# 【国际中学部课程展示①】AP微积分 Hi, I am Benjamin Wang. I teach Precalculus, and Calculus in Joy International High School (JIHS). I believe conceptual understanding and practice are essential for math study. Besides, language is a very special factor that contributed to their academic success to international school students.

Precalculus completes the formal study of the elementary functions begun in Algebra 1 and 2 and is a gateway to Calculus and College level mathematics. The course is intended to provide the necessary background for continued study in mathematics as well as further prepare students for the mathematics section of college entrance exams. Students taking this rigorous course should have a strong background in both algebra and geometry. Graphing calculator technology is integrated throughout the course as problems are presented both algebraically and graphically. Topics covered include linear relations and functions, polynomial and rational functions, exponential and logarithmic functions, trigonometric functions and their graphs and inverses, graphical analysis, polar coordinates and parametric equations, vectors, conic sections, matrices, sequences and series.

##### 本课程主要包括线性关系和函数、多项式函数、有理函数、指数和对数函数、三角函数及其图形和逆函数、图形分析、极坐标和参数方程、向量、二次曲线、矩阵、数列和级数。

AP Calculus is designed for students who have excelled in Analytic Geometry & Precalculus and plan to take the Advanced Placement Examination in Calculus. This  course  covers  all  topics  included  in  the  Calculus  AB  topic  outline  as  it  appears  in  the  AP  Calculus Course  Description.  The  main  objective  of  the  course  is  to  provide  a  strong  foundation  that  will  give students  the  tools  to  succeed  in future  mathematics  courses.  The  course  will  give  students  the understanding  of  calculus  concepts,  related  mathematical  skills,  and  the  appropriate  technology  to enhance  the  process.  Within  a  multi-representational  approach,  a  balance  between  abstract  concepts and real applications is sought.

AP微积分面向擅长几何和微积分前课程、并计划参加AP微积分考试的学生。本课程涵盖AP微积分AB考试大纲的所有主题。课程的主要目标是为学生在未来的数学课程中取得成功提供一个坚实的基础。学生会通过对微积分概念的理解，相关的数学技能和适当的技巧的学习等来完成学习，在多种不同的表示方法中，寻找到抽象概念和具体应用的平衡。

Generally speaking, the math curriculum standards in American high schools are roughly the same as those in Chinese high schools. Compared to the Chinese systems, the mathematics course of JIHS provides more opportunities and wider freedom for students.

I will help the students solve the language problem first. JIHS adopts the original American math textbooks. For students entering the international school, language is the first problem they face. In learning of each unit, we will first study English math terms, English words from common situations of application problems. There are basically 30-60 new words in each unit, and some of these words have been learned in English class, but they just don’t know the corresponding mathematical meaning. After a period of practice, language problems are relatively easy to solve.

JIHS advocates a student-centered educational philosophy. After solving the language problem, some students seem to have fear and aversion to math. In fact, if you look carefully, there is no student who doesn’t want to learn math well. However, for some reason, they have difficulties in learning math now. It is good to help them solve them. By studying various situations, I will find out the reasons for students’ difficulties and give them some targeted suggestions and help to improve their math scores.

In the classroom, I also adhere to the student-centered teaching method. One class of my math is two periods together and 80 minutes long. I usually explain for 40-60 minutes and spend the rest of the time answering questions, finding out if the students really understand how to solve the questions, etc. When a formula is presented in class, I prefer students to learn how to get the formula, rather than memorize it mechanically through training. When I answer questions, if a student makes a mistake, I will give him some guidance based on his idea of solving questions and inspire him to think about how to solve the question in the right way. At the end of each class explanation, I will summarize what knowledge points we learn in the class, how they relate to each other, how they relate to the previous knowledge points in the unit, and so on, to help students connect the knowledge points together. For example, when we learn derivatives, we start from investigating limits and their properties. The special type of limit that is used to find tangents and velocities gives rise to the central idea in differential calculus, the derivative.

Here I want to give some tips for math academic success.

#### 01 循序渐进

Learning is a step-by-step process. Always keep up with and complete your assignments because you must understand each topic in order to learn the next.

#### 02 寻求帮助

When you are working problems for homework, show every step in your solution. If you make an error, it will be easier for you or your teacher to find it.

#### 03 四个步骤

There are four parts to each homework assignment: a) work all the problems, b) check the odd answers that are provided in the back of the book, 3) rework the odd problems that you missed and check the results of the even problems, 4)mark the problems that you cannot get to work and ask to see those problems the next day.

#### 05 查漏补缺

If you are absent, be sure to read the textbook, copy someone’s notes, and ask your teacher if you need help.