Abstract Combinatorics has many applications in different disciplines, however, only a few studies have explored students’ combinatorial thinking at the upper secondary and tertiary levels concurrently. The present research is a grounded theory study of eight Year 12 and five undergraduate students, who have participated in semi-structured interviews and responded to eight combinatorial tasks. Three types of combinatorial tasks were designed: combinatorial reasoning, evaluating, and problem-posing tasks. In the open coding phase of data analysis, seventy-one codes were identified which categorized into seven main categories at the axial coding phase. At the selective coding phase, five relationships between categories were identified that led to designing a model of students’ combinatorial thinking. The model consists of three movements: Horizontal, vertical downward, and vertical upward movement. It is asserted that this model could be used to improve the quality of teaching combinatorics, and also as a lens to explore students’ combinatorial thinking.

中文翻译：

---

建立学生组合思维模式

摘要 组合数学在不同学科有很多应用，然而，只有少数研究同时探索高中和大学阶段学生的组合思维。本研究是对 8 名 12 年级学生和 5 名本科生进行的扎根理论研究，他们参加了半结构化访谈并回答了八项组合任务。设计了三种类型的组合任务：组合推理、评估和提出问题的任务。在数据分析的开放编码阶段，确定了71个编码，在轴向编码阶段分为七个主要类别。在选择性编码阶段，确定了类别之间的五种关系，从而设计了学生组合思维的模型。该模型由三个动作组成：水平、垂直向下和垂直向上运动。据称，该模型可用于提高组合数学的教学质量，也可作为探索学生组合思维的一个镜头。