajzen, I. (1991). The theory of planned behavior. 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Evaluating the effects of a problem-based learning business-planning course on student entrepreneurial intentions. Journal of Entrepreneurship Education, 18(1), 169-182. Bermudez, J., Chalela, S., Valencia, J. & Valencia, A. (2017). Research Trends in the Study of ICT Based Learning Communities: A Bibliometric Analysis. EURASIA Journal of Mathematics, Science & Technology Education. 13(5), 1539-1562. DOI: 10.12973/eurasia.2017.00684a Bernhofer, L. & Han, Z. (2014). Contextual factors and their effects on future entrepreneurs in China: a comparative study of entrepreneurial intentions International Journal of Technology Management, 65(1), 125-150. Botsaris, C. y Vamvaka, V. (2016). Attitude toward entrepreneurship: structure, prediction from behavioral beliefs, and relation to entrepreneurial intention. Journal of the Knowledge Economy, 7(2), 433-460. Busenitz, L., Plummer, L., Klotz, A., Shahzad, A. & Rhoads, K. (2014). 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The Impact of entrepreneurship education: A study of Iranian students' entrepreneurial intentions and opportunity identification. Journal of Small Business Management, 54(1), 187-209. Kelley, K., Clark, B., Brown, V.& Sitzia, J. (2003). Good practice in the conduct and reporting of survey research. International Journal for Quality in Health Care, 15(3), 261–266. Khalili, H., Zali, M. & Kaboli, E. (2015). A structural model of the effects of social norms on entrepreneurial intention: evidence from gem data. International Journal of Advanced Research in Management and Social Sciences, 4(8), 37-57. Krueger, N. & Carsrud, A. (1993). Entrepreneurial intentions: applying the theory of planned behavior. Entrepreneurship & Regional Development, 5(4), 315-330. Krueger, N., Reilly, M. & Carsrud, A. (2000). Competing models of entrepreneurial intentions. Journal of Business Venturing, 15(5), 411–432. Küttim, M., Kallaste, M., Venesaar, U. y Kiis, A. (2014). 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International Entrepreneurship and Management Journal, 11(4), 935-957. Lv, R., Chen, Xiao J. & Chen, W. (2014). The Configuration of Scientific and Technical Personnel Entrepreneurial Intention Model Based on Theory of Planned Behavior. Advanced Materials Research, 860-863 Maes, J., Leroy, H. & Sels, L. (2014). Gender differences in entrepreneurial intentions: A TPB multi-group analysis at factor and indicator level. European Management Journal, 32(5), 784–794. Marqués, C., Ferreira, J., Gomes, D. & Gouveia-Rodrigues, R. (2012). Entrepreneurship education: How psychological, demographic and behavioural factors predict the entrepreneurial intention. Education+ Training, 54(8-9), 657-672. Medina-Brito, M., Bolívar-Cruz, A. & Lemes-Hernández, A. (2014). Un paso más en la investigación de la intención emprendedora del estudiante universitario: GUESSS. Revista de Estudios Empresariales. Segunda Época), 2, 63–80. Montoya, I., Valencia, A. & Montoya, A. (2016). 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Do entrepreneurship programmes raise entrepreneurial intention of science and engineering students? The effect of learning, inspiration and resources. Journal of Business venturing, 22(4), 566-591. Sun, H. & Lo, C. (2012). Impact of role models on the entrepreneurial intentions of engineering students. .proceedings of IEEE International Conference on Teaching, Assessment and Learning for Engineering (TALE), Hong Kong, 20-23, IEEE Torres, J., Valencia-Arias, A., Bermúdez, J., Díez-Echavarría, L., Urrego, M., & Maussa, F. (2017). Characterization of entrepreneurial intention in university students as from Systemic Entrepreneurship Intention Model: a case study. Cuadernos De Gestión, 17(2), 1-17. http://dx.doi.org/10.5295/cdg.160670jt Tshikovhi, N. & Shambare, R. (2015). Entrepreneurial knowledge, personal attitudes, and entrepreneurship intentions among South African Enactus students. Problems and Perspectives in Management, 13(1), 152-158. Valencia Arias, A., Benjumea Arias, M. L., & Rodríguez-Lora, V. (2014). Intención de uso del e-learning en el programa de administración tecnológica desde la perspectiva del modelo de aceptación tecnológica. Revista Electrónica Educare, 18(2), 247-264 doi: http://dx.doi.org/10.15359/ree.18-2.13 Valencia, A & Benjumea, M. (2013). Una visión del emprendimiento desde arquetipos sistémicos. Sinapsis, 5(5), 105-113. Valencia, A, Gonzalez, G. & Castañeda, M. (2016). Structural equation model for studying the mobile-learning acceptance. IEEE Latin America Transactions, 14(4), 1988-1992. DOI: https://doi.org/10.1109/TLA.2016.7483544 Valencia, A., Cadavid, L., Ríos, D. Carolina & Awad, G. (2012). Factores que inciden en las intenciones emprendedoras de los estudiantes. Revista Venezolana de Gerencia, 17(57), 132-148. Valencia, A., Montoya, I. & Montoya, A. (2015a). Influence of perceived behavioral control in entrepreneurial intentions of engineering students. Turkish Online Journal of Educational Technology, 7(1), 341-347 Valencia, A., Montoya, I. & Montoya, A. (2015b). Factores explicativos de las intenciones emprendedoras en estudiantes universitarios. Espacios, 36(5), 1-15. Valencia, A., Montoya, I. & Montoya, A. (2016). Intención emprendedora en estudiantes universitarios: un estudio bibliométrico. Intangible Capital, 12(4), 881-922 Valencia, J., Macias, J., & Valencia, A. (2015). Formative research in higher education: Some reflections. Procedia-Social and Behavioral Sciences, 176(1), 940-945. DOI: https://doi.org/10.1016/j.sbspro.2015.01.562 Valencia-Arias, A., Gutiérrez Flórez, L., Montoya Restrepo, L. A., Umba López, A. M. U. L., & Montoya Restrepo, I. (2017). Consideraciones acerca del emprendimiento estratégico como síntesis funcional de la identificación de oportunidades y la creación de ventajas competitivas. Revista Virtual Universidad Católica del Norte, 52(1), 143-159. Vélez, M., Gutiérrez, D. & Valencia, A. (2015). Student's Perception and Expectation towards the Creation and Implementation of a Technology Management Laboratory at the Metropolitan Technology Institute MTI. Periodica Polytechnica. Social and Management Sciences, 23(2), 99-105. DOI: http://dx.doi.org/10.3311/PPso.7915 Villa Enciso, E. M., Picón Jácome, E., Valencia-Arias, A., & Jiménez Hernández, C. N. (2017). Analysis of University Management of Emerging Technologies and Recommendations for Developing Countries. Turkish Online Journal of Educational Technology-TOJET, 16(2), 1-10. http://www.tojet.net/volumes/v16i2.pdf Villa Enciso, E., Valencia Arias, J., & Valencia Arias, A. (2016). El papel de las narrativas digitales como nueva estrategia educativa: resultados desde un análisis bibliométrico. Kepes, 13(1), 196-231. DOI: http://dx.doi.org/10.17151/kepes.2016.13.13.10 Wilson, Fiona., Kickul, Jill & Marlino, Deborah (2007). Gender, entrepreneurial self-efficacy, and entrepreneurial career intentions: Implications for entrepreneurship education. Entrepreneurship: Theory and Practice. 31(3), 387–406. Xiang, H. & Lei, J. (2013). Student entrepreneurial intentions in Chinese universities based on the ISO model. Journal of Tsinghua University, 53(1), 1-23. Yang, J. (2013). The theory of planned behavior and prediction of entrepreneurial intention among Chinese undergraduates. Social Behavior and Personality: an international journal, 41(3), 367-376. Yurtkoru, S., Kuşcu, Z. & Doğanay, A. (2014). Exploring the antecedents of entrepreneurial intention on Turkish university students. Procedia-Social and Behavioral Sciences, 150, 841-850. Zampetakis, L. (2008). The role of creativity and proactivity on perceived entrepreneurial desirability. Thinking Skills and Creativity, (3)2, 154-162. Zapkau, F., Schwens, C., Steinmetz, H. & Kabst, R. (2015). Disentangling the effect of prior entrepreneurial exposure on entrepreneurial intention. Journal of Business Research, 68(3), 639-653. Zhang, J., Cao, W. & Zeng, P. (2014). A study on the relationship among entrepreneurship education, social capital and college students' entrepreneurial intention proceedings of IEEE International Conference on Granular Computing (GrC), IEEE, 367-373. Zhang, Y., Duysters, G. & Cloodt, M. (2014). The role of entrepreneurship education as a predictor of university students’ entrepreneurial intention. International entrepreneurship and management journal, 10(3), 623-641. |
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Architectural morphology and decoration elements of Dome-home of Ardabil Jame MosqueHabib Shahbazi Shiran
pp. 53-67 | Article Number: ijese.2018.005
Abstract Ardabil, a land reposed in kindly arms of nature, den of mystery of art, scene of God’s beauties, abode of beloved, covert of sweetheart, spring of waiting and eagerness, source of blessing, harem of descended possibilities and effects, and a vast archaeological square with such precedence as history that is a face came out, presented the clear splendid and bright foregoing, ancient civilization of this habitat, an anonymous and evident treasure and presence sight. Throughout the history, one can trace different towns and villages under various names, several places and even different people in heart of the mountains and wide stream of plains of this field of Iran. A clime with many secrets and coverts that hidden them in the heart like a patient sage; and seeks a man searching reality in order to restate it