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This paper compares the contents of "geometric transformation" in Mathematics, a compulsory education curriculum standard experimental textbook published by Beijing Normal University, with Mathematics Link published by Oxford, and finds that there are obvious differences.

Through comparative analysis, we get three inspirations from the integration of different disciplines and information technology: concise teaching materials and detailed teaching materials should highlight the essence of transformation.

Keywords: junior high school mathematics; Geometric transformation; Text comparison

"Geometric transformation" mainly includes graphic symmetry, graphic rotation, graphic translation and graphic similarity. It is one of the important tools for all students to identify graphics, discover the internal relations of graphics and explore the thinking of reasoning and argumentation, which is conducive to cultivating students' geometric intuition, spatial concept and reasoning and argumentation ability.

What are the characteristics of the handling and organization of "geometric transformation" in British mathematics textbooks? This paper discusses the content organization, knowledge content and knowledge content of Mathematics Link published by Oxford University in 2009 (hereinafter referred to as Oxford textbook (and Mathematics, the experimental textbook of compulsory education curriculum standard published by Beijing Normal University).

Comparison of Content Arrangement and Organization of Chinese and English Textbooks

The contents of Geometric Transformation, a textbook of Beijing Normal University, mainly include axial symmetry, translation, rotation, central symmetry, line segment proportion, similar polygon, similar triangles, similar conditions and properties, and phase. The contents are arranged in the order of Chapter 7 "Axisymmetry in Life" in the second volume of Grade 7 and Chapter 3 "Graphic Translation and Rotation" in the first volume of Grade 8.

Oxford textbooks mainly include symmetry axis, translation, rotation, rotational symmetry, enlargement and reduction, scale diagram and so on. Chapter 7 13 "Transformation and symmetry" Chapter 8 "Transformation and symmetry".

British textbooks only learn one chapter about geometric transformation every year, which is less than that of China.

The arrangement of the textbook of Beijing Normal University puts all the knowledge points in one chapter.

For example, in the seventh chapter of the second volume of the seventh grade, "Axisymmetry in Life", after understanding the axisymmetric figure, you can draw the axis of symmetry of the axisymmetric figure. Then it is gradually extended to the knowledge points related to axisymmetric properties and conclusions, such as equiangular bisector, perpendicular bisector, isosceles triangle, equilateral triangle and so on. Finally, the properties of symmetry axis are deeply studied. This chapter gives most knowledge points of axisymmetry.

Oxford textbooks pay attention to the stages of knowledge learning, and the content arrangement focuses on the deepening of knowledge points with the rise of grades.

For example, among the seventh-grade students, we can find the symmetry axis of an axisymmetric figure, and only need to know which axisymmetric figure not only has an symmetry axis, but also which figure has no symmetry axis.

In the eighth grade, first find out the symmetry axis of the seventh grade figure, and then increase the symmetry axis of the regular polygon.

It can be seen that the textbook of Beijing Normal University focuses on organizing similar knowledge and improving the integrity of students' learning knowledge points.

The characteristic of Oxford textbooks is that knowledge points are distributed in a series of chapters of textbooks, and students' learning is strengthened through the spiral rise of knowledge points.

2. Comparison of knowledge content between Chinese and English textbooks

1. Comparison of knowledge introduction

The introduction of knowledge reflects the writing style of teaching materials.

In Oxford textbooks, examples of the application of mathematical knowledge in real life are given at the beginning of each chapter, which links the study of mathematical knowledge with the reality of life.

The textbook of Beijing Normal University is also made in this way.

The difference is that while introducing new knowledge, Oxford textbooks set up three or four exercises in the preface to review what they have learned before, while Beijing Normal University textbooks did not set up inspection exercises.

The introduction of "geometric transformation" knowledge points in the textbook of Beijing Normal University adopts the way of "mathematical concept of situational problems". That is, first set the situation of practical problems, which leads to the gradual deepening of the definition, concept and nature of the learning content in this section, and the spiral rise of knowledge difficulty.

This makes students feel the application and practicability of mathematical knowledge and stimulates students' interest in learning mathematical knowledge.

The introduction of various knowledge points of geometric transformation in Oxford textbooks only provides a part of the content. Through narration, students can understand the meaning of the situation, and pure mathematical knowledge accounts for a large proportion.

The Oxford textbook lists the learning objectives of this section at the beginning of each section, and the following contents will be arranged around the learning objectives set in this section.

For example, grade 13a (chapter 13, section 1) provides an example. The learning goal is to find the symmetry line and then find the symmetry axis immediately.

This way of knowledge introduction in Oxford textbooks makes teachers and students have clear teaching and learning goals in the process of teaching and learning, and teaching is more targeted.

