PISA2003以後のドイツの数学教育の動向(1) : 「実質陶冶」から「数学に固有な形式陶冶」へ

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Since PISA2003 many discussions about mathematics education take place in Germany. Soon, KMK (Kurturministerkonferenz) revise curriculum at Elementary(till 4^<th> grade), middle Stage (10^<th> grade), secondary School (Hauptschule: 9^<th> grade) and announce standards. The characteristic is "from material building to mathematical formal building". i.e. (1) Attach more importance to mathematical general competence than material competence. Ex. "to solve problem mathematically", "mathematically modeling", "to make use of mathematical expression", "to argument mathematically", "to communicate mathematically", "to treat symbolic, formal and technical elements of mathematics" (2) Attach mathematical ideas [table] (3) Present three levels of problems first level: reproduction second level: making a relationship third level: generalization and reflection Implication to Japanese Mathematics Education (1) Attach important to learning environments (2) Developing learning environments (3) Bring up many competences in one learning environment (4) Practice intelligently or productively (5) Attach importance to longer performance (6) Improve a quality of lessons Finally I hope Japanese mathematics teaching is more open and long-term than earlier.