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不刷题,不内卷也能学好数学?“一人一张课表”、分层选课,深度个性化发现每个孩子的天赋

01-15 08:28发布于江苏

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在狄邦华曜有这样一些学者,他们或许是经历了公立的不适,转轨进了国际化学校,在寻找更适合的“非标准化”教育;或许是从海外回国,经历了跨国的文化、语言差异,在寻找适合的国际化环境与教育;或许是天赋异禀、特长突出的孩子,经历了“吃不饱”的教育体系,在寻找适合个性化发展的“沃土”。


  G9 Rission: 六年级从昆山公立学校转入狄邦华曜,经历了从单一中文学习数学到用双语学习及应用数学学科的转化。Rission在小学的时候,并不喜欢数学这门学科,也没有信心,转入的时候数学只是基础CP-A班,但9年级的他现在已经在数学第三个层级ECP班中学习,而且也爱上了数学,甚至计划挑战与数学紧密相关的学科竞赛。


  G7 Victoria: 四年级从上海徐汇一所一梯队民办学校转到狄邦华曜,现在是7年级,但她的数学已经基本学完了9年级的课程。为了备战AMC10的考试,这个学期Mr. Guo Yi每周给她单独开设了一对一的进阶数学课(Advanced Math)。

  G10 Joanna:从小在美国加州顶尖私立学校学习,八年级从美国加州转入狄邦华曜,一年内不仅数学跳了一级;九年级学期末,她独立写出了一篇数学学术论文:《杨辉三角和斐波那契数列的规律》(Patterns in Pascal’s Triangle and Fibonacci Sequence》;还拿到了美国高中数学建模大赛(HiMCM)的荣誉奖。


1年, 3年,4年,这些不同背景的学者们…..他们在这里成长蜕变,在“个性化教育”体系下,找到了适合自己发展之路。在这里既没有同质化的“内卷”,也没有任意的“放养“,无论是学校、家长、还是学者,都不会感到焦虑,在自由选择空间中,发掘兴趣与天赋,取得优异的学术成绩和全面的发展。



In Dipont Huayao Collegiate School Kunshan, there are some scholars who may have experienced the discomfort of the public schools, and then entered the internationalized schools, looking for a more suitable "non-standardized" education; or perhaps they are the children who have returned from overseas and experienced the cultural and language differences across the borders, looking for the suitable internationalized environment and education; or perhaps they are the children who are gifted with outstanding strengths and have experienced the "underfed" education system, looking for the "fertile ground" for individualized development.


 G9 Rission: Transferred to HC from a public school in Kunshan in 6th grade, he has experienced the transition from learning math in a single Chinese language to learning and applying the subject in a bilingual way. Rission did not enjoy or have confidence in math in elementary school, and was only in a basic CP-A class in math at the time of his transfer, but in 9th grade he is now in the ECP class, and loves math and even plans to challenge himself to competitions in subjects closely related to math.

 

 G7 Victoria: Transferred to HC from a Top private school in Xuhui Shanghai in Grade 4, is now in Grade 7, but she has basically completed Grade 9 in Math. In order to prepare for the AMC10 exam, Mr. Guo Yi has been giving her a separate one-on-one Advanced Math class every week this semester.

 

 G10 Joanna: Growing up in a top private school in California, she transferred to HC as an eighth grader, and not only did she jump one grade in math within a year; at the end of the ninth grade semester, she independently wrote a mathematical academic paper, Patterns in Pascal's Triangle and Fibonacci Sequence; and also received an honorable mention in the High School Math Modeling Competition (HiMCM).


One year, three years, four years, they grow and change here, in the "personalized education" system, to find a suitable path for their own development. There is neither homogenized "internal scroll" nor arbitrary "free-range", and neither schools, parents, nor scholars will feel anxious, and in the space of free choice, they will explore their interests and talents, and achieve excellent academic results and comprehensive development.


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每个学者都有自己的学习节奏,让学者们在最合适的节奏里学有所得。越到高年级,数学学习的难度越大。太难的挑战会降低学者的学习动力,太密集的简单挑战又会导致学者脚步琐碎,无法快读前进。相反,个性化教育经过精心设计和周密实施的可以为学者提供最适合的学科教育。


Every scholar learns at their own pace, allowing scholars to learn at the pace that works best for them. The higher the grade level, the more difficult the math learning becomes. Challenges that are too difficult can reduce a scholar's motivation to learn, and challenges that are too dense and simple can cause a scholar to be on his or her toes and unable to move forward quickly. On the contrary, personalized education can provide scholars with the most suitable academic education through careful design and implementation.


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初中灵活分层选课,满足每个人的学习需求

Flexible stratified course selection in middle grades to meet everyone's learning needs

狄邦华曜中学部数学组组长Mr. Guo Hui介绍,在教学任务和学习方式上,老师会根据学者们不同水平和接受程度建立不同的挑战难度,采用分层教学为每位学者带来个性化支持。正如美国著名心理学家和教育学家布鲁纳提出的脚手架理论,狄邦华曜注重为每位学者搭建最适合的脚手架,让他们从容、快速向上攀登。

Mr. Guo Hui, Head of Maths at SS, explains:

In terms of teaching tasks and learning styles, teachers will establish different levels of challenge according to the scholars' different levels, and use layered teaching to bring personalized support to each scholar. Just like the scaffolding theory put forward by Bruner, the famous American psychologist and educationalist, Dipont Huayao Collegiate School Kunshan focuses on building the most suitable scaffolding for each scholar, so that they can climb upward comfortably and quickly.



初中7-9年级


狄邦华曜会根据学者的数学水平和英文水平,设置了4个不同层级,由低到高分别是CP、CP-A、ECP、ECP-I。


其中CP和CP-A采用双语授课,ECP和ECP-I这两个层级则采用全英文授课——每个学年都有几个时间节点,学生可以申请调整到不同层级;



Middle Grades


Dipont Huayao Collegiate School Kunshan Middle Grades has 4 different levels based on students' math and English levels, from lowest to highest, CP, CP-A, ECP, and ECP-I.


The CP and CP-A are bilingual, while the two other levels, ECP and ECP-I, are taught in full English - there are several time points in each academic year where students can apply to adjust to a different level;



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对于初中的学者,无论是哪个层级所学的内容知识点都是一致的,都是以义务教育大纲为核心骨架,融合国际课程优势。在更高层级的班里,不仅会覆盖需要教学的内容,还会拓展加深后续内容,结合实际生活中的例子去讲解,比如说用数学思维计算学校受灾时的疏散方案,帮助学生有意识的把课堂知识和实际应用结合起来。


分层教学是一个动态变化的过程。


Mr. Guo Yi向我们介绍,学科分层我们首先会参考每位学者在之前的卷面成绩,但是试卷其实并不能完全体现学生的学科学习能力。在学期初完成分班后,我们会及时在课堂内观察、评估和调整。尤其是对于从其他体系或者其他地方转过来的一部分学者,老师和助教会指导他们的学习方式和语言、学术问题,也会开设延展课,提供额外的支持和培优。对于有英语方面的语言障碍的学者,会为学者增加数学相关的词汇学习,每周进行听写,增强英语水平。对于学术能力较弱的学者,老师会在每节课后给学者进行测试,1道题快速测试,实时跟进学者的学习情况。


Rission也说道,当他之前基础还比较薄弱,在CP-A的班时,他的数学老师Ms. Luyao会用一种就是比较易懂的方式。这学期升入ECP的班里,同班同学的数学基础都比较好,上课的内容明显发生了很大的变化。老师在保持知识点讲解的基础上,会做很多知识点应用类的拓展,或就一个题让大家提出更多的解题方式。 课堂中明显讨论更多了,大家对数学从理解进入了实际应用的阶段。这与传统学校学习数学是完全不同的,这种循序渐进的方式让他对数学的畏惧减少了,好感增多了,也在丰富的项目体验中渐渐喜欢上了数学。


从小在美国数学体系下学习的Joanna回想起自己八年级刚从美国加州转回狄邦华曜,前两三个月时间里,她的确是感受到了“不适”,这种不适不是来自于文化的冲击感,也不是师生间的相处,而是中美课程的衔接,的确不能一刀切的通过年级来过渡衔接。“这些学科内容我在美国都上过,如果再学一遍有点浪费时间。所以当时经过评估,学校决定这几门课我都和九年级的学生一起上。”这种个性化的课程搭配让她很快的适应了中学学习生活。九年级学期末,她还独立写出了一篇数学学术论文:《杨辉三角和斐波那契数列的规律》(Patterns in Pascal’s Triangle and Fibonacci Sequence》。


For middle grade scholars, the knowledge points learned are the same regardless of the level, with the compulsory education syllabus as the core skeleton, incorporating the strengths of the international curriculum. At higher levels, the classes will not only cover what needs to be taught, but will also expand and deepen the subsequent content, incorporating real-life examples, such as using mathematical thinking to calculate evacuation plans in the event of a school disaster, to help students consciously combine classroom knowledge with practical applications.


