Since two decades, the curriculum reformation in science education, so-called modernization of science-education, has been developed all over the world. Such a new education also has been practisedin our country for the past decades, but recently it has been pointed out that the teaching method inclined to indoctrinate scientific knowledge only, and that the majority of students lost their scientific interests and lacked their scientific abilities and attitudes. Then in this paper, I intend to propose the following from a Popperian viewpoint and the Freudenthal's mathematical-activistic standpoint: (1) In the science (including mathematics) education, we should force our students to conjecture boldly their own solutions of various and interesting problems, and to test (or to refute) them by theoretical inferences or observations or experiments (thought-experiments). (2) We should regard school science not as ready-made but as acted-out (or activity) in the sense of Freudenthal's activism. Therefore we ought to adopt our teaching method not as indoctrination but as the sort of above proposal (1), in other words, we should compel our students to act out their own science (to discover new scientific facts and to acquire new scientific knowledges).
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