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各种数学概念、公式、法则、定理、推论等,都是一些具体的数学模型《.数学课程标准》指出:数学教学活动不仅要考虑数学自身的特点,更要遵循学生学习数学的心理规律,强调从学生已有的生活经验出发,让学生亲身经历把实际问题抽象成数学模型并进行解释与应用的过程,倡导“问题情境—建立模型—释意、拓展—实践与应用”的教学模式.基于此,我们认为,新课程下数学模型的教学宜分六步进行,即模型的引入、提炼、模仿、拓展、迁移和应用.本文试以人教版课标试验教材中的一个探究问题(见例1)所折射出的一个极值模型为例,对数学模型的教学过程进行探讨,和广大一线教师交流.
Various mathematical concepts, formulas, laws, theorems, and inferences are all specific mathematical models. The “Mathematics Curriculum Standards” states that mathematics teaching activities should not only consider the characteristics of mathematics itself, but also follow the psychological laws of students’ learning mathematics. Emphasizes starting from the student’s existing life experiences, allowing students to personally experience the process of abstracting practical problems into mathematical models and explaining and applying them, advocating “problem situations--building models-explanation-extension-practice and application” Based on this, we believe that the mathematics model teaching under the new curriculum should be divided into six steps, namely the introduction, extraction, imitation, expansion, migration and application of the model. This paper tries to explore a lesson in the teaching materials of the PEPT curriculum standard. The problem (see Example 1) reflects an extremum model as an example, discusses the teaching process of the mathematical model, and communicates with the majority of front-line teachers.