Stratification is a dynamic process.


Mr. Guo Yi explained to us that the first thing we do is to refer to each scholar's previous paper scores, which do not fully reflect the student's learning ability. At the beginning of the semester, we will observe, evaluate and adjust in the classroom in a timely manner. Especially for some scholars who have transferred from other systems or places, teachers and TFs will guide them on learning styles and language and learning issues, as well as offer extension classes for additional support and excellence. For scholars with language barriers in English, additional math-related vocabulary study and weekly dictation are provided to enhance English language proficiency. For academically weak scholars, the teacher will give scholars a test after each class, a 1-question quick test, to follow up with scholars in real time.


Rission also said that when he was in CP-A, his math teacher, Ms. Luyao, taught him in a way that was easier to understand when his foundation was still weak. When he moved up to ECP's class this semester, his fellow classmates had a better foundation in math, and the content of the class obviously changed a lot. On the basis of maintaining the explanation of knowledge, the teacher will do a lot of extension of the application of knowledge, or let everyone propose more ways to solve a problem. There is obviously more discussion in the classroom, and everyone has moved from understanding to practical use of math. This is completely different from learning math in a traditional school. This step-by-step approach has made him less afraid of math, more favorable, and he has gradually enjoyed math in the rich experience of the program.


Joanna, who grew up in an American math system, recalled that she had just transferred to HC from California in the eighth grade, and during the first two to three months, she did feel "uncomfortable", which did not come from a sense of culture shock, nor from the teachers' and students' relationship with each other, but rather, it was the articulation of the curriculum between the U.S. and China, which indeed could not be bridged by one single grade.  "I've taken all of these subjects in the U.S., so it would be a bit of a waste of time to learn them all over again. So at that time, after evaluation, the school decided that I would take these classes with the ninth graders." This individualized course pairing allowed her to adapt quickly to middle school life. At the end of the ninth grade semester, she even wrote an academic math paper independently, Patterns in Pascal's Triangle and Fibonacci Sequence.


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超越初中最高层,一个人的定制化数学课

Beyond the highest levels of middle school, a customized math class for one person




在探访数学课堂时,我们看到了一间正在进行一对一的进阶数学课。 G7的Victoria与Mr. Guo Yi在这间教室汇总,这是郭老师为这位有着独特天赋的学者开设的辅导课程。数学组的老师们评价Victoria在数学上天资过人,虽然只有7年级,但已经拥有9年级的同等水平。

面对这样的学者,Mr. Guo Yi说,他问过Victoria的想法,她希望能在数学素养上上一个台阶,而不是冲中考高分去的。因此在备课时,刻意减少刷题训练,增加了更多需要思考、开放性的问题,甚至还会有数学建模的作业,衔接高中内容。


“虽然是9年级水平,但我也不会只讲9年级的内容,而是自由化地垂直拔高,保留知识点的完整度,并进行横向拓展。”Mr. Guo Yi介绍说,这套数学教学的理念,不仅用在给Victoria开小灶中,也适用于其他9年级的学生。


While visiting a math classroom, we came across a room where a one-on-one advanced math class was taking place. G7's Victoria was in this classroom with Mr. Guo Yi, a tutoring program that Mr. Guo runs for this uniquely gifted scholar. Teachers in the Maths team commented that Victoria is gifted in Maths and although she is only in Grade 7, she already has the same level of proficiency as a Grade 9 scholar.


When faced with such a gifted scholar, Mr. Guo Yi said he asked Victoria what she wanted to do, and that she wanted to take a step up in her math literacy rather than aiming for a high score in the exams. Therefore, in preparing for the class, there is a conscious effort to reduce brush-up training and add more questions that require thinking and are open-ended, and there will even be mathematical modeling assignments to bridge the upper grade content.


"Although she's at 9th grade level, I won't just cover 9th grade content, but rather liberalize the vertical pull-outs, retaining the integrity of the knowledge points and expanding horizontally." Mr. Guo Yi describes this philosophy of teaching math as one that is not only used in opening up a small class to Victoria, but is also applicable to other 9th grade scholars.


