【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.
大家好，我是王立朋。我在嘉洋高中部教授微积分前和微积分课程。我相信概念理解和必要的练习是数学学习必不可少的。此外，对于国际学校的学生来说，语言也是取得学术成功的一个非常不同的因素。
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.
微积分前课程完成了从代数1和代数2开始的初等函数的正式学习，打开了学习微积分和开始大学阶段数学课程的大门。本课程旨在为继续学习数学提供必要的背景知识，并为学生准备大学入学考试的数学部分做进一步准备。选择修这门课的学生应该具备扎实的代数和几何基础。学习过程中，图形计算器的使用是需要的，因为题目都是代数和图形的。
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.
总体来讲，美国高中的数学标准和中国高中的范围大体一致。相对公立学校，嘉洋高中部的数学课程为学生们了提供了更多的机会和更广的自由。
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.
我首先会帮助学生解决语言关。嘉洋国际学校采用美国原版数学教材，对于初入国际学校的学生来说，语言是他们面临的第一个问题。我们会首先学习在本单元会涉及到的数学词汇、应用题的常见情景等。每个单元基本上有30-60个生词，而且这里面有一些单词学生在英语课上已经学过、只是不了解它对应的数学意思。经过一段时间的练习，语言问题相对比较容易解决。
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.
嘉洋高中部提倡以学生为中心的教育理念。在解决了语言问题以后，还有一些同学看起来对数学有一种恐惧和厌恶。其实仔细观察起来，没有学生不想学好数学的，但是由于一些原因，他们现在学习数学存在困难，帮助他们解决就好了。通过研究各种情况，我会发现学生的困难原因，给学生一些针对性的建议和帮助，以提高他们的数学成绩。
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.
课堂内，我同样坚持以学生为中心的教学方式。我的数学一次课是两节课、80分钟。我一般会讲解40-60分钟，其他时间用来答疑、判断学生是否真的做会了题目等。当课堂讲解遇到公式时，我更希望学生学会这个公式是怎么得出来的，而不是通过题海训练来机械地记住它。当答疑时，如果有学生做题错误，我会结合他的解题思路给他一些引导，启发他如何思考以做对题目。当每次讲课部分结束时，我会总结这节课我们学了什么知识点，他们是如何联系的，他们在本单元中是如何和前面的知识点结合的等等，帮助学生把知识点串联起来。例如，当我们学习导数时，我们从研究极限及其性质开始。用求切线和速度这两个特殊类型的极限，引出微分学的中心思想——导数。
Here I want to give some tips for math academic success.
在此，我想针对数学学习取得成功给出一些建议。
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.
学习是一个循序渐进的过程。要能持续的及时完成作业，因为你必须理解每一个学到的主题，才能更好的学习下一个。
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.
当你做作业时，把解题步骤都展示出来。如果你的答案不对，你或者你的老师可以更好的发现错误在哪里。
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.
每个作业有四个步骤：1）做完所有的题目，2）参考课本的后面提供的奇数题目答案，检查自己的答案，3）重做做错的题目，找出错误的点，修正后，检查偶数题目，4）标注出自己不会的题目，去问同学、老师。
04 仔细检查
Review your work carefully, making sure you understand where and how you made errors. Ask your teacher for help in understanding your errors.
仔细检查你的作业，确保你明白你错在哪里、怎么错的。向老师寻求帮助。
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.
如果你某次课缺席，一定要看课本，抄录其他同学的笔记，需要帮助时，及时找老师。
06 检查更新
Check your thinkwave.com for updates.
检查thinkwave的成绩更新。
JIHS offers six math courses currently, while you need to complete four to graduate. Therefore, students of different levels can choose appropriate courses according to their own situations. For example, students with good mathematical skills can choose the four difficult courses to prove their mathematical ability to the college admissions officer, while students with weak mathematical skills can choose the first four courses to ensure their good academic performance. In this way, students can make use of their strengths and bypass their weaknesses to get ahead in college applications!
嘉洋高中部目前提供了6门数学课程，而高中毕业需要学完4门课程。所以不同水平的学生可以结合自己的情况选择合适的课程，比如数学水平较好的学生可以选择比较难的4门课来向大学招生官证明自己的数学能力，而水平弱一些的学生可以选择前4门课来保证自己有一个好的学术成绩。如此，学生能够扬长避短，在大学申请中更胜一筹！
As far as I can see, there is no unsmart student nowadays, and all of them want to do well in math and get a good score. As a math teacher, my responsibility is to help students solve their difficulties, provide a quality math class with a student-centered style, while learning math knowledge, improve and expand students’ mathematical thinking, and help them go further and better in their future studies.
就我的观察来看，现在没有不聪明的学生，而且所有的学生都想把数学学好、考一个好的分数。那么我作为一位数学教师，责任就是要帮助学生解决困难，以学生为中心，讲好数学课，在学习数学知识的同时，提高和扩展学生们的数学思维，帮助他们在未来的学业上走得更远、更好。