to him. A land settled on a belt of rich and great heritage; and its historical monuments is sucking and engrossing in terms of volume, vastness, density, sequence, richness, magnificence, modesty, reverence and magical majesty and like a suspension bridge between history and reality and a way towards this or that charmer. Throughout Ardebil County, there are unmatched heritage, cultural splendid effects and product of long term experiences of generations who came one after the other in the stream of history; and indeed it can be considered as a museum and symbol of Iran’s honorable past. Ruins of archaeological campuses and also towns, castles and magnificent domiciles and enchanting art works that left as memorials all over this ancient and historic valley cry greatness, depth of thought and high level of culture and civilization of its residents as live witnesses and entrance onlookers in such a way that they are attracted into their special time and space unintentionally; and feel themselves in a world of brightness, softness and breeziness. The valuable examples of this majesty can be seen in the ruins of a majestic mosque (columned bedchamber in its Deylami shape and with a combination of four roofs and porches in its Seljuk shape that in fact shows accomplished artistic taste and religious belief of their builders. Research method in this study is descriptive- analytic and the tools of data collecting is desk study and empirical that its foundation is field study of archaeological documents. Keywords: Ardabil, Jame Mosque, bedchamber, Dome home References Shahbazi Shiran, Habib (1383). Tracing and Analyzing Architectural Components and Elements of Ardabil Jome Mosque. Tabriz, Sadra Publications. Shahbazi Shiran, Habib (1395). Analytic investigation of Skeletal and Spatial Visional Elements of bedchamber of Ardabil Jame Mosque. Third Worldwide Conference of Recent Initiatives in Civil Engineering, Architecture and Urbanization. Tehran. Nikan Institution. Hillenbrand, Robert. (1387). Islamic Architecture. Translated by Ayat ul-lazadeh Shirazi baqer. Forth Publication. Tehran. Rozaneh. Mousavi, Mahmoud (1376). Ardabil Jame Mosque /History, Building Descriptions and Architecture. Series of Articles of Mosque Architecture Conference: Past, Present, Future/, Volume 1. Isfahan. Art University. Safari, Baba (1370). Ardabil in History Passage. Volume 2, Second Publication, Tehran. Islamic Azad University, Ardabil Branch. Torabi Tabatabaee, Seyed Jamal (1355). Azerbaijan Ancient Works. volume 2. Tehran. Association of National Works. Shahbazi Shiran, Habib (1395). Investigation of Architecture and Decorations of Seljuk Dome home and Ilkhani Mehrab of Ardabil Jame Mosque. Second International Conference of Architecture, Civil Engineering and Urbanization in the Early third Millennium. Tehran. Consortium of Anabaft Shahr, Association of Architecture and Urbanization of Alborz County. Society of Planner Engineers of Banashahr Paydar Institution- Cultural and Art Institution of Salvaye Nasr. Moqadasi, Abou Abd ul-lah Mohammad ibne Ahmad (1361). Ahsan ul- taqasim fi Marefat ul-aqalim. Translated by Monzavi Alinaqi, Volume 2. Tehran. Company of Iran’s Authors and Translators. Barbier, Ch. (1869). Dictionnairegeographque, historiqueetlitteraire de la perse et des contreesadjacentes. Publisher: Imprimerie Imperial. Siro, Maxim (1367). Ardabil Jome Mosque. Translated by Imani Nadieh, Asar Magazine, No. 15 & 16. Wilber, D. (1955). The Architecture of Islamic Iran. New York, Greenwood Press. |
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Beginning Chemistry Teachers’ Depictions of the Chemistry ContentKrista L. Adams; Julie A. Luft
pp. 69-95 | Article Number: ijese.2018.006
Abstract Teaching and learning chemistry involves multiple levels of representation: macroscopic (macro), submicroscopic (submicro), and symbolic. A more recent trend includes the human element, a fourth representation level that contextualizes the chemistry content through real-world applications. This three-year study follows eight beginning chemistry teachers in order to understand how the chemistry content is depicted in the classroom. Teachers need to be engaged in the analysis of key concepts in the content and common representations to recognize instruction should focus on helping students negotiate the representation levels. Support for teachers with examples will help beginning teachers better implement the tetrahedral model and empower beginning teachers to intentionally point out the connections among the different representational levels for students. This may require support to extend beyond the first three years in the classroom. 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