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高中“一人一张课表”,比大学更大学的自由选择

"One person, one schedule" in Upper Grades, more free choice than college

到了高中阶段,狄邦华曜的学者可以根据自己的升学需求定制课表,实现“一人一张课表”。


中学部数学组组长Mr. Guo Hui介绍说,高中阶段的课程设置是与美国顶尖精英寄宿高中共同合作开发的“美式校本课程”,设立了大学预备课程(CP)、荣誉课程(ECP)、大学先修课程(AP)和大学先修进阶课程(EAP),难度逐级递增。学者选课不再以年级划分,而是像在大学里一样,数学达到什么水平就去上什么课。

In Upper Grade, HC scholars can customize their class schedules according to their own needs, realizing "one person, one class schedule".


Mr. Guo Hui, Head of Maths at SS, said that the curriculum of the upper grade is the "American school-based curriculum" developed in cooperation with the top elite boarding high schools in the U.S. The curriculum is organized into four levels of difficulty: CP, ECP, AP, and EAP. Scholars no longer select courses by grade level, but rather go to whatever level of math they have achieved, as they would in college.



数学组共设计了11门数学课供学者自由选择:




The math team designed a total of 11 math classes for scholars to freely choose from:




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因为课程太丰富了,Mr. Guo Hui说,不同学术水平的学生可以有各种排列组合的选择,最大程度上满足了每个人的个性化发展需求。比如: 


数学程度高的学者




10年级AP预备微积分, 11年级AP微积分BC, 12年级AP统计学、线性代数或金融数学;


数学中游的学者




10年级CP微积分预备, 11年级AP微积分AB, 12年级AP统计学;


数学一般的学者




10年级CP代数几何, 11年级CP预备微积分, 12年级AP微积分AB……



As the courses are so rich, Mr. Guo Hui said, students with different academic levels can have various permutations and combinations of choices, which maximizes the individual development needs of each person. For example:


Scholars with a high level of math




can take AP Pre-Calculus in 10th grade, AP Calculus BC in 11th grade, and AP Statistics, Linear Algebra, or Financial Math in 12th grade;


Scholars in the mid-level of math




may take CP Pre-Calculus in 10th grade, AP Calculus AB in 11th grade, and AP Statistics in 12th grade;


Scholars with average math




10th grade access to CP Algebra Geometry, 11th grade CP Pre-Calculus, 12th grade AP Calculus AB ......



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“一人一张课表”的极致个性化真的不是说说的。而这只是帮助学者提升学术的第一步,在课堂教学上,狄邦华曜的老师们也是下足了功夫。

The ultimate personalization of "one person, one schedule" is really not just words. This is just the first step to help scholars improve their academic performance. HC's teachers also put in a lot of effort in teaching.


多样的学习形式,培养数学的核心素养

Multiple forms of learning to develop core literacy in mathematics




在中学部数学组组长Mr. Guo Hui看来,一个好的数学教育,一定要能激发学生学习数学兴趣,提高学者解决实际生活问题的能力,培养学者的数学思维能力。


狄邦华曜的中学部数学课堂不同于传统式的数学课堂,不仅有翻转课堂、学生vlog录制、课程试讲、小讲座等不同教学形式,让学者们对学习充满兴趣;还会把知识点融入到项目制学习里,引导学者对简单的数学问题进行深入的思考,拓展思维广度。


In Mr. Guo Hui's opinion, a good math education must be able to stimulate students' interest, improve scholars' ability to solve real-life problems, and cultivate scholars' mathematical thinking ability.


Our secondary math classroom is different from the traditional math classroom in that it not only has different teaching forms such as flipped classroom, student vlogging, trial lectures, and mini-lectures to make scholars interested in learning, but it also integrates the knowledge points into the project-based learning, which guides the scholars to think deeply about the simple math problems and expands the breadth of their thinking.


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从课堂到课外,数学在学校的场景里无处不在,数学老师们还会设计了诸如“π-Day寻宝”等活动,通过有趣的游戏——用三角函数的知识来测量国旗杆的高度,计算学校异型窗户的面积,用餐厅的餐盘计算概率问题等等,让学生将所学知识与真实问题相结合,不仅提升他们解决问题的能力,也让他们看到数学在现实世界的运用。



From the classroom to the outside, math is everywhere in the school environment. Math teachers also design activities such as the "π-Day Treasure Hunt", in which scholars measure the height of the flagpole using trigonometry, calculate the area of the school's shaped windows using a cafeteria tray, etc.-students are able to combine what they have learned with real-world problems, which not only enhances their problem-solving skills, but also allows them to see how math can be used in the real world.


