谈到初等数学推理时，人们下意识地就会想到欧氏几何，随着计算机技术的发展，代数推理的应用日益增加且中学阶段也多有渗透。但是目前国内鲜有对代数推理能力的理论研究，也没有公认的测评工具。因此本文在梳理国内外相关研究的基础上，给出代数推理能力相关概念界定以及初三学生代数推理能力的测评框架；在北京市某中学的题库中选取考察不同知识要素和能力要素的试题编制预测试卷并设定评价标准，使用SPSS软件分析信效度，在进行预测试后通过改进，形成正式测试卷进行调查研究，分析得出结论并提出教学建议。

关于初三学生代数推理能力测评框架得出结论可以分为四个要素——处理代数关系能力、表征能力、计算能力、论证能力。本研究对学生的代数推理能力的测评以代数知识为载体，代数知识可以分为三个要素——数与式、方程与不等式、函数。

关于初三学生代数推理能力现状得到五条研究结论：第一，初三学生总体代数推理能力较强，但是个体之间能力差异较大；第二，大部分初三学生只能在直观、元素较少时发现关系和描述关系；第三，大部分初三学生较好地使用文字符号图形进行生成表征和转化表征；第四，大部分初三学生较好地找到思路实施并计算结果和检验结果；第五，大部分初三学生能在部分情境中尝试证明合理并用简洁的语言说理。

根据研究结论，提出如下三条教学建议供一线教师参考：第一，可以让学生通过举例应用、淡化概念和定理形式发展学生发现关系和描述关系的能力；第二，可以让学生通过对典型例题例的归纳掌握举一反三的思想，从而发展学生用简洁语言完成代数证明的能力；第三，可以培养学生能够对题目中的关键信息进行识别和理解，并与学过的知识相联系以发展学生的代数推理能力。

When talking about elementary mathematics reasoning, people will subconsciously think of the European set, with the development of computer technology, the possession of algebraic reasoning is increasing, and the middle school stage also has penetration. However, there are few theoretical studies on algebraic reasoning ability in China, and there is no recognized evaluation tool. Therefore, on the basis of combing the relevant research at home and abroad, this paper gives the definition of algebraic reasoning ability and the evaluation framework of algebraic reasoning ability of junior three students. And in a middle school in Beijing to examine the selection of different knowledge elements and ability elements of the test preparation, prediction papers, and set evaluation criteria, and then use SPSS to analyze the reliability and validity, in the prediction, through the improvement of the formation of formal test papers for investigation and analysis of conclusions and teaching recommendations.

The algebraic reasoning ability of junior three students can be evaluated from the following four elements, namely, the ability to deal with algebraic relations, characterization ability, calculation ability and demonstration ability. The evaluation of students' algebraic reasoning ability in this study is based on algebraic knowledge, which can be divided into three dimensions: number and formula, equation and inequality, and function.

The current situation of the third grade students' algebraic reasoning ability is as follows: First, the third grade students' overall algebraic reasoning ability is strong, but there is a big difference between individuals. Second, most of the third grade students can only find and describe the relationship in the intuitive situation and when there are fewer elements. Third, most of the third grade students can better use the word language symbol element, graphic language to generate representation and transformation standards. Fourth, the majority of third grade students can better find ideas and implementation, calculation results and test results. Fifth, the third grade students can basically prove in simple situations and describe the process in concise language.

According to the above situation, the following three teaching suggestions are put forward for the reference of front-line teachers. Firstly, students can develop their ability to discover and describe relations by giving examples and weakening the forms of concepts and theorems. Secondly, students can master the idea of drawing inferences about other cases from one instance by summarizing typical examples, so as to develop their ability to complete algebraic proof in concise language. Thirdly, students should be trained to recognize and understand the key information in the topic, and to relate it to the existing knowledge, so as to develop students'algebraic reasoning ability.