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讀書會消息 : Self-study textbook for Junior Secondary School (Geometry Chapters 1 to 8)
發布者 孫文先 在 2023-04-11 12:09:29 (8018 閱讀過)
Self-study textbook for Junior Secondary School (Geometry Chapters 1 to 8)
Free download for students


To promote the idea that "Mathematics is not taught but learnt", the Chiu Chang Mathematics Education Foundation from Taiwan is publishing a new series of Junior Secondary School books designed for self-study purposes.

The English version of this series has been translated from the original Chinese version. Many thanks to the volunteers and to Mrs Kitty Phillips from South Africa who helpe us correct the translation of the geometry section. We will upload the translated chapters on our website. Any student wishing to improve their skill in geometry may download this book for free.

Due to the explosion of knowledge, the education departments of many countries worldwide have greatly reduced the content of their mathematics courses for schoolchildren. Geometry is the most difficult and time-consuming section to learn. Therefore, the content of geometry in middle schools has been greatly reduced, resulting in the fragmentation of the entire geometry structure. It is now even harder for students to learn! Not only are students half-informed, but teachers are often under such pressure to complete their syllabus that the teaching of Geometry becomes a boring imparting of facts!

There are various objects around us in our daily life. We often need to study the shape, size and positional relationship of objects. The importance of geometry is beyond doubt. Mathematicians have repeatedly emphasized that advanced mathematics and physics cannot be learnt without geometric intuition. Even with the assistance of computers and AI, we still need to have geometric capabilities and understanding.

Most of the geometry textbooks and geometry exploration books on the market are either too brief or they skip too many basic concepts of geometry, making it difficult for readers to understand. This book makes up for these shortcomings by starting from the image of actual objects, and the definition of geometric terms, and gradually reasoning into geometric theorems and their proofs. In addition, it provides a wealth of exercises to allow students to establish strong geometric concepts and lay the foundation for advanced scientific research.

This book comprises 8 chapters:
a) Chapters 1 to 4 are designed for the second term in Grade 8.
b) Chapters 5 to 8 are designed for the second term in Grade 9.

It is believed that the 8 chapters cover all the geometry topics required in junior secondary mathematics in many countries, although the exact order of chapters may vary slightly from country to country.

Here are some suggestions for students and parents on how to use this self-study book for maximum benefit.

1. Suggestions for junior secondary students:

Regardless of your mathematics level, if you can spend 4 hours each day learning by yourself using this book, we can assure you that you will greatly improve your mathematics abilities beyond your expectation.

This book is developed based on a series of mathematical concepts, aiming to build a solid foundation of mathematics knowledge and practice.

You must honestly carry out the steps and methods suggested in the book. You may feel some difficulty initially, but gradually, within a short period of time, you will find your mathematics proficiency improving and you will become empowered and more confident in your mathematical ability.

As the examples and exercises in this book have been carefully designed, the level of difficulty is gradually inceased. It is absolutely possible for students to self-study, without seeking teachers’ or tutors’ guidance in the learning and understanding mathematics.

Although the exercises in the book may exceed the number of exercises found in most textbooks, it is important that students patiently work out each exercise. Students must draw each geometric figure exactly, knowing that precise geometric figures facilitate thinking.

You may wish to know the reason why Asian students generally have a higher standard in mathematics than their counterparts in other countries. The reason is that they are generally exposed to a comparatively larger number of practice and revision exercises.

It is suggested that students form student groups so that they can discuss the exercises and encourage each other in the learning process. This will enhance their progress.

2. Suggestions for parents of junior secondary students:

If the mathematics ability of your child in school is high, a good way to achieve even higher success is to raise the level of their mathematical ability through self study while maintaining their academic excellence. Possessing higher mathematical ability is beneficial for advancing to the senior secondary level in the future.

If the mathematics ability of your child in school is average, marginal, or below the passing grade, there is not much benefit in engaging a tutor or sending the child to a tutoring school. The best recourse is to encourage your child to self-study this book, giving him/her an avenue to restore his/her confidence in thinking that there is a way he/she can gradually become an excellent student in his/her mathematics class.

If your child can find some good friends to study and discuss the book’s exercises as a group, you as parents must find a way to help look for convenient time and place for them to do the group study. You should also support by monitoring their progress from time to time.

If your child's mathematics ability has improved to grade A or above, we would suggest encouraging your child to study more by giving extrinsic motivation, like a reward system.

Since the launching of this book, there has been over a thousand students downloading it online for self-study. Currently, there are many students who carry out our suggestion to self-study the book and achieve significant improvement. We wish that your child’s mathematical abilities will also improve and soar high.


Chapter 1. Basic concepts
I. Lines, Rays and Line Segments
II. Angles

Chapter 2. Intersecting Lines, Parallel Lines
I. Intersecting Lines and Perpendicular Lines
II. Parallel Lines
III. Proposition, Theorem and Proof

Chapter 3. Triangles
I. Triangles
II. Congruent Triangles
III. Isosceles Triangles
IV. Basic Constructions
V. Right Triangles6
VI. Converse Theorem and Symmetry

Chapter 4. Quadrilaterals
I. Quadrilaterals
II. Parallelograms
III. Trapezoids

Chapter 5. Area and Pythagorean Theorem
I. Area
II. Pythagorean Theorem

Chapter 6. Similarity
I. Proportional Line Segments
II. Similar Triangles
III*.Homothetic Figures

Chapter 7. Circles
I. Some Properties of a Circle
II. Positional relationship between line and circle
III. Positional relationship between circle and circle
IV. Regular Polygons and Circles
V. Locus of a Point
Appendix. Circumference and Area of circles

Chapter 8 * Perspective Drawings and Activities


 

 
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