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同时,在Mr. Guo Yi看来,数学建模比赛也是一次很好的PBL项目式学习的机会,让学生们能将平时课堂所学的数学知识,用于解决现实生活中的实际问题。


去年HiMCM比赛的主题是关于“创建一个数学模型,预测蒲公英在1、2、3、6、12个月的蔓延情况”,并且要确保模型包含了各种气候条件(如温带、干旱和热带气候)对蒲公英生长的影响。



At the same time, Mr. Guo Yi believes that mathematical modeling competitions are also a good opportunity for project-based learning, allowing students to apply the mathematical knowledge they have learned in the classroom to solve real-life problems.


The theme of last year's HiMCM competition was about "creating a mathematical model to predict the spread of dandelions in January, February, March, June, and December", and making sure that the model included the effects of various climatic conditions (e.g., temperate, arid, and tropical climates) on the growth of dandelions.


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在参赛过程中,学者们不仅学到了如何建立数学模型解决真实问题,还学到了生物学、地理学等跨学科知识,以及数据收集、分析、学术论文写作、团队合作、批判性思维等各方面的能力。这些可迁移能力都会让学者受益终身。

连续参加了两届数学建模大赛的Joanna告诉我们,在去年的建模比赛中,她主要负责建立数学模型,还和小伙伴一举拿下了荣誉奖(Honorable Mention)!而在今年的比赛,她主要负责论文的撰写,每次团队分工都让她学到了不一样的技能。



During the competition, scholars not only learned how to build mathematical models to solve real problems, but also learned interdisciplinary knowledge such as biology and geography, as well as various aspects of data collection, analysis, academic paper writing, teamwork, and critical thinking. All these transferable abilities will benefit the scholars for life.

 

Joanna, who has participated in two consecutive Mathematical Modeling Competitions, told us that in last year's modeling competition, she was mainly responsible for building the mathematical model, and also won the Honorable Mention with her partner! In this year's competition, she was mainly responsible for writing the paper, and each time the team divided up the work, she learned a different skill.



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在今年的建模比赛中,她的队友Victoria是以初中生的身份第一次参加高中比赛。11月初,Victoria的妈妈忍不住在朋友圈里写下这样一段话:


“2023HiMCM开题。18点结束第一场小组讨论,对学姐们赞不绝口,回程一路直呼‘过瘾’;到家便一头扎进书房,晚餐也在噼里啪啦键盘声中消失无形。这就是同伴的力量吧!”


从因材施教的分层选课,到一人一张课表,再到多样的学习方式,每个狄邦华曜的学者都在这里找到了适合他们成长的正确方式!从懵懂到自信,从优秀到卓越,他们又在狄邦华曜发生着哪些翻天覆地的故事,成长不停歇,精彩也在不断上演…… 下一期数学主题,我们也会讲述那些在数学领域有着浓厚兴趣和学习能力的学者故事!



In this year's modeling competition, her teammate Victoria is participating in the high school competition for the first time as a middle school student.In early November, Victoria's mom couldn't help but write this in her circle of friends:


"2023HiMCM opening. 18:00 end of the first panel discussion, the schoolmates were full of praise, the way back home calling out 'addicted'; to the home then head into the study, dinner also in the sounds of the crackling keyboard. That's the power of peers, right?"


From the hierarchical selection of classes according to the students' abilities, to the one-person-one-class-schedule, to the variety of learning styles, every HC scholar has found the right way for their growth here! From confusion to self-confidence, from good to excellent, and what stories are happening to them at HC, the growth does not stop, and the excitement continues to unfold ...... In the next issue of Math Theme, we will also tell the stories of those scholars who have a strong interest in the field of math and their ability to learn!



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狄邦华曜学校欢迎更多优秀学者加入


2024春季插班招生

一年级至十一年级


考试/面试时间:


【昆山】

2024年1月29日(周一)9:00

考试地点:

昆山狄邦华曜学校(景王东路988号)



【上海】

2024年1月29日(周一)14:00

考试地点:

上海静安区南京西路1788号33楼

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