抛锚式教学法是建构主义理论中常用的一种教学方法。在《指数函数的概念》教学中,教师利用抛锚式教学法创设相应情境,并根据情境确定目标问题,带领学生在自主思考与合作探究中探索指数函数的概念,解决目标问题。最后针对课堂教学过程进行效果评价。旨在为《指数函数的概念》教学提供借鉴。Anchored instruction is a commonly used teaching method in constructivist theory. In the teaching of the “Concept of Exponential Function”, teachers use anchored instruction to create corresponding situations and determine the target problem based on the situation. They lead students to explore the concept of exponential function through independent thinking and collaborative exploration, and solve the target problem. Finally, an evaluation of the effectiveness of the classroom teaching process is conducted. The aim is to provide a reference for the teaching of the “Concept of Exponential Functions”.
APOS理论是一种数学教育理论,强调通过操作、过程、对象和图式四个阶段促进学生的数学概念建构。余弦定理作为高中数学的核心内容,具有深刻的数学内涵和丰富的物理背景,是数形结合的良好载体和有效的解题工具。本研究以高中数学“余弦定理”相关内容为研究对象,采用文献研究法和案例分析法对APOS理论的来源、内涵与特点进行分析,结合余弦定理的教材内容与《普通高中数学课程标准(2017版)》解读,分析以APOS理论为指导的高中数学教学案例,提出余弦定理的教学策略和具体的教学设计案例。APOS theory is a kind of mathematics education theory, which emphasizes the promotion of students’ mathematical concept construction through the four stages of operation, process, object and schema. As the core content of high school mathematics, cosine theorem has profound mathematical connotation and rich physical background. It is a good carrier and effective problem-solving tool for the combination of number and shape. This study takes the relevant content of high school mathematics “cosine theorem” as the research object, uses literature research method and case analysis method to analyze the source, connotation and characteristics of APOS theory, combines the textbook content of cosine theorem with the interpretation of “Ordinary High School Mathematics Curriculum Standard (2017 Edition)”, analyzes the high school mathematics teaching cases guided by APOS theory, and puts forward the teaching strategies and specific teaching design cases of cosine theorem.
逻辑推理是六大核心素养之一,数学证明过程中所涉及的循环论证与学生的逻辑推理等核心素养有着很强的相关性。在实际教学中,循环论证并不少见。研究结合人教版普通教科书2019版(以下简称人教版)及各类练习题,按照知识点归纳高中数学学习中常见的循环论证问题,分为函数单调性、勾股定理、三角函数和立体几何四部分,为教材改革和教师教学提供新的方向。Logical reasoning is one of the six core literacy, and the circular argument involved in the mathematical proof process has a strong correlation with the core literacy of students’ logical reasoning. In actual teaching, circular argumentation is not uncommon. The research combines the 2019 edition of the ordinary textbook of the People’s Education Edition (hereinafter referred to as the People’s Education Edition) and various exercises to summarise the common circular argumentation problems in high school mathematics learning according to the knowledge points, which are divided into four parts: function monotony, Pythagorean theorem, trigonometric function and three-dimensional geometry, providing a new direction for textbook reform and teacher teaching.
随着新课程改革的推进,高中数学教学逐渐转向能力培养型,具身认知理论为数学教学提供了新的视角。通过探讨具身认知理论对高中数学活动课教学的指导作用,在分析高中数学活动课实施中面临的现实困境基础上,提出通过提升教师活动课教学能力、创设教学情境施行跨学科教学、加强活动课资源建设和改进课程评价方式等教学改革策略,提高学生的学习兴趣和数学思维能力,进而提升数学教学质量和学生的数学核心素养。With the advancement of the new curriculum reform, high school mathematics teaching is gradually shifting towards a competence-oriented approach. Embodied cognition theory provides a new perspective for mathematics instruction. By exploring the guiding role of embodied cognition theory in the teaching of high school mathematics activity courses, and based on an analysis of the realistic dilemmas faced in the implementation of such courses, this paper proposes teaching reform strategies such as enhancing teachers’ ability to teach activity courses, creating teaching situations for interdisciplinary instruction, strengthening the construction of activity course resources, and improving course evaluation methods. These strategies aim to enhance students’ interest in learning and their mathematical thinking ability, thereby improving the quality of mathematics teaching and students’ core mathematical competencies.
建构主义理论倡导以学生为核心,运用多样化的教学策略激发学生的知识自主建构与深刻理解。该研究选取“对数函数的图象和性质”为例,构建了基于建构主义理论的高中数学教学设计,通过反思和总结,旨在协助学生牢固掌握核心知识点,并锻炼其数学逻辑思维与问题解决技巧。Constructivist theory advocates for a student-centered approach, employing a variety of teaching strategies to stimulate students’ autonomous construction of knowledge and profound understanding. This study selects “the graph and characteristics of logarithmic functions” as an example, constructing a high school mathematics teaching design based on constructivist theory. Through reflection and summary, the aim is to assist students in firmly grasping core knowledge points and to exercise their mathematical logical thinking and problem-solving skills.
