i on 5 18.7 18.6 23.7 22.6 28.3 28.3 30.0 25.8 23.3 22.2 6 20.0 20.0 20.7 20.7 23.3 23.3 26.6 26.7 27.8 26.7 Deductio n 7 12.9 12.4 17.4 16.3 18.3 16.7 14.2 13.3 22.2 22.2 8 11.0 11.0 18.2 18.2 20.6 20.6 19.2 19.2 17.8 14.4 Rigor 9 9.1 8.1 8.1 7.4 10.0 9.4 11.7 11.6 10.0 10.0 10 2.38 2.38 4.81 4.81 6.11 6.11 9.17 9.17 5.56 4.44 N Sample 210 of Student Teachers 270 of Student Teachers 180 of Student Teachers 120 of Student Teachers 90 of Student Teachers Information: CA: Correct Answer CR: Correct Reason Based on these results it can be concluded that the student teachers from 2013 to 2017 were able to answer correctly more than 50% at the level of visualization and analysis. In addition, the student teachers were able to answer only about 30% of the level of abstraction, 22% of the deduction level, and 11% of the rigor level. The results showed that the student teachers did not understand the definition well and did not classify well the various types of quadrilateral at the level of abstraction, deduction, and rigor. This result was a serious problem for student teachers as they will transfer knowledge to their students in elementary, junior, and senior high schools after they have completed their study at the State Islamic University of Riau Province. The observations during five years were conducted by detecting students' difficulties in learning through FGD (Focus Group Discussion) with six mathematics lecturers teaching Geometry. The FGD was conducted to discuss the researchers' findings of the difficulties of the student teachers in learning Geometry. From the results of the FGD, six lecturers agreed with the research findings that the student teachers had difficulties in learning geometry specifically in defining, connecting and classifying the quadrilateral types. From the FGD, the researchers offered a solution to make a media in the form of a module to help the student teachers to understand, define, and classify quadrilateral types. The module was very important to develop because it was based on the problems found during learning. The media in the form of geometry textbooks that the student teachers used did not help the student teachers achieve the learning objectives covering drawing conclusions about defining and classifying various types of the quadrilateral. The second stage, the design stage, was to design module to be attractive, to determine the competencies to be achieved, and to determine the problems related to the concept Risnawati, Andrian, Azmi, Amir & Nurdin 547 International Journal of Instruction, July 2019 ● Vol.12, No.3 of defining and classifying quadrilateral. In the design stage, a module design was produced consisting of three parts, namely introduction, content, and closing. The third stage is the development stage. The researcher developed the module validity or feasibility assessment sheets, practicality sheets, questionnaires and test to assess the effectiveness of the module. The validity or feasibility assessment module was used to identify the level of validity and feasibility of the module developed. Practicality assessment sheets were used to see how far the module was practically developed in aspects of being easy to use, easy to understand, interesting to use in learning and able to accelerate understanding in Geometry learning. The questionnaire was developed to obtain information about student teachers' opinions about the practicality of the module being developed. The test aimed to check the student teachers' mathematical reasoning ability after participating in learning using the module. The fourth stage is the implementation stage. The implementation stage was the stage of testing the module. The implementation stage aimed to identify the level of validity of the module. This validation was carried out by the experts on measurement, the experts on mathematical material and the experts on mathematics learning media as well as the practitioners (the lecturers). The validated aspects included module feasibility in terms of material and media design. Material validation and media design aimed to test the feasibility of the content, feasibility of presentation, language assessment, and learning assessment. Validation of student response