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以探求斐波那契数列的通项公式为目的来体会和运用待定系数法,理解类比思想、转化与化归思想,帮助学生体会、运用研究数学的一般性方法。学生不仅知道了待定系数法的来源,而且知道待定系数法的类别,这个“系数”不仅仅可以是常数,也可以是某项的常数倍。通过这样的类比迁移,可以让高中生理解和接受二阶线性递推关系的特征方程,还可以迁移到高阶线性递推关系式的处理。求斐波那契数列通项公式的方法不止一种,对于高中学生而言,能够理解和接受的方法并不多,虽然特征方程法是简单的推导方法,且采用类比迁移、转化与划归的思想方法更符合“最近发展区”阐释的认知特点,学生更易于理解与接受,更有意义的是,学生可以体会到数学方法的强大作用与重要价值,在学习中逐步有意识地运用数学思想方法,提高数学核心素养中的“逻辑推理”能力,提升数学思维的严谨性。
To explore the Fibonacci sequence formula for the purpose of understanding and the use of undetermined coefficient method to understand the analogy thinking, conversion and the return of ideas to help students understand the use of mathematical methods to study the general method. Students not only know the source of the law to be determined, but also know the category of the coefficient method to be determined, this “coefficient ” not only can be constant, it can also be a constant times. Through such analogy migration, high school students can understand and accept the second order linear recurrence relational characteristic equation, and can also migrate to higher order linear recurrence relational processing. There are more than one way to find out the general formula of Fibonacci numbers. For high school students, there are not many methods that can be understood and accepted. Although Eigenvalue method is a simple method of derivation, it adopts the method of analogical transfer, transformation and classification Is more in line with the cognitive characteristics explained in the “recent development zone”, and it is more easy for students to understand and accept. What is more significant is that students can understand the powerful role and important value of mathematical methods and gradually and consciously Apply mathematical thinking and methods to improve the “logical reasoning” ability in mathematical core literacy and improve the rigor of mathematical thinking.