你真的了解数学吗？| 亨利的开箱问题引发的数学深思

今天小编搜罗了你真的了解数学吗？| 亨利的开箱问题引发的数学深思希望给择校的家长们提供参考。

数学到底是什么?

What's Mathematics?

数学不只是简单的计算，得出结果。数学其实是我们日常生活中用来解决问题所使用的工具。

数学教育不仅可以提高学生们的分析思维能力，也可以培养他们的批判性思维和创造性思维能力。在南通诺德安达的数学课程中，我们的目标不仅是向孩子们传授抽象的数学概念，同时也旨在提高学生们的思维能力。

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Mathematics is not just making operations and getting some results. It is a tool that we use in our daily lives to solve issues.

Mathematics education should enhance students' analytical thinking skills, critical thinking skills, and creative thinking skills.

In Mathematics lessons at Nord Anglia School Nantong, our aim is not only to teach students abstract mathematical concepts but also to improve students' thinking skills.

关于数学教育

About Mathematics Education

数学是一门语言。仅使用数学符号，就可以将如何解决问题的思想，假设和方法传递给全世界，并且数学无国界，不会受限于语种。所以，在这方面，数学也许是世界上使用最广泛的通用语言。

因此仅仅教学生们解决问题的办法是远远不够的。与此同时，我们还需要确保孩子们可以正确有效地使用数学语言。

和其他学科一样，数学也是以辩论，讨论和思想交流为基础的。因此，我们应该在21世纪的数学教育中创造出一个可供学生讨论其思想的自由环境，让不同的思想在这里碰撞，摩擦，产生火花。我认为不管是对是错，学生们的每一个想法都很重要。在这些过程中，学生们必须学会辨别且证明数学假设的对错。

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Mathematics is a language. Using only Mathematical notations, you can transfer your thoughts, hypotheses, and methods you use to solve problems to the whole world, regardless of your native language. In this regard, Mathematics is perhaps the most widely used common language in the world.

So it is not enough to teach students only problem-solving methods. At the same time, we need to ensure that students use the language of Mathematics effectively and correctly.

Like any discipline, Mathematics feeds on debates, discussions and exchange of ideas. Therefore, free environments where students can discuss their ideas should be created in 21st-century mathematics education. Every idea counts, regardless of whether it's right or wrong. Students must learn to prove a Mathematical hypothesis is true or wrong.

南通诺德安达的数学课堂

Mathematics Class in NAS Nantong

经典数学优化问题--开箱问题

The oldest optimization questions---Open Box

当然，没有任何一种方法可用于实现所有这些目标。但是，与其专注于发展经典的问题解决方法和代数技能，不如将“开放式”问题引向学生，并使学生能够集体讨论和发展解决方法，从而使学生能够同时使用多种技能。

开箱问题是最古老的优化问题之一，这个问题首先在1903年亨利·杜德尼（Henry Dudeney）的拼图专栏中在“每周一次派遣”中发现，并在1908年再次出现，该问题在卡塞尔杂志（Cassell's Magazine）的拼图专栏中被重新定义且表述了。之后，在1911年Granville和Smith发表的一篇文章中可以也看到它的身影。

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Of course, there is no single method that can be applied to achieve all these goals. However, instead of focusing on developing classical problem solving and algebraic skills, leading 'open-ended' questions to students and enabling students to discuss and develop solution methods as a group enables students to use many skills at the same time.

The Open Box problem is one of the oldest optimization questions. This problem was first seen in the 1903 Henry Dudeney's puzzle column in the Weekly Dispatch and again in 1908, it was rephrased for his puzzle column in Cassell's Magazine. After that, it was seen in an article published in 1911 by Granville and Smith.

开箱问题有许多种版本，我们使用了其中一个版本问题采访我们南通诺德安达学校10年级的同学，那就是“有一个长方形的硬纸板，其周长为80厘米。你从硬纸板的每个角切了2厘米的正方形，制成了一个敞开的盒子。要得到最大体积的敞开的盒子，硬纸板的尺寸是多少？”

学生们分组讨论问题，并使用各种方法想要解决该问题。他们试图获得一个最能表达问题解决方案的通用公式，并证明了该公式。他们将结果汇编为科学报告，在整个过程中，学生已经使用和发展了他们的沟通，批判性思维和创造性思维技能。

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There are many versions of this problem. One of the versions was asked to Nord Anglia School Nantong Grade 10 students. "You have rectangular cardboard of which perimeter is 80 cm. You cut 2 cm squares from each corner of the cardboard to make an open box. What can be the dimensions of the cardboard to get an open box with the highest volume?"

Students worked as a group, discussed the question, and used various methods to solve this question. They tried to obtain a general formula that best expressed the solution of the problem and proved this formula. They compiled their results as a scientific report. Throughout this entire process, students have used and developed their communication, critical thinking and creative thinking skills.

课后一练

A OPEN BOX question

你解决了这个问题吗？如果已经得到了这个问题的结论，那么请考虑以下问题。如果要将足球包装作为圣诞节礼物，并且打算将这个足球放入盒子中，则用来制造盒子的纸板的最小尺寸是多少？

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Did you solve the question? If so, think about the following one. If you want to pack a soccer ball as a Christmas gift and you are going to put this soccer ball in a box, what is the least dimensions of the cardboard you will use to make the box?

---本文由IB DP协调员兼高中数学老师 Ms. Müge Özgönül提供

Written by Ms. Müge Özgönü who is IBDP Coordinator & Secondary Mathematics Teacher