哈罗教育说 | 如何激发孩子的数学热情？-国际教育网

哈罗教育说 | 如何激发孩子的数学热情？

Harrow哈罗礼德横琴

2023-05-29发布于广东

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作为一门重要的基础学科

数学是高阶理工学科的基础

作为公立教育体系的学术强项

国际化学校的数学学习

一直以来都被诟病为短板

然而事实真的是这样吗？

在2022年的UKMT数学竞赛中

哈罗珠海的学子们总共获得

10个金奖，9个银奖，15个铜奖

如此傲人的成绩究竟是如何达成

哈罗珠海的数学教育又有什么奥秘？

本期哈罗教育说

我们采访了哈罗珠海数学组组长

翻阅了9篇专业研究论文

通过5个要点来告诉家长们

哈罗如何激发孩子们的数学热情

温馨提示：本文所提及教学法为国际化学校常见的数学教育方式，对于公立教育体系的家长的家庭数学教育，亦有充分借鉴意义。

在游戏中发掘数学乐趣

在数学学习中，融入游戏、拼图和实践活动，创造一个积极和愉快的学习环境是非常重要的。事实上，好玩的游戏都有非常显著的数学基础，因此，在学习中加入游戏概念会有神奇的效果。在哈罗，老师们使用丰富多彩的教具，在线数学游戏，或互动应用程序，使数学学习变得趣味横生充满互动，学生也乐于积极地参与到这些数学活动中来。

皮亚杰在他的建构主义理论中强调，学习者通过与环境的互动来主动建构他们的知识。融入实践活动和游戏符合建构主义原则，因为它们鼓励学生自己去探索、操作物体和发现数学概念。

把数学融入到生活化场景中

教育专家们认为，通过日常生活中的案例来学习，能够有效提升孩子们的数学学习。日常场景中的例子，诸如数物体，做饭时测量食材，或购物时计算金钱，都是与数学有关。哈罗珠海的数学课堂上，许多问题都是从日常生活中延伸出来的。这种方法可以帮助孩子们看到数学与生活的相关性，方便他们理解与应用。

根据霍华德-加德纳的多元智能理论，不同的人会有不同的学习和处理信息的方式。通过提供视觉教具、实践活动和现实生活中的数学应用，可以让大多数学生迎合更广泛的智能，包括视觉-空间、逻辑-数学和身体-运动智能。

采用视觉辅助与可触摸的教具

视觉辅助工具，如图表、示意图和几何图形，可以帮助学生们掌握抽象的数学概念。哈罗的老师们倾向于使用数字线、分数条或几何图形等视觉模型来说明数学运算和数理关系，这样也能够促进学生对复杂问题的理解。对于低年级的孩子来说，使用操作材料和具体的表现形式也能使数学更容易被掌握。

具体-代表-抽象（CRA）教学发在西方的数学教育中被广泛使用。该教学法建议学生应该从具体（操作实物）到表象（使用视觉模型），然后再到抽象（使用数字和符号）进行渐进式的学习。使用操作材料和视觉辅助工具符合这一方法，能够帮助学生在进入抽象数学概念的学习之前打下坚实基础。

鼓励解决问题与辩证思维

学生作业，左右滑动查看更多

在哈罗，教师总是通过提出需要逻辑推理和批判性思维的数学挑战来促进解决问题的能力。好的数学老师通常会鼓励学生思考问题，将其分解成更小的部分，并运用不同的策略来寻找解决方案。这种方法可以培养学生的分析能力，增强他们处理数学问题和其他问题的信心。

教育学家希尔佛建议，基于问题的学习方法能够向学生展示现实世界的问题，并鼓励他们通过批判性思维和解决问题来寻找解决方案。通过纳入解决问题的活动，教师可以让学生参与到高阶思维技能中，并促进对数学概念的深入理解。

个性化的教学与支持

珠海哈罗认识到，每个学生都有独特的学习需求和能力。我们的英式个性关怀辅导体系为哈罗学子们提供个性化的关注和支持，根据他们的技能水平制定教学计划。特别是在数学方面，我们的老师为学习速度慢的学生提供支架式辅助，而为学习速度快的学生提供额外的练习或更具挑战性的问题。我们的教师还会通过小组活动或一对一课程，提供额外指导，以解决针对性的问题。

在汤姆林森理论的支持下，差异化教学认识到学生有不同的学习风格、能力和需求。通过提供个性化的教学和支持，教育者承认这些差异，并创造一个学习环境，以满足每个学习者的独特需求。这种方法能够提高参与度，并使学习成果最大化。

