概念学习是数学学习的出发点,APOS理论是一种基于建构主义的学习理论,是很好的概念学习的理论模型。文章采用文献研究法和文本分析法,以APOS理论为基础,进行指数函数概念的教学设计,旨在帮助学生经历“活动、过程、对象、图式”四个阶段...概念学习是数学学习的出发点,APOS理论是一种基于建构主义的学习理论,是很好的概念学习的理论模型。文章采用文献研究法和文本分析法,以APOS理论为基础,进行指数函数概念的教学设计,旨在帮助学生经历“活动、过程、对象、图式”四个阶段,深度理解知识和主动建构知识。最后提出了在概念教学中教师应注重概念引入生活性、学生学习主体性和知识体系建构性的教学建议。Concept learning is the starting point of mathematics, and APOS theory is a learning theory based on constructivism, which is a good theoretical model of concept learning. The article adopts the literature research method and text analysis method, based on the APOS theory, to carry out the teaching design of the exponential function concept, aiming at helping students to go through the four phases of “activity, process, object, schema” to deeply understand the knowledge and actively construct the knowledge. Finally, it is proposed that in conceptual teaching, teachers should focus on introducing concepts into life, emphasizing students’ subjectivity in learning and the constructiveness of the knowledge system.展开更多
本文主要探讨指数函数族中一类特殊参数——非回归参数的Hausdorff维数问题,这一研究是在邱维元关于指数函数族逃逸参数的Hausdorff维数为2的重要发现基础上进行的自然延伸与深化。本文旨在证明,在给定的一个固定区域内,指数函数族中非...本文主要探讨指数函数族中一类特殊参数——非回归参数的Hausdorff维数问题,这一研究是在邱维元关于指数函数族逃逸参数的Hausdorff维数为2的重要发现基础上进行的自然延伸与深化。本文旨在证明,在给定的一个固定区域内,指数函数族中非回归且非逃逸参数的集合具有的Hausdorff维数严格小于某个给定的正数。This paper primarily delves into the Hausdorff dimension of a special class of parameters within the exponential family—the non-recurrent parameters. This investigation constitutes a natural extension and deepening of Qiu’s seminal finding that the Hausdorff dimension of escaping parameters of the exponential family is 2. The objective of this paper is to prove that, within a given fixed region, the Hausdorff dimension of the set of non-escaping non-recurrent parameters in the exponential function family is strictly less than a specified positive number.展开更多
文摘概念学习是数学学习的出发点,APOS理论是一种基于建构主义的学习理论,是很好的概念学习的理论模型。文章采用文献研究法和文本分析法,以APOS理论为基础,进行指数函数概念的教学设计,旨在帮助学生经历“活动、过程、对象、图式”四个阶段,深度理解知识和主动建构知识。最后提出了在概念教学中教师应注重概念引入生活性、学生学习主体性和知识体系建构性的教学建议。Concept learning is the starting point of mathematics, and APOS theory is a learning theory based on constructivism, which is a good theoretical model of concept learning. The article adopts the literature research method and text analysis method, based on the APOS theory, to carry out the teaching design of the exponential function concept, aiming at helping students to go through the four phases of “activity, process, object, schema” to deeply understand the knowledge and actively construct the knowledge. Finally, it is proposed that in conceptual teaching, teachers should focus on introducing concepts into life, emphasizing students’ subjectivity in learning and the constructiveness of the knowledge system.
文摘本文主要探讨指数函数族中一类特殊参数——非回归参数的Hausdorff维数问题,这一研究是在邱维元关于指数函数族逃逸参数的Hausdorff维数为2的重要发现基础上进行的自然延伸与深化。本文旨在证明,在给定的一个固定区域内,指数函数族中非回归且非逃逸参数的集合具有的Hausdorff维数严格小于某个给定的正数。This paper primarily delves into the Hausdorff dimension of a special class of parameters within the exponential family—the non-recurrent parameters. This investigation constitutes a natural extension and deepening of Qiu’s seminal finding that the Hausdorff dimension of escaping parameters of the exponential family is 2. The objective of this paper is to prove that, within a given fixed region, the Hausdorff dimension of the set of non-escaping non-recurrent parameters in the exponential function family is strictly less than a specified positive number.
