运用基于热点的数学教材提高逻辑思维能力

N Anriani, A S Pamungkas, K Iskandar and A Istiandaru

Universitas Sultan Ageng Tirtayasa, Jl. Jakarta KM 4 Serang Banten Indonesia

Universitas Ahmad Dahlan, Jl. Ringroad Selatan, Tamanan Bantul, Indonesia

摘要:本研究的目的在于以高阶思维技能为基础，制作数学教材，以提高初中生的逻辑思维能力。对于八年级的初中学生，此资源中的材料为“固体”。 这项研究是研发。 使用的开发模型包括潜在问题，信息收集，产品设计，设计验证，设计改进，产品试用和产品修订。产品的有效性和实用性测试由专家、教师和学生进行评估。最后的产品试验在万丹省的几所学校进行。而产品有效性的检验则是通过观察学生逻辑思维能力的前测值和后测值的显著差异来进行推理统计检验。结果表明，根据专家的评价，包括类别在内的发展成果的产品是非常有效的，实际上是根据教师和学生的评价。根据平均差异检验，得出的结果也很有效，结果表明，在5%的显著性水平下，教材发放前后存在显著性差异。

1. 介绍

中学数学学习的目的是培养学生通过逻辑、理性、批判、准确、诚实、高效、有效的思维，来应对生活中不断变化的环境和不断扩大的世界。这个想法类似于这样的观点，即数学教育有两个大目标：一是培养孩子的逻辑推理能力和个人形成能力;二是重视数学的应用和解决问题的能力。以上符合NCTM的总体目标，即:学习沟通、推理、解决问题、连接思想、数学处理[3]。能力熟悉数学技能。有关数学的特点可以分为低级思维和高级思维。较低层次的思维活动包括执行简单的计数操作，直接应用数学公式，遵循标准程序。而更高层次的思维活动则是深入理解数学的思想，观察数据，探索隐含的思想，安排猜想、类比、概括、推理、非常规的解题数学沟通，以及相关的数学思想[4]。与数学特征密切相关的高阶思维活动之一是逻辑思维;这是因为数学问题是通过推理来理解的。逻辑思维能力在数学学习中的重要性是由于这些方面与学生的成绩的联系[5-8]。但事实的发现,学生的逻辑思维能力仍然较低,如赫尔曼所说的那样,初中学生解决与证明相关的非常规问题，数学推理，猜想，并找到给出的数据或事实之间的关系的能力非常弱[9]。

一些初中生的逻辑思维能力较低是由于教师在学习过程中过于注重解决程序性和机械性问题的练习，而没有注重对数学理解能力的教导[10]。在传统的学习活动中，教师通常通过提供信息丰富的概念来开始学习，提出问题，然后通过提出练习题来结束学习。因此，在这样的活动中，学习过程以教师为中心，数学材料由课堂讲授，学生是被动的，很少出现来自学生的问题，通常以一个正确的答案为导向。这样的活动并不能给学生提供发展其他数学技能的机会。在这样的情况下，政府在2013年对课程进行了改变，在学习过程中采用了科学的方法。随着课程改革的理念，人们期望数学技能，尤其是那些具有较高思维水平的技能能够得到很好的发展。政府2013年出版的教师书籍和学生书籍，有助于课程在课堂上的应用。

但是，当他们在使用教科书时，问题就出现了，其中一些是教科书的机械性，使用的是封闭的问题，这些问题相对于获得答案的过程更注重最终得到的结果。在这种情况下，学生在学习过程中的思维创造力并没有得到很好的发展。这种现象是由于批判答案的能力和注重如何回答问题的能力变得不寻常，因为教师已提前教授过解决问题的程序和规则了。

基于这些事实，我们开发了基于热点的教材来培养学生的逻辑思维能力。教材是学习的重要工具，好的教材包含更系统、更有效、更高效的课堂学习过程。数学教材不仅要呈现教材内容，而且应当引导学生形成良好的学习过程。根据Suneetha，Rao和Rao以及美国国家能力培训中心的说法，数学教材应当具备一些功能，例如教师教学指导，教学参考书和教学工具，使学习变得有效，帮助教师创建工作表并激励学生思维和学生的推理能力[11，12]。

本研究开发的教材为教师手册和学生活动，包含了RPP和评价。教师手册包含学习过程指南和学生活动的材料说明。教师手册是指2013年课程中推荐的科学阶段。最终，本产品开发的希望在于提供基于HOTS的替代教材，以培养初中生的逻辑思维能力。