2. Comparison of knowledge presentation order

The order of knowledge expression in the textbook of Beijing Normal University Edition under the content of "geometric transformation" is: axisymmetric translation and rotational similarity.

The order of knowledge expression in Oxford textbooks under the content of "geometric transformation" is: symmetrical axis reflection translation rotation symmetry enlargement and reduction of similar scale diagram.

Because the central axisymmetric content of the textbook published by Beijing Normal University includes reflection, the similar content includes the enlargement and reduction of the Oxford textbook and the similar content.

Therefore, the order of prompting knowledge points in the two editions of textbooks is basically the same.

This is also related to the content organization of the "geometric transformation" content itself.

In specific chapters, the knowledge order of the textbook published by Beijing Normal University is: according to situational problems, introduce the concept of learning content knowledge points and define examples for in-class exercises.

The order of knowledge in Oxford textbooks is a concrete application example exercise of the concept of learning target knowledge points in this section.

From the order of knowledge, we can see that the learning order of the textbooks published by Beijing Normal University is the deepening of the application practice of what to learn.

The learning steps of Oxford textbooks are as follows: make clear what needs to be learned, learn how to solve related knowledge problems, and apply parallel exercises.

As can be seen from the above, the knowledge expression order and learning order of the textbook published by Beijing Normal University are gradually advancing.

The order of knowledge presentation and learning in Oxford textbooks can be understood as the knowledge and methods that need to be learned to solve a problem.

The knowledge of the textbook Geometric Transformation published by Beijing Normal University is scattered in chapters, which are independent of each other and have little connection. However, in each section of the same chapter, some knowledge points are shallow (for example, Chapter 7 "Axisymmetry in Life" in the second volume of Grade 7), and some knowledge points are parallel first and then connected (for example, Chapter 3 "Translation and Rotation of Graphics" in the first volume of Grade 8).

The knowledge of "geometric transformation" in Oxford textbooks is in one chapter, and the content is scattered in various sections, which helps students to grasp the integrity of knowledge and the relationship between the contents before and after.

Third, Chinese and English textbooks deal with the same knowledge.

Due to the differences between Chinese and English cultures, the requirements of curriculum standards and teaching concepts are not only different in mastering the same knowledge point and the focus of learning knowledge, but also in solving problems.

Taking the translation drawing in Oxford textbooks as an example, we can experience the differences between the two versions of textbooks.

Combining the contents of Beijing Normal University Edition, we can see that the textbook of Beijing Normal University Edition has a strict explanation process, while the Oxford textbook is only a simple oral description. Secondly, the translation in Oxford textbooks is carried out in the coordinate system. In fact, in the knowledge content of "geometric transformation" in Oxford textbook, almost all graphics are transformed by coordinate system and volume, and this transformation method can only be carried out smoothly by relying on coordinate system.

In the textbook of Beijing Normal University, there is also the practice of moving graphics in the box, but it is regarded as a simple exercise.

Four. Comparison of Examples and Exercises in Chinese and English Textbooks

As can be seen from the table 1, the number of exercises in the textbook of Beijing Normal University is about twice that of the textbook of Oxford.

No matter the textbooks of Beijing Normal University or Oxford, exercises are set after each section, and review questions are set after each chapter.

The difference is that there are no exercises in Oxford textbooks, and there are no review questions before class in Beijing Normal University textbooks.

The exercises in Chinese and English textbooks are all based on the knowledge set in this section, which is a transition and consolidation.

The review questions of the textbook published by Beijing Normal University are the integration and mixing of the knowledge points in this chapter, while the review questions of the British textbook are divided by the knowledge content of each section.

In addition, the exercises in the textbook of Beijing Normal University are selected from four modules: knowledge and skills, mathematical understanding, problem solving and connection extension, and the difficulty of the exercises is on the rise.

The exercises in Oxford textbooks mainly focus on the mastery of basic knowledge, and the exercises are less difficult, and most of them are exercises for repeated practice of a certain knowledge point.

Table 1: comparison of examples and exercises in Chinese and English textbooks

Pre-class test questions, in-class exercises, after-class exercises and after-class review questions total Beijing Normal University textbook 034 1326228 Oxford textbook10762810/5 Description: According to the question number, each question is counted as one question.

Another obvious difference is that the exercises and review questions in Oxford textbooks are all given various geometric figures, and the knowledge points learned are all completed by changing the given figures.

There are some literal exercises in the textbook exercises of Beijing Normal University. Students can draw independently according to the requirements of exercise questions, and the graphics are mainly triangles.

There are many exercises related to daily life in the textbook of Beijing Normal University.

Oxford textbooks focus on solving pure mathematical problems in the types of exercises.

