基于数学游戏的教育价值和培养学生数学学习兴趣的需要，本文以约瑟夫问题该数学游戏为例，研究数学游戏对初中生数学学习兴趣的影响，根据文献综述将数学学习兴趣分为情境兴趣和个体兴趣，分别研究数学游戏对两者的影响。以厦门市某学校部分九年级学生为研究对象，采用准实验研究方法、问卷调查法和质性研究方法，设置实验班和对照班，对照班正常教学，不实施数学游戏课程，实验班除了正常教学外，实施数学游戏课程。对实验班学生发放数学学习情境兴趣问卷并设置开放题，分析数学游戏对学生数学学习情境兴趣的影响；在实施数学游戏课程前后对照班和实验班都发放了数学学习个体兴趣调查问卷进行前测和后测，分析数学游戏对学生数学学习个体兴趣的影响，研究结果如下：

（1）首先梳理约瑟夫问题中的数学知识，从简易的约瑟夫问题、经典的约瑟夫问题、广义的约瑟夫问题、约瑟夫问题的变式、约瑟夫排列出发整理相关命题与定理，并给出证明。归纳其中的数学思想方法，包括合情推理与演绎推理、化归思想、递归思想、分类讨论思想，最后给出教学安排以及教学设计案例。

（2）数学游戏能够激发学生的数学学习情境兴趣，研究假设H1成立；数学游戏对学生数学学习情境兴趣的影响在性别方面无显著差异，研究假设H2成立；数学游戏对学生数学学习情境兴趣的影响在成绩方面无显著差异，研究假设H3成立。从情感体验和认知体验两个维度对学生游戏课程的感受和体会进行质性分析，情感体验上，大部分学生觉得游戏课程有趣好玩，体会到探究思考的快乐，并且对数学这门学科的观念和情感发生了一些变化，觉得数学有趣有魅力而不枯燥，更喜欢数学。在认知体验上，学生不仅掌握了约瑟夫问题的取胜策略，还学会了其中的数学思想方法，并且在游戏的影响下，进一步认识到数学的价值，如数学应用的广泛性以及重要性和基础性。

（3）后测实验班学生的数学学习个体兴趣以及价值认识维度显著高于对照班，实验班后测的数学学习个体兴趣以及情感体验维度显著高于前测，说明数学游戏对学生的数学学习个体兴趣以及情感体验维度和价值认识维度有显著影响，研究假设H4成立。数学游戏对女生的个体兴趣及其各维度的提高与影响更大，但这一影响不存在显著差异，研究假设H5成立；数学游戏对成绩为C水平学生的数学学习兴趣影响和提升最大，远超A水平和B水平的学生。可能的原因是对于A、B水平的学生，他们本身数学学习成绩较好，对数学的兴趣水平也较高，因此不通过数学游戏也能对数学产生兴趣，修正了研究假设H6。

Based on the educational value of math games and the need to cultivate students' interest in math learning, this paper studies the influence of math games on junior middle school students' interest in math learning by taking the math game named Josephus Problem as an example. According to the literature review, math learning interest is divided into situational interest and individual interest, and the influence of math games on them is studied respectively.Taking some grade 9 students in a school in Xiamen City as the research object, this paper adopts quasi-experimental research methods, questionnaire survey and qualitative research methods to set up experimental class and control class. The control class teaches normally and does not implement mathematics game course, while the experimental class implements mathematics game course in addition to normal teaching.To analyze the influence of mathematical games on students' interest in mathematical learning situation, questionnaires and open questions were distributed to students in experimental class.Before and after the implementation of the math game course, both the control class and the experimental class issued questionnaires on individual interest in math learning for pre-test and post-test to analyze the influence of math games on students' individual interest in math learning. The research results are as follows:

(1) Firstly, the mathematical knowledge in Josephus problem is sorted out, and relevant propositions and theorems are sorted out from simple Josephus problem, classical Josephus problem, generalized Josephus problem, variations of Josephus problem and Josephus permutation, and the proof is given.It summarizes the mathematical thinking methods, including reasonable reasoning and deductive reasoning, transformation thought, recursion thought, classified discussion thought, and finally gives the teaching arrangement and teaching design cases.

(2) Math games can stimulate students' situational interest in math learning , so hypothesis H1 is valid;The influence of mathematical games on students' situational interest in math learning has no significant difference in gender, so the research hypothesis H2 is valid.The influence of mathematical games on students' situational interest in math learning has no significant difference in academic performance, and the research hypothesis H3 is valid.Qualitative analysis is made on students' feelings and experience of game course from two dimensions of emotional experience and cognitive experience. In terms of emotional experience, most students think game course is interesting and fun, and feel the happiness of exploring and thinking. Moreover, their ideas and feelings towards mathematics have changed, and they think mathematics is interesting and charming rather than boring, and prefer mathematics.In terms of cognitive experience, students not only master the winning strategy of Josephus problem, but also learn its mathematical thinking and methods. Under the influence of games, they further realize the value of mathematics, such as the universality, importance and foundation of mathematical application.

(3) The individual interest in mathematics learning and the value perception dimension in the post-test experimental class are significantly higher than those in the control class, and the individual interest in mathematics learning and the affective experience dimension in the post-test experimental class are significantly higher than those in the pre-test, indicating that math games have a significant impact on students' individual interest in math learning, dimension of emotional experience and dimension of value understanding. The research hypothesis H4 is valid.The mathematical games have a greater increase and impact on girls' individual interest and its dimensions, but this impact dosen’t differ significantly, and research hypothesis H5 holds;Math games have the greatest influence on and improve the interest of math learning of students at C level, far more than students with grade levels A and B.The possible reason is that students with A and B levels have a good performance in mathematics and a high level of interest in mathematics, so they can become interested in mathematics without math games, revising research hypothesis H6.