1. 方法

通过修改Dick amp; Carey[13]的开发模型，进行研究开发。这一开发的阶段包括收集信息、开发RPP、选择和开发教材、初步试验、修订、重点试验和最终产品修订。在万丹省多达11所学校的初中进行了初步和主要的试验。所开发教材的质量是根据教材的信度和效度来衡量的。教材的有效性由材料和媒体专家验证。教师和学生以教材使用者的身份评估教材的实用性。以学生逻辑思维的前测和后测成绩为基础，对教材的有效性进行评估，并对教材在课堂学习中使用前后的逻辑思维能力进行比较。本研究的数据分析目的是通过所开发的数据来描述所开发产品的有效性、有效性和实用性。效度和实用性检验采用描述性统计方法，效度检验采用配对平均差检验。

1. 结果与讨论

3.1效度

效度测试旨在为所开发的仪器和产品提供理论评估。本研究由专家进行实验测试，三位专家是来自苏丹大学数学教育系的讲师，其中两位专家负责产品验证测试，一位专家负责仪器验证测试。研究仪器的验证由评估专家执行。评估对象为RPP验证表、师生手册、逻辑思维能力测试验证卷。通常，由于已经满足了验证者的建议，验证表和研究工具的评估结果是可行的并且是高度有效的。

产品验证由材料专家和媒体专家进行。评估对象是指英国国家统计局发布的数学评估工具。通常，对这两个验证器的产品的评估值得与修订一起使用，有效性计算的结果非常有效。

3.2实用性

对产品的易读性和实用性进行了初步试验。本试验是针对SMPN 7 Kota Serang的数学教师和学生进行的，对象为37名学生。教师和学生的评估结果通常表明，所开发的产品足够实用，可供教师和学生使用。

初步试验后，下一步是主要试验。这次试验的目的是了解大规模开发的产品的应用。这项试验在万丹省的11名初中生中进行。在执行测试时，教师在RPP(即教师手册和学生手册)的指导下进行学习。在进行初等培训之前，老师会在使用教科书时提供早期和晚期测试。

3.3有效性

有效性测试的目的是查看所开发的教材是否被有效地大规模使用。这个测试使用推论统计检验，该检验是对平均数差的检验。在此测试中处理的数据是前测和后测试数据，是基于获得的先决条件分析结果得出的数据不符合正态性测试，因此该测试使用Wilcoxon检验。本研究提出的研究假设是学生在接受教材前后的逻辑思维能力是否存在差异。

由表1可知，p值小于0.05，因此拒绝Ho，接受Ha。这说明在使用教材之前和之后的逻辑思维能力是不同的。从这些测试中可以看出，教材的运用开发有效地运用于培养学生的逻辑思维能力。

面对21世纪的发展，培养学生的逻辑思维能力是非常重要的。因为21世纪需要的能力之一是逻辑思维的能力。根据逻辑思维能力测试的结果得出，在拿到教材之前，学生的逻辑思维能力仍处于较低的23.10分水平

来自SMI 100的分数。这个分数说明学生的逻辑思维能力不强，说明之前所描述的事实是真实的。它是根据学校的采访和观察结果得出的;学生们对所给的问题感到奇怪。因为他们从来没有遇到过非常规的解决问题的方法。

但是在获得了基于HOTS的教材之后，学生的逻辑思维能力得到了发展，足以达到68.64分。这说明教材的使用有助于学生逻辑思维能力的发展。当学生有机会探索一个特定的数学概念时，学生的能力将会提高，学生在学习活动中对科学的细微差别表现得很活跃。提供给教师的教材提供了指导性的指导，使学习过程得以实现。对于学生的利益，学生的活动是系统的，学生根据科学阶段提出的问题寻找隐含的概念。因此，使用基于热点的教材可以有效地培养学生的逻辑思维能力，特别是在扎实的主题上。

1. 结论

通过对本研究开发的产品的验证结果可以得出结论，本研究的产品是基于热点的教材，培养学生的逻辑思维能力的，该类教材是非常有效的。根据教师和学生的用户评分结果，总的来说，可以说开发的产品属于实用的范畴。根据有效性测试的结果，可以得出结论，使用这种教学材料的学习在培养学生的逻辑思维能力方面是有效的。

根据得出的结论，然后提出一些提高数学学习质量的建议，尤其是逻辑思维能力的提高，不仅是关于“坚实”主题的材料的发展，而且还涉及各个层次的其他主题的材料的发展。

外文文献出处：Journal of Physics: Conference Series

附外文文献原文

Abstract. The purpose of this research is to produce a mathematics material based on high order thinking skills in improving the logical thinking skills of junior high school students. The material in this resource is lsquo;SOLID” for junior high school students of class VIII. This research is research and development. The development model used includes potential problems, information gathering, product design, design validation, design improvements, product trials and product revisions. The test of validity and practicality of the product is assessed by experts, teachers and students. The final product trial was conducted in several schools in Banten province. While the test of product effectiveness is tested using inferential statistical test by looking at the significant difference of pretest and posttest value regarding students logical thinking skills. The results showed that the product of development results including the category is very valid according to the experts, practically according to the assessment of teachers and students. The resulting product was also effective according to the mean difference test showing that there were significant differences before and after the teaching materials were given at a significance level of 5%.

