What Makes a Sign a Mathematical Sign? – An Epistemological Perspective on Mathematical Interaction

Mathematical signs and symbols have a decisive role for coding, constructing and communicating mathematical knowledge. Nevertheless these mathematical signs do not already contain mathematical meaning and conceptual ideas themselves. The contribution will present basic elements of an epistemology of mathematical knowledge and then apply these theoretical ideas for analyzing case studies of two teaching episodes from elementary mathematics teaching. In this way different roles of mathematical signs as means of communication (oral function), of indicating (deictic function) and of writing (symbolic function) will be elaborated.     

The early manifestation of developmental dyslexia: Evidence from German children

The present study retrospectively examined early difficulties with phonological coding and phonemic segmentation of German children who after four years in school were diagnosed as dyslexic. German, in comparison to English, exhibits rather simple and straight-forward grapheme-phoneme correspondences, and the initial teaching approach was phonics oriented. Despite these favorable circumstances for the acquisition of phonological coding, the majority of the later dyslexic children had particular difficulties with the accurate reading of nonwords and of unfamiliar words after about seven months of reading instruction. However, there were enormous differences between the dyslexic children. Two of them were completely unable to blend phonemes into pronunciations, another seven were slow and error prone decoders, and three children had slow and laborious pronunciation assembly as the core problem. The majority of the later dyslexic children also exhibited phonemic segmentation deficits as tested with a nonword spelling task and a phoneme reversal task. In correspondence with findings from older German dyslexic children, the early difficulties with accurate phonological coding and phonemic segmentation were no longer found at the end of grade four. Children then suffered from very slow reading and poor spelling. In general, the difficulties of German dyslexic children emphasize the phonological impairment account of dyslexia. More specifically, these findings suggest that the assembly of letter sounds into pronunciations is particularly affected in the early phase of learning to read a consistent orthography.     

春天的天鹅

张开犹如协和式飞机机翼般的翅膀,今天早上佛瑞德和伊西尔姿态优美地降落在我们那个部分还结着冰的池塘,然后开始了它们一年一度的造访。在沿着密西西比河候鸟迁徙所经路径上有150万只加拿大天鹅,这个洲际鸟类迁徙地区从墨西哥湾湿地一直延伸到哈得逊湾。那么我是如何认识这两只叫     

Using the Internet to Improve University Education: Problem-Oriented Web-Based Learning with MUNICS

Up to this point, university education has largely remained unaffected by the developments of novel approaches to web-based learning. The paper presents a principled approach to the design of problem-oriented, web-based learning at the university level. The principles include providing authentic contexts with multimedia, supporting collaborative knowledge construction, making thinking visible with dynamic visualisation, quick access to content resources via information and communication technologies, and flexible support by tele-tutoring. These principles are used in the MUNICS learning environment, which is designed to support students of computer science to apply their factual knowledge from the lectures to complex real-world problems. For example, students may model the knowledge management in an educational organisation with a graphical simulation tool. Some more general findings from a formative evaluation study with the MUNICS prototype are reported and discussed. For example, the students’ ignorance of the additional content resources is discussed in the light of the well-known finding of insufficient use of help systems in software applications.     

Tomorrow’s teachers—selecting the best: An exploration of the quality rationale behind academic and experiential selection criteria for initial teacher education programmes

Using Ireland as an example, this paper explores the rationale behind various selection criteria currently used to select suitable candidates for initial teacher education courses. It investigates and discusses patterns of association between second-level student teachers’ background characteristics on entry to their teacher education programme Professional Diploma in Education (PDE) and their achievement in terms of their final academic and teaching practice grades. It draws on a longitudinal analysis of application and examination data collected from eight student teacher cohorts (2000–2007, N?=?1,023) who completed their second-level initial teacher education at one Irish university. Special attention will be paid to the predictive value of entrants’ prior academic performance and teaching experience for their success in the academic as well as practical components of their teacher education course. The quality rationale behind academic selection criteria is contested on the basis of findings from this study. The positive impact of prior teaching experience on teaching practice performance and the differences in achievement observed between students from different academic fields are discussed.     

Why choose teaching? An international review of empirical studies exploring student teachers’ career motivations and levels of commitment to teaching

Why do individuals all over the world choose to become school teachers? What motivates them to become educators of young people, and how committed are they to this cause when they enter their teacher education courses? Considering that teacher motivation and commitment have been identified as crucial factors for the future success of education and schools (Huberman, 1993 Huberman, M. (1993). The lives of teachers (J. Neufeld, Trans.). London: Cassell Villiers House. [Google Scholar]; Manning & Patterson, 2005 Manning, M., & Patterson, J. (2005). Special publications. Childhood Education, 81, 249–251. doi: 10.1080/00094056.2005.10522284[Taylor & Francis Online] , [Google Scholar]; Rikard, 1999 Rikard, G. L. (1999). Promoting teacher commitment in pre-service teachers. Journal of Physical Education, Recreation & Dance, 70(9), 53–56. doi: 10.1080/07303084.1999.10605969[Taylor & Francis Online] , [Google Scholar]), these are important questions for policy makers and societies to address. This paper provides a systematic and conceptual review of empirical research studies exploring student teachers’ career motivations and commitment in 23 countries from 5 continents. A variety of motivating factors are explored, their relative importance in student teachers’ career decisions is discussed, and differences between various subgroups and cultural contexts are highlighted. Attention is drawn to methodological limitations as well as recent developments in this important area of research.     

Teaching and Learning the Interplay Between Chance and Determinism in Nonlinear Systems

That the interplay of random and deterministic processes may result in both the limited predictability of nonlinear systems and the formation of structures seems to be a most valuable general insight into the nature of science. This study investigates the possibility of teaching and learning the interplay of chance and determinism in nonlinear systems in school science instruction. An analysis of the relevant scientific literature and an explorative learning process study with 30 11th-grade students are included. Three experiments displaying the behaviour of nonlinear systems (deterministic chaos, self-organization and fractals) and one experiment demonstrating the behaviour of linear systems were discussed using a teaching experiment design. The findings show that although the majority of students initially considered chance and determinism as contradictory conceptions, they finally developed sound explanations concerning the interplay of chance and determinism in the investigated nonlinear systems.