From natural numbers to numbers and curves in nature —I

The interconnection between number theory, algebra, geometry and calculus is shown through Fibonacci sequence, golden section and logarithmic spiral. In this two-part article, we discuss how simple growth models based on these entities may be used to explain numbers and curves abundantly found in nature     

教师专业化与教师应对教育改革的能力

本文论述的是中国教育改革发展变化过程中的教师专业化问题,所以提出这一问题的背景,是联合国教科文组织讨论了“全民教育”的各项活动和中国教育改革.当前教育改革的目的,在于提高个体和全民发展的能力.因此,教育质量成为人们日益关注的重要问题.教师的工作职能是要推动教育改革的各项措施得到实施.本文认为,“信息时代”的要求和“知识经济”的兴起,使人们对人才的特点有了新的理解,也证实了在教育儿童和青少年成为未来工作者和公民方面存在的不足.综观中国教育改革,它是一个被迫出现的过程,导致学校对教育改革的反应不灵敏.教师作为专业人员,应该支持改革,但是他们的效能还是存在一定的问题.本文进一步认为,中国教师当前面临的主要问题是不具备应对改革的能力.有关研究表明,教师工作的本质及其关注的问题与教育改革的预期大相径庭.这一问题即使通过行政命令、在职培训、或者投入更多的教育资源也难以解决.本文认为,进行全面改革的同时,要改革学生评价和选拔制度,从文化和社会层面上来思考教师职业,树立新的教师专业发展理念.     

Word-learning skills of deaf preschoolers: the development of novel mapping and rapid word-learning strategies

Word-learning skills of 19 deaf/hard-of-hearing preschoolers were assessed by observing their ability to learn new words in two contexts. The first context required the use of a novel mapping strategy (i.e., making the inference that a novel word refers to a novel object) to learn the new words. The second context assessed the ability to learn new words after minimal exposure when reference was explicitly established. The children displayed three levels of word-learning skills. Eleven children learned words in both contexts. Five were able to learn new words rapidly only when reference was explicitly established. Two children did not learn new words rapidly in either context. The latter seven children were followed longitudinally. All children eventually acquired the ability to learn new words in both contexts. The deaf children's word-learning abilities were related to the size of their vocabularies. The present study suggests that word-learning strategies are acquired even when children are severely delayed in their language development and they learn language in an atypical environment.     

Induced in incorrect generalizations leading to misconceptions—an exploratory investigation about the laws of reflection of light

The phenomena of induced incorrect generalization (IIG) as a generative cause for the formation of a misconception among a group of pupils is identified. In the process of learning the laws of reflection of light the effect of IIG is discussed through an exploratory experiment. Strategies are suggested to eliminate the formation of such IIG in a classroom situation.     

Characteristics of students who benefit from high-quality mathematics instruction

The present study examined characteristics of students who took advantage of the opportunity to learn Algebra II from a highly skilled teacher. In particular, student information was gathered concerning: (a) the amount of mathematics students knew prior to the class, (b) their motivation for learning mathematics, (c) the number and types of interactions they had with the teacher during class, (d) degree of self-regulation, and (e) general aptitude. A model for achievement was used that suggests both opportunity and propensity are important (i.e., students must be willing and able to take advantage of opportunity). Support for the model was found. Propensity to take advantage of a highly favorable opportunity accounted for almost sixty percent of the variance in achievement. In particular, students who were self-regulated, had strong mathematics backgrounds, and had low levels of frustration benefited more from high-quality instruction.     

Lecturers on teaching within the ‘supercomplexity’ of Higher Education

While a vast literature exists on students and their learning, work on lecturers and their teaching continues to lag some way behind. This paper explores the notion that the complexity of Higher Education (HE) today significantly impacts upon what goes on in the classroom through a two-tiered study. Semi-structured interviews were conducted to explore lecturers’ perceptions and experiences of teaching a specific module. Interviewees raised issues pertaining to the wider departmental, institutional and socio-political context. Consequently, focus groups were run with key people in the University to explore their perceptions of teaching and learning within the current HE climate. The findings suggest that lecturers perceive numerous external factors to impinge upon their teaching and attempt to militate against these in various ways in order to achieve ongoing enhancement of learning for students.

Disciplinary Literacies and Learning to Read for Understanding: A Conceptual Framework for Disciplinary Literacy

This article presents a framework and methodology for designing learning goals targeted at what students need to know and be able to do in order to attain high levels of literacy and achievement in three disciplinary areas—literature, science, and history. For each discipline, a team of researchers, teachers, and specialists in that discipline engaged in conceptual meta-analysis of theory and research on the reading, reasoning, and inquiry practices exhibited by disciplinary experts as contrasted with novices. Each team identified discipline-specific clusters of types of knowledge. Across teams, the clusters for each discipline were grouped into 5 higher order categories of core constructs: (a) epistemology; (b) inquiry practices/strategies of reasoning; (c) overarching concepts, themes, and frameworks; (d) forms of information representation/types of texts; and (e) discourse and language structures. The substance of the clusters gave rise to discipline-specific goals and tasks involved in reading across multiple texts, as well as reading, reasoning, and argumentation practices tailored to discipline-specific criteria for evidence-based knowledge claims. The framework of constructs and processes provides a valuable tool for researchers and classroom teachers' (re)conceptualizations of literacy and argumentation learning goals in their specific disciplines.