questionnaires aimed to check the questionnaire format, the language used, and the questionnaire statement to assess the module. Test validation aimed to check the suitability of the problem with mathematical reasoning ability. The next stage of the implementation is testing the practicality level of the module. Practicality test aimed to see the use of a module that were practical to use, easy to understand, interesting to use, useful and able to accelerate the student teachers in understanding geometry. Practical tests were carried out through the assessment of experts, practitioners and teacher candidates. The module effectiveness trial aimed to check the differences in mathematical reasoning skills between student teachers who took part in learning by using a quadrilateral definition and classification module with the students who did not use the module. The module effectiveness test on students' mathematical reasoning ability was done by giving treatments to one class and another class with the condition that both classes were homogeneous. Mathematical reasoning ability in two classes were compared based on the scores obtained at the end of the quadrilateral type learning. Fifth, the evaluate stage was the stage of evaluating the effectiveness of the module that had been developed. Description of Module The quadrilateral types definition and classification module consist of three parts, namely the introduction, content, and closing. The introductory section consists of cover, preface, table of contents, competency standards (achievement of graduate learning), the final ability of each stage of learning, checking the readiness of students regarding prerequisite material, and key answers. The material content section consists of various quadrilateral wide problem presentations that can be done using formulas, elaboration of the material along with the student activity sheets on the definition of 548 Development of a Definition Maps-Based Plane Geometry ... International Journal of Instruction, July 2019 ● Vol.12, No.3 various quadrilateral types, and an evaluation consisting of four issues regarding the classification of different types of quadrilateral, namely developing the ability to think logically, developing spatial intuition, instilling knowledge of further level of mathematics, and interpreting arguments mathematically. The closing section of the module consists of conclusions, exercises on mathematical reasoning, key answers to various problems, student assessment sheets, and reference lists. Assessment of Module Feasibility An assessment of the feasibility of the module was carried out to see how far the module developed was suitable for the mathematics student teachers. Feasibility of the module was the main point to be assessed. The feasibility of the module was assessed from the aspects of the material used in the module, the competencies expected to be mastered by the student teachers, and the feasibility of the language used to develop the module. The feasibility of the module was assessed by 3 experts (measurement experts, mathematics learning experts, learning media experts) and 4 practitioners (mathematics lecturers). The results of the expert assessment can be seen in Table 2. Table 2 Results of Module Feasibility Assessment Aspect Validated Expert Average Practitioner Average Total Average Criteria μ ЅD μ ЅD μ ЅD The module developed is in accordance with the problems that will be resolved. 3.67 0.58 4.00 0.00 3.83 0.29 Very Feasible The material developed in the module is in accordance with competencies taught 3.33 0.58 4.00 0.00 3.67 0.29 Very Feasible The material developed in the module is in accordance with the level of education 4.00 0.00 4.00 0.00 4.00 0.00 Very Feasible The module uses punctuation marks, command marks and clear question words 3.67 0.58 3.67 0.58 3.67 0.58 Very Feasible There are clear instructions on how to work on the test items on the module 3.67 0.58 3.67 0.58 3.67 0.58 Very Feasible Tables, pictures, graphs, maps are clearly presented in the module 3.67 0.58 3.00 0.00 3.33 0.29 Very Feasible The formulation of the sentence on the test items in the module is communicative 3.33 0.58 3.00 0.00 3.17 0.29 Feasible The module uses a standard