感謝Mila等小學(xué)部數(shù)學(xué)老師對本文的支持
Thanks to Mila and other Elementary School math teachers for their support on this article
【資料圖】
溫度計、3D模型、手工剪紙…當(dāng)這些作品同時出現(xiàn)在一間教室的時候，不要懷疑，我們走進(jìn)了昆山狄邦華曜學(xué)校的數(shù)學(xué)課堂。
這些從一開始就透露出與眾不同的學(xué)習(xí)成果究竟是如何而來的？創(chuàng)校至今已有三年，沉浸式雙語教學(xué)（Dual Language Immersion）、跨學(xué)科融合項目式教學(xué)（iSTEAM-PBL）靈活學(xué)習(xí)小組（Flexible Grouping）這些亮點又是如何在課堂中實現(xiàn)的？
為此，我們特意走進(jìn)狄邦華曜小學(xué)部的數(shù)學(xué)課堂，看看扎實的學(xué)術(shù)基礎(chǔ)、創(chuàng)新的思維、解決實際問題的能力，是如何在課堂中實現(xiàn)兼得。
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Thermometers, 3D models, hand-cut paper... Don’t doubt it when you see all these works appear in a same classroom at a same time, we are walking into a math class at Dipont Huayao Collegiate School Kunshan (Dipont HC for short).
How did these extraordinary learning outcomes come about in the first place? It has been three years since the establishment of the school, how are these highlights of Dual Language Immersion and Flexible Grouping and iSTEAM-PBL achieved in the classrooms?
Now, we are coming into a math classroom at Dipont HC Elementary School to see how a solid academic foundation, innovative thinking, and the ability to solve practical problems can be achieved in the classrooms.
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“真實”提高學(xué)者的數(shù)學(xué)核心素養(yǎng)
The "real things" improves the mathematics core literacy of scholars
扎實的基礎(chǔ)和創(chuàng)新的思維、解決實際問題的能力并不沖突。要在現(xiàn)實情景中運用數(shù)學(xué)知識解決問題，就必須要有扎實的基礎(chǔ)知識和基本技能。
狄邦華曜的老師們在數(shù)學(xué)課程教學(xué)環(huán)節(jié)的設(shè)計中，將學(xué)者們置于真實情境，通過基于探究和基于項目（inquiry-based and project-based）的學(xué)習(xí)方法，引導(dǎo)學(xué)者學(xué)會用數(shù)學(xué)的眼光觀察現(xiàn)實世界，用數(shù)學(xué)的思維思考現(xiàn)實世界，用數(shù)學(xué)的語言表達(dá)現(xiàn)實世界，憑借多樣化的項目活動經(jīng)驗，習(xí)得知識，鍛煉能力，找到解決現(xiàn)實問題的方法。
這種基于項目的學(xué)習(xí)，與我們習(xí)以為常的課堂不同，我們習(xí)慣了先學(xué)習(xí)一個知識點，然后通過“刷題”來加深理解。基于項目的學(xué)習(xí)是將基礎(chǔ)知識與項目學(xué)習(xí)融合在一起，無論是中文數(shù)學(xué)還是英文數(shù)學(xué)，老師們都會設(shè)計大大小小、各式各樣的項目活動融入日常教學(xué)，讓學(xué)者們邊練邊學(xué)。
了解數(shù)學(xué)不僅僅是了解事實，學(xué)者掌控自己的學(xué)習(xí)并且能將知識應(yīng)用于新的情況。
比如：
G2的學(xué)者學(xué)習(xí)乘法，老師會引導(dǎo)學(xué)者把謎題盒（puzzle-box）制作成自己喜歡的樣子，幫助學(xué)者理解原理，記憶乘法口訣。
G3的學(xué)者學(xué)習(xí)分?jǐn)?shù)，可以嘗試參照食譜制作一個餡餅，3/4的洋蔥、1/4的糖…將不同的食材、調(diào)料組合在一起。
G5的學(xué)者學(xué)習(xí)面積公式，可以通過繪制房屋平面圖并建立三維模型將面積應(yīng)用到現(xiàn)實生活；學(xué)習(xí)多邊形，老師會帶領(lǐng)學(xué)者們丈量學(xué)校、小區(qū)或公園的綠地面積，按比例尺繪制面積圖并進(jìn)行面積計算。
G6的學(xué)者學(xué)習(xí)負(fù)數(shù)，不僅要認(rèn)識并嘗試制作溫度計，還要在制作過程中演講，分享制作的方法和自己的思考。
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In fact, a solid foundation does not conflict with innovative thinking or the abilities to solve practical problems. To use mathematical knowledge to solve problems in real situations, we must have a solid foundation of knowledge and basic skills.
