【作者】 梅荣；

【导师】 毕力格图；

【作者基本信息】 内蒙古师范大学 ， 教育硕士（专业学位）， 2023， 硕士

【摘要】 《义务教育数学课程标准(2022年版)》把解决问题作为重要的课程目标,并指出:学生在解决实际问题时能够利用数学知识和数学方法从数学的角度尝试着从数学的角度利用数学知识和数学方法解决“数与代数”应用题。初中数学“数与代数”应用题解题方面学生不仅要学会如何解题,更应该不断地更新补充自己的解题方法。初中数学“数与代数”内容是至关重要的一部分,也是学生解决问题的重要工具。在课堂上利用辅助图解题是一种很好的解题办法,也是学生需要必备的解题能力。在中考题当中也是很常见的一个题型,直接给出图象解题或者让学生作图。为初中数学“数与代数”应用题教学提供参考,采用文献研究法,访谈调查法,问卷调查法,课堂观摩法,案例分析法等研究方法。根据访谈调查和问卷调查发现,辅助图在“数与代数”应用题中使用率很高,在函数应用题中使用的最多,其次就是使用数轴图也很多。在“数与代数”应用题中一定要适当的利用辅助图,不是所有的题型都适合辅助图,在适合的问题里正确使用很重要。对于画辅助图方面也是很需要注意的,教师和学生在教学中需要注意辅助图的简洁性和规范性。通过课堂观摩和案例分析发现,辅助图可以让学生清晰的看出数量关系,方便知道题意,辅助图也可以在日后的学习中也能使用,同时也能提高学习数学的兴趣。研究发现存在的问题有:(1)画出的辅助图不合题意,没注意取值范围;(2)适当的使用辅助图,有些题不用画图就能解决;(3)画出的辅助图不够简洁,不够规范,注意辅助图的多样性。根据以上问题提出教学建议:(1)一定要重视辅助图的规范性和简洁性;(2)根据题意选出最优解题方法,不是只有画图能解决问题,要合理使用辅助图;(3)画出的辅助图紧密联系题意;(4)注重培养学生的数形结合思想。更多还原

【Abstract】 The Mathematics Curriculum Standards for Compulsory Education(2022 Edition)makes problem solving an important curriculum goal and states that students should be able to use mathematical knowledge and mathematical methods to try to solve "number and algebra" application problems from a mathematical point of view.Students should not only learn how to solve problems in middle school mathematics "number and algebra" application problems,but should also update their problem solving methods.The content of "Number and Algebra" is a vital part of middle school mathematics,and an important tool for students to solve problems.The use of auxiliary diagrams in the classroom is a good way to solve problems,and is a necessary problem solving skill for students.It is also a very common type of problem in Chinese exams,where the graph is given directly or the student is asked to make a diagram.The research method used is literature research,interview survey,questionnaire survey,classroom observation,and case study.According to the interview and questionnaire survey,the use of auxiliary diagrams in "Number and Algebra" application problems is very high,the most used in the function application problems,followed by the use of the number axis diagram.Not all types of problems are suitable for auxiliary diagrams,and it is important to use them correctly in the appropriate problems.Teachers and students need to pay attention to the simplicity and standardization of auxiliary diagrams in teaching.Through classroom observation and case studies,it was found that auxiliary diagrams allow students to clearly see the quantitative relationships and facilitate knowing the meaning of the problem,and auxiliary diagrams can also be used in future learning as well as to increase interest in learning mathematics.The problems found in the study are:(1)the auxiliary diagrams drawn do not fit the meaning of the question,not paying attention to the range of values;(2)the appropriate use of auxiliary diagrams,some problems can be solved without drawing a diagram;(3)the auxiliary diagrams drawn are not concise enough,not enough standard,pay attention to the diversity of auxiliary diagrams.According to the above problems,the following teaching suggestions are made:(1)the standardization and simplicity of auxiliary diagrams must be paid attention to;(2)the optimal solution is selected according to the meaning of the problem,not only the drawing can solve the problem,but also the reasonable use of auxiliary diagrams;(3)the auxiliary diagrams drawn are closely related to the meaning of the problem;(4)attention is paid to the cultivation of students’ ideas of combining numbers and shapes.更多还原