Mathematically gifted students have a high potential for understanding and thinking through mathematical relations and connections between mathematical concepts. Currently, it is thought that generalizing patterns algebraically can serve to provide challenges and opportunities that match their potential. This article focuses on a mathematically gifted student’s use of generalization strategies to identify linear and nonlinear patterns in the context of a matchstick problem. Data were collected from a 10th-grade gifted student’s problem-solving process in a qualitative research design. It was observed that the gifted student’s ways of generalizing the linear and nonlinear patterns were different. In a generalization process, the student used figural reasoning in the linear pattern and numerical reasoning in the nonlinear patterns. It was noted that the student explored using Gauss’s approach in structuring the general rules of nonlinear patterns. Accordingly, aside from assisting their more gifted students, mathematics teachers may want to consider ways to introduce Gaussian thinking to the benefit of all their students.

数学天才的学生通过数学关系和数学概念之间的联系，具有很高的理解力和思考力。当前，认为代数化模式可以用来提供与其潜力相匹配的挑战和机遇。本文重点介绍数学上有天赋的学生如何使用广义化策略在火柴棍问题中识别线性​​和非线性模式。在定性研究设计中，从10年级天才学生的问题解决过程中收集了数据。据观察，资优学生概括线性和非线性模式的方式是不同的。在一般化过程中，学生在线性模式中使用图形推理，在非线性模式中使用数值推理。值得注意的是，该学生探索了使用高斯的方法来构造非线性模式的一般规则。因此，除了帮助他们的才华横溢的学生外，数学老师可能还想考虑将高斯思想介绍给所有学生的方法。