On Mathematical Problem Posing.
On Mathematical Problem Posing.
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关于数学问题的提出。
DOI：
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
E. Silver
中科院分区：
文献类型：
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作者：
E. Silver
在世界上所有国家的各级学校的数学课上，都可以看到学生在解决问题。近年来，这些数学问题的质量和真实性一直是许多讨论和辩论的主题。这种关注导致了一个丰富的，更多样化的收集问题被纳入学校数学课程。虽然这些问题本身已经得到了很大的审查，但很少有人注意到学生在学校被要求考虑的问题的来源多样化。学生几乎总是被要求只解决老师或教科书上提出的问题。学生们很少有机会以某种公开的方式提出自己的数学问题。传统的数学教学和学习的传输/接收模式，强调学生被动地接受知识作为传输教学的结果，是兼容的教学法，把问题提出的责任完全掌握在教师和教科书作者手中。另一方面，当代建构主义的教学理论要求我们承认学生生成问题作为教学活动的一个组成部分的重要性。提出问题已经被数学和数学教育领域的一些杰出领导者确定为数学教育的一个重要方面[例如，Freudenthal，1973; Polya，1954]。提出问题是近年来数学教育课程改革和教学改革的一个热点问题。在美国，例如，最近的报告，如课程和评价标准的学校数学[NCTM，1989年]和专业标准的教学数学[NCTM，1991年]，要求增加使用提出问题的活动在数学课堂上。这两份报告都建议，除了让学生解决预先制定的问题外，还应纳入强调学生提出的问题的活动，这在以下数学教学专业标准摘录中得到了明确说明：
In mathematics classes at all levels of schooling in all countries of the world, students can be observed solving problems. The quality and authenticity of these mathematics problems has been the subject of many discussions and debates in recent years. Much of this attention has resulted in a rich, more diverse collection of problems being incorporated into school mathematics curricula. Although the problems themselves have received much scrutiny, less attention has been paid to diversifying the sources for the problems that students are asked to consider in school. Students are almost always asked to solve only the problems that have been presented by a teacher or a textbook. Students are rarely, if ever, given opportunities to pose in some public way their own mathematics problems. Traditional transmission/reception models of mathematics instruction and learning, which emphasized students passively receiving knowledge as a result of transmission teaching, were compatible with a pedagogy that placed the responsibility for problem posing exclusively in the hands of teachers and textbook authors. On the other hand, contemporary constructivist theories of teaching and learning require that we acknowledge the importance of studentgenerated problem posing as a component of instructional activity. Problem posing has been identified by some distinguished leaders in mathematics and mathematics education as an important aspect of mathematics education [e.g., Freudenthal, 1973; Polya, 1954]. And problem posing has recently begun to receive increased attention in the literature on curricular and pedagogical innovation in mathematics education. In the United States, for example, recent reports, such as the Curriculum and evaluation standards for school mathematics [NCTM, 1989] and the Professional standards for teaching mathematics [NCTM, 1991], have called for an increase in the use of problem-posing activities in the mathematics classroom. Both reports have suggested the inclusion of activities emphasizing studentgenerated problems in addition to having students solve pre-formulated problems, as is clearly illustrated in the following excerpt from the Professional standards for teaching mathematics: