数学作业是高中数学教学和数学学习的重要载体之一。学生通过作业巩固当天所学新知，即使查漏补缺，构建自我知识体系。教师通过丰富多样的题型可以培养学生的自主能力，创新精神，激发他们的学习热情。然而对于处于初高中转换期的高一学生来说，高中数学作业容量较大，对学生的数学思维和学习方法要求相对较高。这种变换会使很多高一学生难以适应，出现对待数学作业态度消极，丧失数学学习兴趣，成绩出现两极分化等现象。因此教师有必要基于数学作业进行分层设计，来帮助高一学生更好的适应高中学习，同时满足不同数学能力的学生对数学学习的需求。

本研究通过问卷调查的方式对兰州市第四中学全体497名高一学生的数学作业现状进行调查。调查结果如下：

（1）当前作业的量、难度、题目类型只能满足部分或大部分学生的需要，并不能满足所有学生的需求。

（2）喜欢现有作业形式的学生也约只占到75%，现有的作业对于激发学生数学学习兴趣几乎没有助益。

（3）当前作业来源单一，不具有层次性，只是偶尔考虑到学生的能力和水平。

结合调查结果和相关文献分析，笔者对高一数学作业分层设计进行实验研究，根据实验结果以及对学生、家长的访谈交流，总结出适合本校学生数学作业分层设计几点方法：

（1）分层作业的选题可以来源于课本、重点例题、课外资料、高考题、平时检测中的易错题等。注意渗透多种类型的题目培养学生数学素质。

（2）教师将题目进行整合改编并按梯度排列，帮助学生在完成作业过程中梳理知识，提高学习效率。

（3）对于能力较弱的学生而言，在自主完成作业的同时，教师应主动引导鼓励这类学生实现“跨层作业”。

（4）教师和家长建立平台进行合作，限定学生完成分层作业时间并加以监督。

（5）对于当日分层作业教师应及时批改、及时反馈交流。一个学习任务结束后教师及时检测、及时调整当前分层。

经过一年多的实践证明，分层设计的作业模式可以增强学生数学学习的主观能动性，削弱学生对数学作业的抵触情绪，帮助学生尽快适应高中数学学习。帮助教师更清楚的了解学生学习状况，消除两极分化，大规模提高班级成绩。收到学生，家长，教师的一致认可。

Mathematics homework is one of the important carriers of high school mathematics teaching and learning. Students consolidate the new knowledge they have learned that day through homework, even if they find gaps and fill in gaps, and build a self-knowledge system. Teachers can cultivate students' self management ability, innovative spirit and stimulate their enthusiasm for learning through a variety of questions. However, for the high school students in the transition period, There is a lot of homework now, and the students' mathematical thinking and learning methods are relatively high. This kind of transformation will make many high school students difficult to adapt, performance polarization and other phenomena. Therefore, it is necessary for teachers to design mathematics assignments in different levels to help students adapt to high school learning and meet the needs of students with different mathematical abilities.

In this study, a questionnaire survey was conducted among 497 senior one students in Lanzhou No. 4 middle school. The results are as follows:

(1) At present, the amount, difficulty and type of the assignment can only meet the needs of some or most of the students, but not all of them.

(2) About 75% of the students like the current form of homework. The existing homework is not helpful to stimulate students' interest in mathematics learning.

(3) At present, the source of homework is single, not hierarchical, only occasionally considering the ability and level of students.

The author conducted an experimental study on the hierarchical design of mathematics assignments in grade one of senior high school, sum Up for the school's students to design mathematics homework hierarchical methods:

(1) The topic selection of stratified homework can come from textbooks and the error prone questions in normal tests. Pay attention to the infiltration of various types of questions to cultivate students' mathematical quality.

(2) Teachers will integrate and adapt the topics and arrange them according to the gradient to help students sort out knowledge and improve learning efficiency in the process of completing homework.

(3) For students with weak ability, teachers should actively guide and encourage such students to achieve "cross-layer work" while completing their own work.

(4) Teachers and parents set up a platform for cooperation to limit the time for students to complete stratified assignments and cultivate students' efficient and independent learning quality.

(5) Teachers of the day's stratified work should be timely corrected, feedback and exchange. After a learning task is completed, the teacher timely detects and adjusts the current stratification.

Through more than one year's practice, it has been proved that the hierarchical design of homework mode can enhance students 'subjective initiative in mathematics study, weaken students' resistance to mathematics work, and help students to better adapt to high school mathematics learning. Help teachers to understand students' learning situation more accurately and improve class performance. Students, parents and teachers all agree with this practice.