In addition, some textbook exercises of Beijing Normal University Edition are based on the knowledge of translation, rotation and axial symmetry, and share the exercises of design intention with students.

This kind of exercise combines mathematics with design in life, which not only realizes the beauty of mathematics in the transformation of drawing geometric figures, but also provides a platform for cultivating students' creative thinking. I believe students have the opportunity to speak their own patterns and ideas boldly. At this time, students are not passive problem solvers, but active designers. If teachers give encouragement in time, students' interest in mathematics learning can be more stimulated.

Verb (abbreviation of verb) inspiration and thinking

1. Integrate different disciplines and information technology.

The knowledge content of geometric transformation in Oxford textbooks and Beijing Normal University textbooks is mostly based on life.

The connection with other disciplines can only be designed by translation and rotation.

The integration of multi-disciplinary content not only broadens students' horizons, but also makes students feel the importance of mathematics in other disciplines.

For example, translation knowledge can be related to the constant motion of physics, symmetry, art and so on.

Knowledge in different fields promotes mutual integration and may collide with different sparks.

Students can not only operate the sensory transformation by themselves, but also use the geometric sketchpad software to show the dynamic beauty of geometric figures in class, which is helpful to cultivate students' intuition about spatial geometric transformation, which is reflected in the teaching materials of Beijing Normal University.

In addition, from the overall performance of mathematics, the knowledge of "geometric transformation" in middle school textbooks has little connection with other contents of mathematics, which is also a difficult point to be broken in the compilation of textbooks in the future.

2. The textbook is concise and detailed.

The first impression of Oxford textbooks is simple and clear.

One page for each part, plus one page for practice.

This is in sharp contrast with China's mathematics textbooks.

Different from the textbooks published by Beijing Normal University, Oxford textbooks have a strict definition of knowledge points and a rigorous process of proving and solving problems.

Its definition and nature not only include oral description, but also require students to understand abstraction from the problem itself, thus cultivating students' ability of independent discovery and generalization.

Although we can't judge who is good or bad, the simplification of the content will definitely improve students' interest in learning.

Oxford textbooks have keywords in the upper right corner of each section. In other words, when you have just mastered the knowledge of this section, mastered the key words of this section, mastered the overall context, and then returned to the specific knowledge content.

These details have merit. Instead, you can learn to extract keywords and compare them with those in a class.

The training of this thinking mode is helpful to learn Chinese and English and extract information.

3. Emphasize the essence of transformation

Students in Oxford textbooks put forward the idea of graphic movement (including exercises) more actively than students in Beijing Normal University textbooks.

In order to understand the changes of graphics, experience the changing and unchanging nature, and let students draw by themselves, it will not only help students to establish their initial geometric intuition, but also cultivate their spatial imagination and practical ability.

The compilation of the textbook of Beijing Normal University is mainly based on the teacher's explanation, focusing on the nature, characteristics and results of the transformation itself.

The compilation of Oxford textbooks pays attention to students' cognition and preference, as well as the operation process of personal experience transformation.

Middle school students are in the formal calculus stage of Piaget's cognitive development stage theory, abstract logical thinking is taking shape, and dynamic thinking will inevitably impact the original static thinking.

Using the knowledge of "geometric transformation", we actively study, dare to explore and find problems, and through our own practice, summarize the inductive nature, get intuition and conjecture in operation, especially think and solve problems with different thinking and different angles, and highlight the dynamic significance of "geometric transformation"

References:

[1] Zhang Xiangzhou, Shen Wenxuan. Middle school geometry research [M]. Beijing: Higher Education Press, 2006.

[2] Chen Rongrong. Middle school teachers' understanding and teaching research on geometric transformation [D]. Beijing: Capital Normal University, 2009.

[3] Mathematical Link 7.8.9[ m]. Oxford University Press, 2009.

[4] R&D group compulsory education mathematics curriculum standards. Compulsory education curriculum standard experimental textbook mathematics (grade 7 ~ grade 9)) m). Beijing: Beijing Normal University Press, 2005.

[5] Lin Qifen, Li. A Comparative Study of Statistics and Probability in Chinese and English Middle School Mathematics Textbooks —— Taking Mathematics published by Beijing Normal University and Mathematics Link published by Oxford University as examples [J]. Middle school mathematics teaching reference, 20 14(4) 66-68.

[6] new faces, painting spring clouds. A Comparative Analysis of the Contents of Function and Equation in Chinese and English Middle School Mathematics Textbook [J]. Middle School Mathematics Teaching Reference, 20 13(5):67-69.

[7] Lv Shukun. Teaching materials for changing graphics and curriculum content: experimental teaching materials for compulsory education curriculum standards-taking math students in grades 7-9 as an example [D]. Changchun: Northeast Normal University, 2006.

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