In the design of mathematics teaching, the teachers of Dipont HC put scholars in real situations and guided them to observe the real world with mathematical vision and think about the real world with mathematical thinking through inquiry-based and project-based learning methods. They help scholars to express the real world with mathematical language, acquire knowledge, improve abilities and find ways to solve practical problems by relying on diversified project activities experience.
This kind of project-based learning is different from the classroom we were used to, where we were used to learning a knowledge point and then deepen our understanding by simple repetition. Project-based learning integrates basic knowledge with project-based learning. Whether it is Chinese mathematics or English mathematics, teachers will design various project activities, large and small, into daily their teaching, so that scholars can learn while practicing.
Understand that Math is more than knowing facts.
Scholars take control of their own learning.
Allow the application of knowledge to new situations.
For example:
Scholars in G2 learn multiplication, and teachers will guide scholars to make puzzle-boxes as they like, helping scholars better understand principles and memorize multiplication tables.
G3 scholars will learn fractions and try making a pie from a recipe, 3/4 onion, 1/4 sugar... They will combine different ingredients and seasonings together.
Scholars in G5 learn the area formula and can apply the area to real life by drawing house plans and building three-dimensional models. To learn polygon, the teachers will lead the scholars to measure the green area of the school, community or park, draw the area map and calculate the area according to the scale.
To learn negative numbers, G6 scholars not only have to know about and try to make thermometers, but also make presentations in the process of making them, sharing their methods of making and their own thoughts.
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項目式學(xué)習(xí)是一個非常有趣的過程，老師們的教學(xué)設(shè)計通常與真實的生活相關(guān)聯(lián)，一方面引導(dǎo)學(xué)生將所學(xué)的知識點應(yīng)用到實際生活中，另一方面，在項目的探索實施過程中，有可能會遇到新的知識，這時候就需要學(xué)者查找、學(xué)習(xí)，將這些新知識、新技能在項目實踐中鞏固、夯實，并推廣到同類的情境中解決新問題。
通過探究式、項目式學(xué)習(xí)，狄邦華曜的數(shù)學(xué)課堂讓學(xué)者們真正具備數(shù)學(xué)的眼光，能夠在現(xiàn)實中發(fā)現(xiàn)數(shù)學(xué)問題，即在現(xiàn)實情景與數(shù)學(xué)抽象間，做一個聯(lián)系、一個解釋、一個翻譯，并運用數(shù)學(xué)解決真實的問題。
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Project-based learning is a very interesting process. Teachers" teaching design is usually related to real life. On one hand, scholars are guided to apply the knowledge they have learned to real life; on the other hand, in the process of project exploration and implementation, scholars may encounter new knowledge, which requires them to search and learn. They will have to consolidate these new knowledge points and skills in project practice, and extend them to similar situations to solve new problems.
Through inquiry and project-based learning, mathematics classrooms at Dipont HC enables scholars to truly have a mathematical vision, to find mathematical problems in reality, that is, to make a connection, an explanation, a translation between real situations and mathematical abstractions, and to apply mathematics to solve real-life problems.
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發(fā)揮中文數(shù)學(xué)傳統(tǒng)優(yōu)勢，夯實基礎(chǔ)拓展知識
Give full play to the traditional advantages of Chinese mathematics, consolidate the foundation and expand knowledge scale
那么，在有限的課時中，老師們是如何完成如此大量的項目探究活動呢？
依據(jù)最新課程標(biāo)準(zhǔn)，學(xué)者們每周有5節(jié)中文數(shù)學(xué)課，中文數(shù)學(xué)老師會嚴(yán)格按照國家大綱的要求完成教學(xué)。在具體教學(xué)設(shè)計中，老師會針對性地進(jìn)行靈活多樣的設(shè)置，通過內(nèi)容和形式的差異幫助學(xué)生鞏固知識。在同樣40分鐘的課時內(nèi)，完成幾種不同的學(xué)習(xí)方式和幾個不同層次的學(xué)習(xí)內(nèi)容。
G3的Jannie老師說：“學(xué)者們沒必要每天完成一套試卷去刷題，知識的學(xué)習(xí)更重要的是融會貫通。如果真的存在不理解或完成困難的題目，那就要深挖根源，是讀題困難，理解錯誤，還是存在知識盲區(qū)，清楚了根源所在，針對性完成兩三次訓(xùn)練就足夠了。只有困難的根源在于基礎(chǔ)計算或讀題困難時，那才需要多加練習(xí)。對于已掌握的學(xué)者來說，單純的刷題是沒有意義的。”
比如新內(nèi)容的學(xué)習(xí)，Jannie老師通常將其設(shè)計為情境導(dǎo)入/復(fù)習(xí)導(dǎo)入、新知掌握、概念確認(rèn)、應(yīng)用表達(dá)4個環(huán)節(jié)，留有充足的時間引導(dǎo)學(xué)者獨立思考，小組討論，發(fā)表觀點，讓每位學(xué)者都擁有多元思維的能力，不會被知識填鴨。
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So, how can teachers complete such a large amount of project inquiry activities in limited class hours?