language and easy to use 3.67 0.58 3.67 0.58 3.67 0.58 Very Feasible The module does not use words/expressions that give rise to multiple interpretations and causes the user to misinterpret 3.33 0.58 3.67 0.58 3.50 0.58 Very Feasible The module does not use the language area 4.00 0.00 4.00 0.00 4.00 0.00 Very Feasible Based on the assessment of experts and practitioners it was found that all aspects of the feasibility of the module were assessed with a feasible category (1 with a feasible category and 9 with a very feasible category). These results indicated that the experts and practitioners considered the module developed by the researchers was in the appropriate category to be used for mathematics student teachers. The experts and the practitioners assessed the module developed to improve the student teachers’ reasoning. Risnawati, Andrian, Azmi, Amir & Nurdin 549 International Journal of Instruction, July 2019 ● Vol.12, No.3 Aiken validity for the Student Teachers Questionnaire Content validity was assessed by three experts, namely two measurement experts and one mathematical learning expert. Content validity was used to see how far the items developed by the researchers in terms of material, design, and language were feasible. The assessment was to obtain information about the opinions of student teachers on the module developed. The results of Aiken validity can be seen in Table 3. Table 3 The Result of Aiken validity for the Student Teachers

中文翻译：

---

开发基于定义图的平面几何模块提高学生教师数学推理能力

我5 18.7 18.6 23.7 22.6 28.3 28.3 30.0 25.8 23.3 22.2 6 20.0 20.0 20.7 20.7 23.3 23.3 26.6 26.7 27.8 26.7 Deductioñ7 12.9 12.4 17.4 16.3 18.3 16.7 14.2 13.3 22.2 22.2 8 11.0 11.0 18.2 18.2 20.6 20.6 19.2 19.2 17.8 14.4严谨9 9.1 8.1 8.1 7.4 10.0 9.4 11.7 11.6 10.0 10.0 10 2.38 2.38 4.81 4.81 6.11 6.11 9.17 9.17 5.56 N 教师 学生数 10.0 11.7 10 24 24 24 24 教师 学生 教师 样本 20 4 24 24 : 正确原因 根据这些结果可以得出结论，2013年至2017年的学生教师在可视化和分析层面上能够正确回答50%以上。此外，学生教师只能回答抽象水平的30%左右，演绎水平的22%，严谨水平的11%。结果显示，学生教师没有很好地理解定义，也没有在抽象、演绎和严谨的层次上对各种类型的四边形进行很好的分类。这个结果对学生教师来说是一个严重的问题，因为他们将在廖内省国立伊斯兰大学完成学业后将知识传授给小学、初中和高中的学生。五年来的观察是通过与六名教授几何的数学讲师通过 FGD（焦点小组讨论）检测学生的学习困难来进行的。进行 FGD 是为了讨论研究人员对学生教师在学习几何方面的困难的发现。从 FGD 的结果来看，六位讲师同意研究结果，即学生教师在学习几何方面存在困难，特别是在定义、连接和分类四边形类型方面。从 FGD 中，研究人员提供了一种解决方案，以模块的形式制作媒体，以帮助学生教师理解、定义和分类四边形类型。该模块非常重要，因为它基于学习过程中发现的问题。学生教师使用的几何教科书形式的媒体并没有帮助学生教师实现包括对各种四边形的定义和分类得出结论的学习目标。第二阶段，设计阶段，是设计具有吸引力的模块，确定要达到的能力，并确定与概念相关的问题 Risnawati, Andrian, Azmi, Amir & Nurdin 547 International Journal of Instruction, 2019 年 7 月 ● Vol.12, No.3 定义和分类四边形。在设计阶段，产生了一个由引言、内容和结语三部分组成的模块设计。第三阶段是发展阶段。研究人员制定了模块有效性或可行性评估表、实用性表、问卷和测试来评估模块的有效性。有效性或可行性评估模块用于确定所开发模块的有效性和可行性水平。实用性评估表用于查看模块在易于使用、易于理解、在学习中使用很有趣，并且能够加速几何学习的理解。调查问卷旨在获取有关学生教师对正在开发的模块的实用性的意见的信息。该测试旨在检查学生教师使用该模块参与学习后的数学推理能力。第四阶段是实施阶段。实施阶段是测试模块的阶段。实施阶段旨在确定模块的有效性级别。该验证由测量专家、数学材料专家和数学学习媒体专家以及从业者（讲师）进行。经验证的方面包括材料和媒体设计方面的模块可行性。材料验证和媒体设计旨在测试内容的可行性、演示的可行性、语言评估和学习评估。学生回答问卷的验证旨在检查问卷格式、使用的语言以及评估模块的问卷声明。测试验证旨在通过数学推理能力检查问题的适用性。下一阶段的实施是测试模块的实用性水平。实用性测试旨在了解一个模块的使用，该模块实用、易于理解、使用有趣、有用且能够加速学生教师理解几何。实践测试是通过对专家、从业者和教师候选人的评估进行的。模块有效性试验旨在通过使用四边形定义和分类模块来检查参与学习的学生教师与未使用该模块的学生在数学推理能力方面的差异。学生数学推理能力的模块有效性测试是通过对一个班级和另一个班级进行处理，在两个班级相同的条件下进行的。根据四边形学习结束时获得的分数，比较两个班级的数学推理能力。第五，评估阶段是对已开发模块的有效性进行评估的阶段。模块说明 四边形类型定义与分类模块由引言、内容和结束语三部分组成。导论部分包括封面、前言、目录、能力标准（研究生学习成绩）、每个阶段学习的最终能力、检查学生对必备材料的准备情况和关键答案。材料内容部分由各种四边形宽问题演示组成，可以使用公式来完成，详细说明材料以及关于 548 定义基于地图的平面几何的定义的学生活动表......国际教学杂志， 2019年7月 ● Vol.12, No.3 各种四边形类型，以及关于不同类型四边形分类的四个问题的评测，即培养逻辑思维能力，培养空间直觉，灌输更深层次的数学知识，并以数学方式解释论点。该模块的最后部分包括结论、数学推理练习、各种问题的关键答案、学生评估表和参考列表。模块可行性评估 对模块的可行性进行了评估，以了解开发的模块在多大程度上适合数学学生教师。该模块的可行性是要评估的要点。模块的可行性从模块中使用的材料、学生教师期望掌握的能力以及开发模块所用语言的可行性等方面进行评估。该模块的可行性由 3 位专家（测量专家、数学学习专家、学习媒体专家）和 4 名从业者（数学讲师）。专家评估结果见表2。 表2 模块可行性评估结果 Aspect Validated Expert Average 从业者平均总平均标准 μ ЅD μ ЅD μ ЅD 开发的模块是根据将要解决的问题。3.67 0.58 4.00 0.00 3.83 0.29 非常可行 模块中开发的材料与所教授的能力相符 3.33 0.58 4.00 0.00 3.67 0.29 非常可行 模块中开发的材料符合教育水平. 0.004 . 04 . 04模块使用标点符号、命令标记和明确的疑问词 3.67 0.58 3.67 0.58 3.67 0.58 非常可行 3.67 0.58 3.67 0.58 3.67 0.58 3.67 0.58 3. 这些结果表明，专家和从业者认为研究人员开发的模块属于适合数学学生教师使用的类别。专家和从业者评估了为提高学生教师的推理能力而开发的模块。Risnawati, Andrian, Azmi, Amir & Nurdin 549 International Journal of Instruction, 2019 年 7 月 ● Vol.12, No.3 Aiken 学生教师问卷的有效性 内容有效性由三位专家评估，即两位测量专家和一位数学学习专家。内容效度用于查看研究人员在材料、设计和语言方面开发的项目在多大程度上可行。评估是为了获得有关学生教师对所开发模块的意见的信息。