即将出版报告人WernerBlumUnivofKasselGermanyQuality.PPT

Pollak: PLACE OF MM (C) The Relations between mathematics and mathematics education ? (1) Modeling as Vehicle versus Modeling as Content. (2) Primary School (3) Secondary School (4) Back to (A1) : The Secondary-Tertiary Interface (5) Modeling as a source of new insights on mathematics itself Niss: PRESCRIPTIVE MODELLING 相对于descriptive modelling: 建模过程有何相同、不同？ 如： BMI、 GINI、 … 检验： 不可证伪 容易批评 The modelling cycle Extra-mathematical domain D Speci- fication Ideali- sation Idealised situation cum questions Mathematical domain M Mathematised situation cum questions Mathemat-ical answers de-mathematisation Mathematisation f translation answers interpretation We have to devise teaching and learning activities for prescriptive modelling, also for situations in which students cannot complete the rudimentary modelling cycle unassisted. Two focal points of such activities (opportunities): Students should be engaged in analysing the hidden or explicit assumptions, requirements, wishes and pre-requisites underlying the mathematisation (to be) undertaken. Students should be engaged in meta-validation of models Challenges and opportunities Kaiser: Modelling Competencies Important theoretical and empirical approaches with a special focus on the relation of modelling competencies and modelling process Important approaches for measuring modelling competencies (including sub-competencies ) Own activities to promote modelling competencies Modelling days / modelling weeks Effectiveness of the holistic versus the atomistic approach to foster modelling competencies D’Ambrosio: MM as a Strategy … CENTRAL QUESTION: How do humans develop strategies which are the basic components of the complex systems of knowledge and behavior? ? ETHNOMATHEMATICS (DAmbrosio in 1977) ? TICS of MATHEMA in different ETHNOS 民族数学？ 民俗数学？ 民俗科学？ D’Ambrosio: MM as a Strategy … The full cycle of knowledge math modelling (not easy!) Bassanezi : MM Training Courses Mode