According to the latest curriculum standards, scholars will have five Chinese math classes a week, and Chinese math teachers will strictly follow the national syllabus. In the specific teaching design, teachers will make targeted and flexible settings to help scholars consolidate knowledge through the differences in contents and forms. In the same 40 minutes of class, complete several different learning styles and several different levels of learning contents.
G3 teacher Jannie said: "Scholars don"t need to complete a set of papers every day to make repetition, knowledge learning is more important to grasp. If there really is no understanding or difficult to complete the topic, it is necessary to dig deeper to the roots, is it difficult to read the topic, understand it wrong, or is there blind area in knowledge? Make clear the root cause, and complete two or three targeted training will be enough. It is only when the root of the difficulty lies in the basic calculation or reading difficulty that more practice is needed. For scholars who have mastered the subject, it is meaningless to simply make repetition."
For example, the learning of new content is usually designed by Teacher Jannie into four parts: situation introduction/review introduction, mastery of new knowledge, concept confirmation and application expression. She is leaving enough time to guide scholars to think independently, discuss in groups and express their views, so that each scholar has the ability of diversified thinking and will not be simply filled in by knowledge.
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G5 的June老師則強(qiáng)調(diào)，由于小學(xué)階段詞匯量的限制，英文數(shù)學(xué)的難度很難深入，因此對于重難點的攻克更多地側(cè)重在中文數(shù)學(xué)上。老師們會在每個單元設(shè)計有挑戰(zhàn)題和拓展訓(xùn)練，有的偏重于深挖知識點，有的強(qiáng)調(diào)跨學(xué)科時與其他知識內(nèi)容相結(jié)合的綜合性問題，有的則是一題多解，予以學(xué)者不同方向的練習(xí)。
此外狄邦華曜鼓勵學(xué)者參加各類校內(nèi)外的競賽活動，建立自信，豐富經(jīng)驗。
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Teacher June of G5 emphasized that due to the limitation of vocabulary in Elementary School, English math is difficult to go deep, so the key and difficult points should be more focused on Chinese math. Teachers will design challenge questions and extended training in each unit, some of which lay emphasis on digging deep on knowledge points, some emphasize on the comprehensive problems when integrating with other knowledge content, and some of which are with multiple solutions to one question, giving scholars practice in different directions.
In addition, Dipont HC scholars are encouraged to participate in various internal and external competitions to build confidence and enrich experience.
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靈活學(xué)習(xí)小組與分層教學(xué)，在英文數(shù)學(xué)中更好地提升自我
Flexible learning groups and stratified teaching to help scholars improve themselves in English Mathematics
在常規(guī)的中文數(shù)學(xué)之外，每周還安排有3節(jié)英文數(shù)學(xué)課。
小學(xué)數(shù)學(xué)和科學(xué)學(xué)科組組長Mila老師介紹：
“我們中文數(shù)學(xué)與英文數(shù)學(xué)的課程標(biāo)準(zhǔn)是一致的，因此學(xué)者們可以通過中文數(shù)學(xué)課程學(xué)習(xí)基礎(chǔ)知識和基本技能，并且通過基于探究和項目的學(xué)習(xí)方法豐富他們在英文數(shù)學(xué)課程中的學(xué)習(xí)。
中英文數(shù)學(xué)并不是使用不同的語言把相同的內(nèi)容學(xué)兩遍，中文數(shù)學(xué)中講授的內(nèi)容，在英文項目活動中再次涉及，既可以豐富學(xué)者對學(xué)科知識的理解，也是梳理所學(xué)所得的過程。英文數(shù)學(xué)在小學(xué)階段的學(xué)習(xí)目標(biāo)，除了豐富詞匯量，語言提升，打好基礎(chǔ)外，更側(cè)重知識的應(yīng)用，因此學(xué)習(xí)的方法和過程尤為重要。學(xué)者們需要通過探究式、項目式學(xué)習(xí)，了解數(shù)學(xué)與不同學(xué)科之間的聯(lián)系，挖掘數(shù)學(xué)在現(xiàn)實中的意義。
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In addition to the regular Chinese math, there are also three English math classes in each week.
