In the study of the extremal for Sobolev inequality on the Heisenberg group and the Cauchy-Riemann(CR)Yamabe problem,Jerison-Lee found a three-dimensional family of differential identities for critical exponent subell...In the study of the extremal for Sobolev inequality on the Heisenberg group and the Cauchy-Riemann(CR)Yamabe problem,Jerison-Lee found a three-dimensional family of differential identities for critical exponent subelliptic equation on Heisenberg groupℍn by using the computer in[5].They wanted to know whether there is a theoretical framework that would predict the existence and the structure of such formulae.With the help of dimension conservation and invariant tensors,we can answer the above question.展开更多
As universities in Kazakhstan continue to address the challenges that come with developing English-medium instruction(EMI)programs,university Science,Technology,Engineering,and Mathematics(STEM)teachers need to develo...As universities in Kazakhstan continue to address the challenges that come with developing English-medium instruction(EMI)programs,university Science,Technology,Engineering,and Mathematics(STEM)teachers need to develop capacities to teach in English,while their English teacher counterparts need to develop content-specific pedagogical knowledge.Content and Language Integrated Learning(CLIL)pedagogies,defined as the integration of both language and content curricular goals,have emerged as a vehicle to facilitate this development for both types of teachers.However,what it means to be a CLIL teacher may vary considerably as teachers leverage their professional knowledge and personal experiences.We,therefore,explore teachers’conceptions of CLIL and how their disciplinary,linguistic,and pedagogical backgrounds enable or burden them to forge a“CLIL teacher”identity.This qualitative study illustrates the salient points of the journeys taken by two university teachers,one a specialist in oil and gas,the other an English teacher and teacher educator.Drawing on extended one-on-one interviews,we present two teachers’experiences through a series of CLIL-informed workshops.Using a multidisciplinary analytical framework,we map the ways in which the two teacher participants negotiate their identities in relation to CLIL.The findings highlight the importance of understanding teacher experiences,particularly their language learning backgrounds,attitudes toward supporting student learning,and relationships with their colleagues as they work to adapt to teaching English and STEM subjects in university EMI contexts.展开更多
基金supported by the National Natural Science Foundation of China(12141105,12471194)the first author’s research also was supported by the National Key Research and Development Project(SQ2020YFA070080).
文摘In the study of the extremal for Sobolev inequality on the Heisenberg group and the Cauchy-Riemann(CR)Yamabe problem,Jerison-Lee found a three-dimensional family of differential identities for critical exponent subelliptic equation on Heisenberg groupℍn by using the computer in[5].They wanted to know whether there is a theoretical framework that would predict the existence and the structure of such formulae.With the help of dimension conservation and invariant tensors,we can answer the above question.
基金funding from the U.S.-Kazakhstan University Partnerships program funded by the U.S.Mission to Kazakhstan and administered by American Councils[Award number SKZ100-19-CA-0149].
文摘As universities in Kazakhstan continue to address the challenges that come with developing English-medium instruction(EMI)programs,university Science,Technology,Engineering,and Mathematics(STEM)teachers need to develop capacities to teach in English,while their English teacher counterparts need to develop content-specific pedagogical knowledge.Content and Language Integrated Learning(CLIL)pedagogies,defined as the integration of both language and content curricular goals,have emerged as a vehicle to facilitate this development for both types of teachers.However,what it means to be a CLIL teacher may vary considerably as teachers leverage their professional knowledge and personal experiences.We,therefore,explore teachers’conceptions of CLIL and how their disciplinary,linguistic,and pedagogical backgrounds enable or burden them to forge a“CLIL teacher”identity.This qualitative study illustrates the salient points of the journeys taken by two university teachers,one a specialist in oil and gas,the other an English teacher and teacher educator.Drawing on extended one-on-one interviews,we present two teachers’experiences through a series of CLIL-informed workshops.Using a multidisciplinary analytical framework,we map the ways in which the two teacher participants negotiate their identities in relation to CLIL.The findings highlight the importance of understanding teacher experiences,particularly their language learning backgrounds,attitudes toward supporting student learning,and relationships with their colleagues as they work to adapt to teaching English and STEM subjects in university EMI contexts.
