如何通过培养学生的数学关键能力，从而促进学生数学核心素养的发展成为数学教育领域需要解决的现实问题。新兴信息技术和学科教学的深入融合以促进学生学科能力和素养的发展，成为基础教育研究的热点之一。数字化资源是学生进行数字化学习的关键，在实现新型教与学方式中发挥着重要作用，其应用的理论与实践研究已成为研究重点。学生数字化资源学习效果成为教育工作者关注的焦点话题。已有研究主要围绕数字化资源学习效果、数字化资源学习反馈等方面展开：从学习效果评价看，已有研究评价工具以知识导向为主，忽视了能力和素养评价；从学生数字化资源学习反馈看，已有研究以教师和学生访谈、问卷调查为主，侧重定性和主观分析，难以客观把握学生数字化资源学习表现。
      本研究聚焦于互联网+支持下的学习环境中，如何通过数字化资源的学习促进初中生数学关键能力的培养。以新兴信息技术为支撑，以数学关键能力培养为目标，从学生数字化资源学习角度开展数字化资源应用实证研究。本研究在面向关键能力培养的数学教学中设计数字化资源学习，以五所学校七年级520名学生为研究对象，设置实验班和对照班，采取准实验设计探究数字化资源学习效果。在此基础上，追踪初中生数字化资源学习记录，采用比较法、统计法、编码法等研究方法，评价初中生数字化资源学习整体表现，构建初中生数字化资源学习路径，比较不同学生数字化资源学习路径表现。通过对数据的记录、挖掘与分析，得到以下研究结论：
      1. 基于数学关键能力的初中生数字化资源学习效果：本研究依托互联网＋数字化资源学习平台，设计开展了基于数学关键能力的数字化资源学习，通过准实验研究对比数字化资源支持下的数学学习与常规数学学习效果，研究发现：参加数字化资源学习的学生数学关键能力显著提升；随着实验的进行，参加数字化资源学习的学生数学关键能力一直上升；随着实验的进行，实验效果持续提升。
      2. 基于数学关键能力的初中生数字化资源学习表现：按照学习效果和能力表现将学生分组，比较不同学生数字化资源学习表现，研究发现：取得高学习效果的学生数字化资源学习表现优于其他学生；学生基础类资源学习表现优于其他资源。
      3. 基于数学关键能力的初中生数字化资源学习路径表现：首先通过理论和经验构建出数字化资源学习路径类型，然后从统计学意义上分析学生数字化资源学习路径表现特点，紧接着从不同阶段和不同类型两个方面分析学生数字化资源学习路径表现，研究发现：第一，初中生数字化资源学习路径共有六种类型，包括一直上升型、波动上升型、一直下降型、波动下降型、不变型、反复型。第二，取得高学习效果的学生中，高能力学生学习路径从波动上升型、一直上升型逐渐趋向于分散，而中、低能力学生学习路径从分散到以波动上升型路径为主。第三，相较于其他路径，不同学生波动上升型学习路径表现均较优。不同学生波动上升型学习路径比例较高，且该类型学习路径具体指标表现较优。第四，关注学习路径中的复习行为占比等具体指标。学生取得不同学习效果的区别之一在于复习行为占比。第五，将数学关键能力要素纳入学生数字化资源学习路径表现分析指标。
      通过准实验设计验证互联网+环境中基于数学关键能力的初中生数字化资源学习效果，在此基础上评价初中生数字化资源学习整体表现，从学习路径的角度刻画初中生数字化资源学习过程，充分挖掘不同学生各类型学习路径表现，为持续提升数字化资源学习效果提供了更加有力的支撑和多元化的选择，也为数字化资源支持下的数学教学、学生数字化资源学习、数字化资源开发等方面提供了有益的借鉴。