1. Introduction

The purpose of mathematics learning in secondary education is to prepare students to be able to deal with changing circumstances in life and an ever-expanding world, through practice acting by logical, rational, critical, accurate, honest, efficient and effective thinking [1]. This idea is similar to the opinion that mathematics education has two big goals: giving to the logic of reasoning and personal formation of the child and giving emphasis on the application of mathematics and problem solving [2]. The above is in line with the general goal of NCTM, namely: learning to communicate, reason, solve problems, connect ideas, and mathematics disposition [3]. Abilities are familiar with math skills. Relating to mathematical characteristics can be classified into lower and

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Improving logical thinking skills using HOTS-based mathematics teaching material

N Anriani, A S Pamungkas, K Iskandar and A Istiandaru

Universitas Sultan Ageng Tirtayasa, Jl. Jakarta KM 4 Serang Banten Indonesia

Universitas Ahmad Dahlan, Jl. Ringroad Selatan, Tamanan Bantul, Indonesia

Abstract. The purpose of this research is to produce a mathematics material based on high order thinking skills in improving the logical thinking skills of junior high school students. The material in this resource is lsquo;SOLID” for junior high school students of class VIII. This research is research and development. The development model used includes potential problems, information gathering, product design, design validation, design improvements, product trials and product revisions. The test of validity and practicality of the product is assessed by experts, teachers and students. The final product trial was conducted in several schools in Banten province. While the test of product effectiveness is tested using inferential statistical test by looking at the significant difference of pretest and posttest value regarding students logical thinking skills. The results showed that the product of development results including the category is very valid according to the experts, practically according to the assessment of teachers and students. The resulting product was also effective according to the mean difference test showing that there were significant differences before and after the teaching materials were given at a significance level of 5%.

1. Introduction

The purpose of mathematics learning in secondary education is to prepare students to be able to deal with changing circumstances in life and an ever-expanding world, through practice acting by logical, rational, critical, accurate, honest, efficient and effective thinking [1]. This idea is similar to the opinion that mathematics education has two big goals: giving to the logic of reasoning and personal formation of the child and giving emphasis on the application of mathematics and problem solving [2]. The above is in line with the general goal of NCTM, namely: learning to communicate, reason, solve problems, connect ideas, and mathematics disposition [3]. Abilities are familiar with math skills. Relating to mathematical characteristics can be classified into lower and higher thinking. Activities included in lower-level thinking are performing simple counting operations, applying mathematical formulas directly, following standard procedures. While higher-level thinking activity is to understand the idea of mathematics in depth, observing the data and exploring the implied idea, arranging conjecture, analogy, and generalization, reasoning, non-routine problem solving mathematical communication, and associated mathematical ideas [4].

One of the higher-order thinking activities that are closely related to the characteristics of mathematics is logical thinking; this is because the mathematical matter is understood through reasoning. The importance of logical thinking ability in mathematical learning because there is an association between these aspects and student achievement [5-8]. But the facts in the field found that students logical thinking ability is still low, according to the facts expressed by Herman that the ability of junior high school students is very weak in solving non-routine problems related to the proving, solving problems that require mathematical reasoning, conjecture, and find the relationship between data or facts given [9].

The low logical thinking ability of some junior high school students is caused by the teacher, which in his learning process concentrates too heavily on the exercise of solving more procedural and mechanistic problems rather than concentrating on instilling students mathematical understanding [10]. In the conventional learning activities, teachers usually start learning by explaining the concept informatively, giving a problem, and end by giving the exercise questions. So with such activity, the learning process is centered on the teacher, the mathematics material is delivered by lecture, passive students, questions from students rarely appear, oriented to one correct answer. With such activities do not provide opportunities for students to develop other math skills. Under such conditions, the government in 2013 made a curriculum change with a scientific approach in the learning process. With the concept of change curriculum, it is expected that math skills, especially those with higher-level thinking, develop well. Application of the 2013 curriculum in the implementation of learning in the classroom is assisted by the availability of teacher books and student books published by the government.

But problems arise when they are found in the handbook, some of which are textbooks that are mechanistic, using more closed questions that press on the final result than the process of getting the answer. With these findings, the creativity of students in thinking during the learning process is not well developed. This phenomenon is due to the ability to criticize an answer and how to answer it becomes unusual because the procedures and rules in solving the problem have been taught in advance by the teacher.

So based on these facts it is developed HOTS-based teaching materials to develop logical thinking ability. Teaching materials are an important tool of learning. Good teaching materials contain learning processes in the classroom more systematically, effectively and efficiently. The Mathematics textbooks not only present the material but lead to a good learning process [11]. According to Suneetha, Rao amp; Rao and the National Center for Competency-Based Training some of the functions of mathematics teaching materials such as teacher guidance in teaching, reference books and tools for teaching, making

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