在当今信息技术、人工智能极速发展的背景下，国家在新课程标准指出要深化课程改 革，培养学生的核心素养。为了落实在高中数学课堂中发展数学六大核心素养的要求，教 师不应只是向学生知识灌输，学生也不应仅对知识进行机械式的记忆，而应是基于理解的 教与学，这与深度学习的理念不谋而合。深度学习强调学生对知识本质的理解和掌握，在 学习知识的同时，更注重于培养和提升学生的综合能力和核心素养，处于深度学习水平的 学生有着更强的学习动机和更高效的学习策略，能够将知识内化，形成完整的知识架构， 这正是数学核心素养的体现。由此可见，数学核心素养与深度学习有着高度契合的关系。

在高中阶段，三角函数作为数学学科中的重难点，学生对该内容的掌握程度并不理想。 所以，实现三角函数的深度学习是数学教育的现实需要，在此之前，我们就必须要了解高 中生在三角函数内容深度学习的现状和影响因素。

本研究采用问卷调查法、测验调查法、访谈法对郑州市两所高级中学中 200 名学生展 开调查，在已有研究工具的基础上开发了三角函数深度学习评价工具。本研究将学习方式 倾向与思维结构水平作为深度学习的评测指标，将五类学习方式倾向预设为影响因素。首 先，通过问卷调查来评价学生在三角函数学习过程中是否具有深度学习的学习方式倾向， 随后基于 SOLO 分类理论制定各个思维结构水平的评判标准，根据学生具体的解答情况来 判断学生是否达到深度学习水平，最后结合访谈分析得到高中生三角函数深度学习的现状、 通过相关性分析得到影响因素，如下：

高中生三角函数深度学习的情况并不理想，且各班级之间存在明显差异。学习方式倾 向于深度学习的学生仅有 40%，以高二理科生为主，高一整体表现低于平均水平。高中生 在学习三角函数的概念性质、公式推导等内容时，仅有 20%-35%的学生思维结构水平达到 深度学习；在面对简单的三角函数应用时，比例有所提升，约有 50%-60%。综合分析高二 学生比高一学生在三角函数的深度学习中表现得更好，理科班学生比文科班表现得更好。 通过相关性检验发现，高中生三角函数深度学习的主要影响因素是构建联系和反思整理两 类学习方式倾向，次要影响因素是态度动机、批判质疑和迁移应用三类学习方式倾向。

本研究基于上述研究结果总结出了三条原因：1. 学生缺少批判性思维；2. 学生信息整 合能力较低；3. 学生自我反思意识薄弱。并针对以上原因给出了相应的教学建议：1. 问题 引领思考、打破思维定式、培养批判性思维；2. 设计单元教学、促进知识整合、形成知识 架构；3. 加强课堂互动、教师及时反馈、引导自我反思。最后，结合教学建议进行了相应的单元教学设计。 本研究在一定程度上拓展了深度学习评价体系，对后续开展相关研究给予了帮助，为 一线教师提供了新的评价思路。

In the context of today's extremely rapid development of information technology and artificial intelligence, the state in the new curriculum standards pointed out the need to deepen curriculum reform and cultivate students' core literacy. In order to implement the requirement of developing the six core literacies of mathematics in the mathematics classroom, teachers should not simply instill knowledge, and students should not just memorize mechanically, but should teach and learn based on understanding, which coincides with the concept of deep learning. Deep learning emphasizes students' understanding and mastery of the essence of knowledge, and focuses on cultivating and improving students' comprehensive ability and core literacy while learning knowledge. Students at the deep learning level have stronger motivation and more efficient learning strategies, and are able to internalize knowledge and form a complete knowledge structure, which is the embodiment of core literacy in mathematics. This shows that core literacy in mathematics and deep learning are highly compatible.

At the high school level, trigonometric functions, as a major difficulty in the subject of mathematics, are not well understood by students. Therefore, realizing the deep learning of trigonometric functions is a realistic need for mathematics education, before that, it is necessary to grasp the current status and influencing factors of high school students' deep learning in trigonometric content.

In this study, 200 students in two senior high schools in Zhengzhou City were surveyed using questionnaires, test papers, and interviews, and an evaluation tool for deep learning of trigonometric functions was developed based on existing research tools. In this study, learning style tendency and thinking structure level were taken as the evaluation index of deep learning, and five types of learning style tendency were predetermined as the influencing factors. First, a questionnaire survey was used to evaluate whether students have the learning style tendency of deep learning in the process of trigonometric function learning, and then the criteria of each 

thinking structure level were developed based on SOLO classification theory to determine whether students have reached the level of deep learning according to their specific answers, and finally, the current situation of deep learning of trigonometric function of high school students was obtained by combining with interview analysis, and the correlation analysis to obtain influencing factors, as follows.

High school students' deep learning of trigonometric functions is not satisfactory and varies significantly between classes. Only 40% of the students whose learning style tends to be deep learning are dominated by sophomore science students, and the overall performance in senior year is below average. Only 20%-35% of high school students learn the conceptual properties of trigonometric functions and the derivation of formulas at the level of thinking structure to deep learning; the proportion increases in the face of simple trigonometric applications, about 50%60%. A comprehensive analysis showed that sophomores performed better than freshmen in deep learning of trigonometric functions, and students in science classes performed better than those in arts classes. The correlation test revealed that the main influencing factors of deep learning of trigonometric functions for high school students were two types of learning style tendencies: constructing connections and reflective organizing, and the secondary influencing factors were three types of learning style tendencies: attitude motivation, critical questioning and transfer application.

This study summarizes three reasons based on the above findings: 1. students' lack of critical thinking; 2. students' low information integration ability; and 3. students' weak self-reflection awareness. The study also gives corresponding teaching suggestions for the above reasons: 1. questions lead thinking, break thinking stereotypes, and cultivate critical thinking; 2. design unit teaching, promote knowledge integration, and form a knowledge structure; 3. strengthen classroom interaction, provide teachers with timely feedback, and guide self-reflection. Finally, the corresponding unit instructional design was carried out with the teaching suggestions.

To a certain extent, this study expands the evaluation system of deep learning, gives help to the subsequent development of related research, and provides new evaluation ideas for front-line teachers.