Creativity, Mathematizing, and Didactizing: Leen Streefland's work continues

This reaction to the papers in this PME Special Issue of Educational Studies in Mathematics draws a wider perspective on the issues addressed and some of the constructs used in research in Realistic Mathematics Education (RME). In particular, it tries to show that while the problems addressed existed within the world-wide arena of mathematics education and were not unique to the Dutch educational system, the methods used at the Freudenthal Institute to address them were uniquely adapted to that system yet foreshadowed developments in the wider field of mathematics education. The predictive aspects of mathematizing, didactizing, and guided reinvention, in which models-of become models-for on various levels, resonate with trends in mathematics education in recent years, including those promoted by the National Council of Teachers of Mathematics in the USA. Research methodologies, too, have broadened to include more humanistic qualitative methods. Developmental research as epitomized in the RME tradition makes the distinction between quantitative and qualitative research obsolete, because there is no restriction on research methods that may be useful in investigating how to improve the teaching and learning of mathematics, and in the designing of mathematics curricula. Thus some aspects of this research resonate with what have come to be known as multitiered teaching experiments. However, in RME there is also a special content-oriented didactical approach that harmonizes with an emphasis on didactics (rather than pedagogy)in several other European countries. Some implications are drawn for future research directions. This revised version was published online in August 2006 with corrections to the Cover Date.     

论医学数学化的基本途径

现代医学要上两个水平:分子水平与数学化水平。后者将开辟医学体系理论结构的新前景,使医学从实验与经验的范畴迈向严密的科学范畴。 应用模糊数学可以定义疾病集、症状集与疾病集的模糊关系,通过模糊推理、病理数量分析与模式识别可以作医疗诊断决策,从探讨专家系统、电脑问诊系统以及现代医疗器械的数学机制等,可以提高科研与诊断的理论水平,加强医学自身的运行机制,促进医学现代化。     

数学课堂中的"数学化"

“数学化”是近年西方学者提出的一个概念 ,指师生在数学教学过程中共同努力、相互作用 ,使儿童准确理解各种数学表达或运算所需的规则和准则 ,最终形成儿童自身关于各种物体和情境的数学模式。本文以对数学课堂教学的大量观察为基础 ,阐述“数学化”的含义和过程 ,分析影响“数学化”顺利进行的社会因素和心理因素 ,并为数学教学提出一些建设性的建议。这对于我国数学基础教育中儿童数学能力的培养及思维的发展有积极的借鉴意义。