Teacher Milan, team leader of Elementary School Mathematics and Science Subject Groups, said that:“Our Chinese and English Math are aligned so scholars are able to understand the basic math concepts and skills in their Chinese Math classes and we enrich their learning in our English Math classes through the Inquiry and Projects-Based Learning approach.”
Chinese and English mathematics do not mean using different languages to learn the same content twice. The content taught in Chinese mathematics can be covered again in the English math project activities, which can not only enrich the understanding of the subject knowledge, but also sort out the process of learning. In addition to enriching vocabulary, improving language and laying a good foundation, the learning goal of English mathematics in Elementary School lays more emphasis on the application of knowledge, so the learning methods and processes are particularly important. Scholars need to understand the connections between mathematics and different subjects through inquiry and project-based learning, and explore the meaning of mathematics in real life.
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隨著年級的提升，升入G5后英文數(shù)學(xué)開始分層，一般會同時兼顧學(xué)者們的英語成績和數(shù)學(xué)成績，依據(jù)測試進(jìn)行劃分。分層后的班級中，同樣會參照低年級靈活學(xué)習(xí)小組的劃分方式，依據(jù)教學(xué)需求進(jìn)行分組。
高階的學(xué)者，知識和技能掌握程度較好，老師一方面會加強(qiáng)基礎(chǔ)測試，檢查學(xué)者們的掌握情況，同時會設(shè)計更多的內(nèi)容，采用探究式的方法，引導(dǎo)學(xué)者深入思考，更靈活更全面地掌握所學(xué)知識。
中階的學(xué)者則將自我探究與老師指導(dǎo)相結(jié)合，找準(zhǔn)問題，克服語言障礙，提升數(shù)學(xué)能力，補(bǔ)齊短板。
低階的學(xué)者需要更多的指導(dǎo)，Damon老師依據(jù)學(xué)情，從夯實基礎(chǔ)開始，借助豐富多元的項目活動開展教學(xué)。一方面是涵蓋基礎(chǔ)計算能力等方面的練習(xí)。一方面運用不同形式的單詞聽寫幫助學(xué)者鞏固詞匯的學(xué)習(xí)，引導(dǎo)學(xué)者規(guī)范英語數(shù)學(xué)的表達(dá)。同時也會和學(xué)者一起進(jìn)行閱讀訓(xùn)練，閱讀的主題都與學(xué)科知識相關(guān)，幫助學(xué)者更好地理解、表達(dá)、應(yīng)用。Damon老師還會借助各種迷你項目，替代枯燥的習(xí)題，拆分解題步驟，引導(dǎo)學(xué)者掌握數(shù)學(xué)的學(xué)習(xí)方法和邏輯思維。
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With the grades going up, English mathematics began to be stratified since G5. Generally, both English and mathematics scores of scholars were taken into account, and the grades were divided according to the tests results. In the stratified classes, the flexible learning groups will also be divided according to the teaching needs, like that of lower grades.
Advanced scholars have a better grasp of knowledge and skills. Teachers will strengthen basic tests to check the mastery of these scholars. At the same time, they will design more contents and use inquisitorial methods to guide these scholars to think deeper and master the knowledge more flexibly and comprehensively.
Middle-level scholars will combine self-inquiry with teacher guidance to identify problems, overcome language barriers, improve math abilities and fill in the blanks.
Scholars with relatively lower-levels might need more guidance. Teacher Damon will start with a solid foundation and use a variety of program activities to teach based on the learning needs. There are exercises that cover things like basic numeracy. On the other side, different forms of dictation will be used to help scholars to consolidate vocabulary learning and guide scholars to build the expression of English mathematics. At the same time, Damon will also conduct reading training with scholars. The topics of reading are related to subject knowledge to help scholars better understand, express and apply them. Damon also uses mini projects to replace boring exercises, break down the steps, and guide scholars to learn math and logical thinking.
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無論處于哪個層級，學(xué)者們都能在狄邦華曜的課堂上找到提升的途徑與空間。老師們會千方百計地引發(fā)學(xué)者興趣，設(shè)置階梯性學(xué)習(xí)目標(biāo)，幫助學(xué)者建立自信，挑戰(zhàn)自我，依據(jù)每個學(xué)者的學(xué)習(xí)情況，不斷細(xì)分教學(xué)內(nèi)容一步步引導(dǎo)學(xué)者提升。
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Scholars at all levels can find paths and room for improvement in classes of Dipont HC. Teachers will try every means to increase scholars’ engagement, set stepped learning goals, help scholars build confidence and challenge themselves, and constantly subdivide contents to guide scholars to improve step by step according to each scholar"s learning progress.
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