推理与证明是初中学生数学学习中需要着重培养的主要能力之一，数学教科书是师生开展数学教学活动的主要参考依据，教科书中所提供的推理与证明机会对于发展学生数学推理能力有较大的影响。人教版教科书在我国初中数学课程教学中的使用范围十分广泛，对人教版教科书中正文与例习题是否为学生提供推理与证明的机会、提供了哪些推理与证明的类型进行研究分析可以为广大师生在教学实践中有针对性地发展学生推理与证明能力提供参考。

本研究参考现有研究框架，依托推理与证明能力及其培养的相关理论，通过预编码与分析讨论，构建并调整确定对初中数学教科书中为学生提供推理与证明机会及其类型划分进行判断、分类的研究框架，从而对人教版八年级下册数学教科书中所主要呈现的正文与例习题两大方面为学生提供推理与证明的机会及其类型进行编码分析。

研究结果表明，代数、几何、统计与概率三大主要数学学习主线的教科书呈现中，人教版八年级下册数学教科书在正文和例习题部分均有为学生提供一定推理与证明的机会。其中，本册教科书中几何部分包括勾股定理和平行四边形的学习，是发展推理与证明能力的主要领域，且以给出严格证明为主，对猜想或评价论点的考察往往都与需要进一步证明这个猜想或论点为何是真或是假有紧密联系。在代数方面，该册以二次根式和一次函数的学习为主，要求识别模式的正文或例习题的占比在一定程度上相对较高。由于不涉及推理与证明、更侧重于运算能力培养的例习题所占比重较大，代数部分提供的推理与证明机会相较而言不够明显。而对于数据分析这一包含于统计与概率主线的学习内容来说，主要以提供非形式论证的形式、为判断一个论点是否正确提供支撑，更注重于学生能够领悟并指出实际问题解决中涉及的数学原理。

基于上述结论，本文还结合教育实践经验以及对教师访谈获得的反馈等，以教育教学理论和已有相关研究的成果为指导，讨论了数学教师在教学实践中如何更合理、有效地使用教科书和各类教材资源以促进学生推理与证明能力的发展，给出实践性建议如下：（1）不断学习教育教学理论，树立科学的教科书使用观；（2）明确课程标准的目标要求，切实掌握能力发展需要；（3）领悟教科书正文叙述意图，有效创设问题情境；（4）把握教学内容及学情，精选例习题；（5）注重课程资源开发与应用，创造性使用资源；（6）关注每一个数学课程主线中各类型推理与证明机会的创设。

Reasoning and proof is one of the main abilities that middle school students should focus on in mathematics learning. Mathematics textbooks are the main reference basis for teachers and students to carry out mathematics teaching activities. The reasoning and proof opportunities provided in the textbooks have an impact on the development of students' mathematical reasoning ability. The PEP mathematics textbooks are widely used in middle school mathematics teaching in China. It is meaningful to research and analyze whether the narratives and exercises in the PEP mathematics textbooks provide students with opportunities for reasoning and proof, and what types of reasoning and proof are provided, that can provide a reference for teachers and students to train students' ability of reasoning and proof in teaching practice.

This research refers to the existing research framework, based on the relevant theories of reasoning and proof ability and its cultivation, through precoding and analysis and discussion, thus constructing, adjusting and confirming a research framework. To analyze the main narratives and exercises presented in the PEP eighth-grade second-volume mathematics textbook to provide students with opportunities and types of reasoning and proof.

The research results show that for the three main mathematics learning areas of algebra, geometry, and statistics, the narratives and exercises in the second volume mathematics textbook of the PEP eighth-grade mathematics textbooks provide students with certain opportunities for reasoning and proof. Geometry includes the pythagorean theorem and parallelograms, which are the main areas for developing reasoning and proof capabilities. The main task is to provide a rigorous proof, and making a conjecture or evaluating an arguments also requires further proof of the authenticity of the conjectures or arguments. In algebra, the book focuses on the study of quadratic radicals and linear functions. The narrative and exercises to identify a pattern account for more. Because it does not involve reasoning and proof but focuses more on the training of computational ability, the proportion of exercises is relatively large, and the reasoning and proof opportunities provided by the algebra part are not obvious enough. Data analysis represents the study of statistics, which is mainly presented as a request to provide a non-proof argument, thereby explaining the principle of judging the authenticity of an argument. This part pays more attention to students' ability to comprehend and point out the mathematical principles involved in solving practical problems.

Based on the above conclusions, this research also discussed how mathematics teachers should use textbooks reasonably and effectively in teaching practice to promote the development of students' reasoning and proof ability. The following suggestions are based on the experience of educational practice and the feedback obtained from interviews with teachers, guided by educational teaching theory and related research results: ①Continuously study the theory of education and teaching, and establish a scientific view on the use of textbooks. ②Clarify the goals and requirements of the curriculum standards, and earnestly grasp the needs of ability development. ③Comprehend the narrative intentions of the textbooks and effectively create problem context. ④Grasp the teaching content and learning conditions, select examples and exercises.⑤Focus on the development and application of curriculum resources, and use resources creatively. ⑥Focus on the creation of various types of reasoning and proof opportunities in each mathematics field.