The production-oriented approach （POA） has been developed over a decade. It is driven by the need to improve English classroom instruction for university students in China （Wen, 2016）. It is also motivated by the ...The production-oriented approach （POA） has been developed over a decade. It is driven by the need to improve English classroom instruction for university students in China （Wen, 2016）. It is also motivated by the aspiration to enhance the quality of foreign language education in other similar pedagogical contexts outside China. A volume of research has been done by Wen Qiufang and her research team, to formulate the theory of POA and to test its effectiveness in classroom pedagogy （e.g. Wen, 2016, 2015; Yang, 2015; Zhang, 2015）. At the moment, the POA is still at an early stage of theory building and almost all empirical research is done in the Chinese context. In order to improve the quality of this theory and to make it intelligible to the international academic community, a one-day symposium was held in Beijing Foreign Studies University on May 15, 2017. The symposium was entitled ＇The first international forum on innovative foreign language education in China： Appraisal of the POA＇. In the forum, leading experts in applied linguistics were invited to discuss the strengths and weaknesses of the POA and the directions for its future development. The symposium was the first attempt for the POA research team to discuss its latest work with international scholars. This Viewpoint section collects the responses of four experts who participated in the symposium, listed in alphabetical order. The collection of articles covers three topics related to the POA： its pedagogical application, its use for teacher training, and its research. Alister Cumming is Professor Emeritus and the former Head of the Centre for Educational Research on Languages and Literacies, University of Toronto, Canada. His article focuses primarily on POA research as an exemplary case of design-based research. Rod Ellis is Research Professor in the School of Education at Curtin University, Australia. He discusses POA in terms of pedagogy, teacher training and research, with both critiques and constructive suggestions. Paul Kei M展开更多
In this paper, convex solutions for the second type of Feigenbaum's equation f (x) = λ1 f (f (λx)), 0 < λ < 1, f (0) = 1, 0 f (x) 1, x ∈ [0, 1] are investigated. Using constructive methods, we discuss th...In this paper, convex solutions for the second type of Feigenbaum's equation f (x) = λ1 f (f (λx)), 0 < λ < 1, f (0) = 1, 0 f (x) 1, x ∈ [0, 1] are investigated. Using constructive methods, we discuss the existence and uniqueness of continuous convex solutions, C1-convex solutions and C2-convex solutions of the above equation.展开更多
文摘The production-oriented approach （POA） has been developed over a decade. It is driven by the need to improve English classroom instruction for university students in China （Wen, 2016）. It is also motivated by the aspiration to enhance the quality of foreign language education in other similar pedagogical contexts outside China. A volume of research has been done by Wen Qiufang and her research team, to formulate the theory of POA and to test its effectiveness in classroom pedagogy （e.g. Wen, 2016, 2015; Yang, 2015; Zhang, 2015）. At the moment, the POA is still at an early stage of theory building and almost all empirical research is done in the Chinese context. In order to improve the quality of this theory and to make it intelligible to the international academic community, a one-day symposium was held in Beijing Foreign Studies University on May 15, 2017. The symposium was entitled ＇The first international forum on innovative foreign language education in China： Appraisal of the POA＇. In the forum, leading experts in applied linguistics were invited to discuss the strengths and weaknesses of the POA and the directions for its future development. The symposium was the first attempt for the POA research team to discuss its latest work with international scholars. This Viewpoint section collects the responses of four experts who participated in the symposium, listed in alphabetical order. The collection of articles covers three topics related to the POA： its pedagogical application, its use for teacher training, and its research. Alister Cumming is Professor Emeritus and the former Head of the Centre for Educational Research on Languages and Literacies, University of Toronto, Canada. His article focuses primarily on POA research as an exemplary case of design-based research. Rod Ellis is Research Professor in the School of Education at Curtin University, Australia. He discusses POA in terms of pedagogy, teacher training and research, with both critiques and constructive suggestions. Paul Kei M
基金supported by National Natural Science Foundation of China (Grant No. 10871117)Natural Science Foundation of Shandong Province (Grant No. Y2006A07)
文摘In this paper, convex solutions for the second type of Feigenbaum's equation f (x) = λ1 f (f (λx)), 0 < λ < 1, f (0) = 1, 0 f (x) 1, x ∈ [0, 1] are investigated. Using constructive methods, we discuss the existence and uniqueness of continuous convex solutions, C1-convex solutions and C2-convex solutions of the above equation.