How to cultivate students’ mathematical key competence in mathematics teaching so as to promote the development of students’ core literacy in mathematics has become a practical problem that needs to be solved in the field of mathematics education. The in-depth integration of emerging information technology and subject teaching to promote the development of students’ subject competence and literacy has become one of the hotspots of basic education research. Digital resources are the key to students’ digital learning and play an important role in the realization of new teaching and learning methods, and the theoretical and practical research of its application has become the focus of research. The learning effect of students’ digital resources has become the focus of educators. The existing research mainly focuses on the learning effect of digital resources and the learning feedback of digital resources: from the perspective of learning effect evaluation, the existing research evaluation tools focus on knowledge orientation and ignore the evaluation of competence and literacy; from the feedback of students’ learning of digital resources, the existing research focuses on interviews and questionnaires between teachers and students, focusing on qualitative and subjective analysis, which is difficult to objectively grasp the learning performance of students’ digital resources.

Supported by emerging information technology and aiming at the cultivation of mathematical key competence, this study carries out empirical research on the application of digital resources from the perspective of students’ digital resource learning. Therefore, the research question of this research is: in the learning environment supported by the Internet plus, how to promote the cultivation of mathematical key competence of secondary school students through the learning of digital resources? This study designs digital resource learning in mathematics teaching for key competence training. It takes 520 seventh-grade students from five schools as the research object, sets up experimental classes and control classes, and adopts quasi-experimental design to explore the effect of digital resource learning. On this basis, track the learning records of digital resources of secondary school students, use comparative method, statistical method, coding method and other research methods to evaluate students’ learning performance of digital resources, construct students’ learning path of digital resources, and compare the learning path performance of digital resources of different students. Through the recording, mining and analysis of data, the following research conclusions are obtained:

1. The learning effect of secondary school students’ digital resources based on the mathematical key competence: this research relies on the Internet plus digital resource learning platform to design and carry out secondary school mathematics learning supported by digital resources, and compare the effects of mathematics learning supported by digital resources with conventional mathematics learning through quasi-experimental research. The research found that the mathematical key competence of students who participated in the digital resource learning have been significantly improved; as the experiment progressed, the mathematical key competence of the students who participated in the digital resource learning continued to increase; as the experiment progressed, the experimental effect continued to improve.

2. Secondary school students’ digital resource learning performance based on the mathematical key competence: group students according to their learning effect and competence performance, and compare the learning performance of different students’ digital resources. The research found that the overall performance of students with high learning effects in digital resource learning is better than other students; the learning performance of students’ basic resources is better than that of other resources.

3. The performance of secondary school students’ digital resource learning path based on the mathematical key competence: firstly, the types of digital resource learning path are constructed through theoretical experience, and then the performance characteristics of students’ digital resource learning path are analyzed statistically. Then, the performance of students’ digital resource learning path is analyzed from two aspects of different stages and types. First, there are six types of digital resource learning paths for secondary school students, including continuously ascending type, fluctuating ascending type, continuously declining type, fluctuating declining type, invariant type, and repetitive type. Second, among the students who have achieved high learning effects, the learning paths of high-competence students gradually tend to be scattered from fluctuating ascending type and continuously ascending type, while the learning paths of middle and low-competence students tend to be mainly fluctuating ascending type. Third, focus on the fluctuating ascending type learning path. The proportion of different students’ choice of fluctuating ascending type learning path is higher, and the specific indicators of this type of learning path are better. Fourth, pay attention to specific indicators such as the proportion of review behavior in the learning path. One of the differences between students’ different learning effects is the proportion of review behavior. At last, describe students’ learning path performance with two-dimensional data of mathematical key competence elements and learning behavior.

The quasi-experimental design verifies the learning effect of secondary school students’ digital resources based on mathematical key competence in the Internet plus environment, evaluates the learning performance of secondary school students’ digital resources on this basis, characterizes the learning process of secondary school students’ digital resources from the perspective of learning paths, and fully explore the performance of different students’ learning paths, provide a more powerful foundation and diversified choice for continuously improving the learning effect of digital resources, and also provide a useful reference for mathematics teaching supported by digital resources, students’ digital resource learning, and digital resource development, etc.