数学教学在让学生掌握基本的知识技能的同时,还要促进学生数学核心素养的提升及水平的达成。“学习进阶”和“学历案”为培养数学核心素养提供了设计思路和操作框架。笔者以人教A版高中数学必修一的“函数的概念与性质”为例,结合将学习进阶融入学历案设计的三个要点,即要明确阶段性目标、要实现教学评一体化、要创设合适的教学情境,展示了融合学习进阶理论的完整单元学历案和课时学历案学习过程设计,分析了学习进阶理论与学历案设计结合的实践意义,以期为一线教师们提供参考。Mathematics instruction aims to not only equip students with basic knowledge and skills, but also promote the development of their mathematical core competencies and the attainment of their proficiency level. “Learning progression” and “Education program” provide design ideas and operational framework for cultivating mathematics core literacy. Taking “The Concept and Nature of Function” as an example, the author combined the three key points of integrating learning progression into the design of degree plan, that is, to clarify the stage goal, to realize the integration of teaching evaluation, and to create a suitable teaching situation, and demonstrated the design of the learning process of the complete unit degree plan and the class hour degree plan integrating the theory of learning progression. This paper analyzes the practical significance of the combination of learning progression theory and academic record design, in order to provide reference for teachers.
为落实《深化新时代教育评价改革总体方案》,创新评价方式,研究以“问题提出”为评价依据,基于SOLO分类理论划分学生对椭圆知识的理解水平,帮助教师更全面地掌握学情。研究发现学生在部分椭圆知识情境中问题提出表现一般,缺乏灵活性;学生对椭圆知识的理解总体处于多点结构水平,部分学生对椭圆定义的理解存在偏差,对“焦点三角形”知识熟悉程度较低。教师在教学过程中可合理利用学生所提问题,尊重学生个体差异,促进学生全面发展。In order to implement the “Overall Plan for Deepening the Reform of Educational Evaluation in the New Era” and innovate the evaluation method, this paper takes “problem posing” as the evaluation basis and divides students’ understanding level of elliptic knowledge based on SOLO classification theory to help teachers grasp learning situation more comprehensively. It is found that the students’ performance in problem posing in partial elliptic knowledge situation is not good and lacks flexibility. Students’ understanding of ellipse is generally at the level of multi-point structure, some students’ understanding of ellipse definition is wrong, and they are not familiar with “focus triangle” knowledge. In the teaching process, teachers can make reasonable use of the questions raised by students, respect the individual differences of students, and promote the all-round development of students.
文章探讨了波利亚解题理论在初中几何教学中的应用。波利亚解题理论包括弄清问题、拟定计划、执行计划、回顾反思四个步骤,为初中几何教学提供了系统方法和思路。在理论层面,该理论源于波利亚对数学教育的深入研究,在全球范围内广泛传播并产生深远影响。在实践应用方面,其在初中几何证明题发挥重要作用。如在证明题中利用等腰三角形简化问题、应用定义进行转化;在教学效果上,显著提升了学生的思维能力,培养了逻辑推理能力和创新思维,同时提高了教学质量,增强了学生学习兴趣。波利亚解题理论在初中几何教学中具有重要应用价值,为提高学生几何解题能力和培养数学素养提供有力支持。This paper discusses the application of Polya’s problem-solving theory in junior high school geometry teaching. Polya’s problem-solving theory includes four steps: clarifying the problem, formulating the plan, implementing the plan, and reviewing and reflecting, which provides a systematic method and ideas for junior high school geometry teaching. At the theoretical level, the theory stems from Polya’s in-depth research on mathematics education, which has been widely disseminated and has had a profound impact on the world. In terms of practical application, it plays an important role in junior high school geometry proof problems. For example, in the proof question, the isosceles triangle is used to simplify the problem and apply the definition for transformation;in terms of teaching effect, it has significantly improved students’ thinking ability, cultivated logical reasoning ability and innovative thinking, improved teaching quality, and enhanced students’ interest in learning. Polya’s problem-solving theory has important application value in junior high school geometry teaching, which provides strong support for improving students’ geometric problem-solving ability and cultivating mathematical literacy.
几何直观是数学学习中的关键能力,对理解几何概念、发展空间思维和提高解题能力至关重要。研究选取了初二年级数困生、数优生共281名,对两类学生的几何直观能力进行了比较研究。结果表明:男女在几何直观上的发展并无显著差异;几何直观水平在不同程度上影响学生的数学成绩;数优生在直观洞察能力、直观想象能力、直观构建能力三个维度的发展优于数困生,三维度之间存在显著的正相关关系。该研究不仅揭示了数困生和数优生在几何直观能力上的差异,而且为改进初中几何教学提供了有益的启示。Geometric intuition is a key ability in mathematics learning, which is crucial for understanding geometric concepts, developing spatial thinking, and improving problem-solving skills. A total of 281 students in the second year of junior high school, including those with numerical difficulties and those with numerical excellence, were selected for the study to compare their geometric intuition abilities. The results indicate that there is no significant difference in the development of geometric intuition between men and women;The level of geometric intuition affects students’ mathematics grades to varying degrees;Numerical gifted students have better development in the three dimensions of intuitive insight ability, intuitive imagination ability, and intuitive construction ability than numerical poor students, and there is a significant positive correlation between the three dimensions. This study not only reveals the differences in geometric intuition ability between students with numerical difficulties and those with numerical excellence, but also provides useful insights for improving geometry teaching in junior high schools.
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