教育专家说

Sera He

哈罗珠海数学教研组组长

"有效的数学教学包括有目的的提问，以评估和推进学生的推理和理解。重要的是，教师要提出问题，促使学生解释他们的想法并建立联系。强调建立程序的流畅性，确保学生理解程序背后的概念，并能在不同情况下应用它们。支持富有成效的挑战，以鼓励学生深入研究数学思想和关系。我们最终目的是发展他们的数学思维。”

国际化的数学学习或许与传统方式不太一样

没有那么多公式的背诵和试题的堆砌

但正如著名的统计学家，

哈罗校友罗纳德费舍尔所说

“越是不平凡的方式，越可能产出伟大的结果”

——罗纳德费舍尔

哈罗教育重在培育学习思维与方法

通过精心的课程设计与实践的操作

激发孩子主动学习的动力和热情

参考资料：

Piaget, J. (1973). To Understand Is to Invent: The Future of Education. Grossman Publishers.

Bruner, J. (1990). Acts of Meaning. Harvard University Press.

Gardner, H. (1983). Frames of Mind: The Theory of Multiple Intelligences. Basic Books.

Baroody, A. J. (1993). Concrete Cognitive Instruction: A Review of the Instructional Research Literature on Concrete Manipulatives. Educational Psychology Review, 5(3), 235-277.

Clements, D. H., & Sarama, J. (2007). Effects of a Preschool Mathematics Curriculum: Summative Research on the Building Blocks Project. Journal for Research in Mathematics Education, 38(2), 136-163.

Hmelo-Silver, C. E. (2004). Problem-Based Learning: What and How Do Students Learn? Educational Psychology Review, 16(3), 235-266.

Jonassen, D. H. (1999). Designing Constructivist Learning Environments. In C. M. Reigeluth (Ed.), Instructional-Design Theories and Models: A New Paradigm of Instructional Theory (Vol. II, pp. 215-239). Lawrence Erlbaum Associates.

Tomlinson, C. A. (2001). How to Differentiate Instruction in Mixed-Ability Classrooms. Association for Supervision and Curriculum Development.

Clements, D. H., & Sarama, J. (2008). Experimental Evaluation of the Effects of a Research-Based Preschool Mathematics Curriculum. American Educational Research Journal, 45(2), 443-494.

→滑动查看中文版本→

As an important foundation subject

mathematics is the basis for higher science

and engineering disciplines.

As an academic strength

of the public education system

the study of mathematics in international schools has long been criticized as a shortcoming

But is this really the case?

In the 2022 UKMT Competition

Harrow Zhuhai students won in total

10 gold, 9 silver and 15 bronze medals

How did they achieve such impressive results

What is the secret of Harrow Zhuhai's

mathematics education?

In this issue of

Harrow Educator's Tips

We have interviewed the Head of Math

And went through 9 research

papers to show parents

how Harrow inspires our children

in maths in 5 key points

Reminder: The pedagogical approaches mentioned in this article are common in international schools and can also be useful for parents in the public education system for their home mathematics education.

Make it Fun and Engaging

It is very important to create a positive and enjoyable learning environment by incorporating games, puzzles, and hands-on activities. The best games are all made of math, therefore, in learning it would work magic to add in gaming concepts. At Harrow, teachers use colorful manipulatives, online math games, or interactive apps to make math learning exciting and interactive. Students also participate more actively in these math activities.

In his Constructivist theories, Jean Piaget emphasizes that learners actively construct their knowledge by interacting with their environment. Incorporating hands-on activities and games aligns with constructivist principles, as they encourage students to explore, manipulate objects, and discover mathematical concepts on their own.

Relate Math to Real-life Situations

Experts suggest that one of the better ways to help young learners understand the practical applications of math is through their daily lives. Examples from everyday scenarios, such as counting objects, measuring ingredients while cooking, or calculating money during a shopping trip, are all math related. At Harrow Zhuhai, Math problems are usually extensions from daily lives. This approach helps children see the relevance of math and makes it more relatable.

According to Howard Gardner's theory of multiple intelligences, individuals have different ways of learning and processing information. By providing visual aids, hands-on activities, and real-life applications of math, students can cater to a broader range of intelligences, including visual-spatial, logical-mathematical, and bodily-kinesthetic intelligences.

Provide Visual Aids

and Concrete Representations.

Visual aids, such as charts, diagrams, and graphs, can help young learners grasp abstract mathematical concepts. Harrow teachers tend to use visual models like number lines, fraction bars, or geometric shapes to illustrate mathematical operations and relationships, which could facilitate the understanding of complicated problems. For lower school children, use of manipulatives and concrete representations also make math easier to comprehend.

The Concrete-Representational-Abstract (CRA) Approach is widely used in mathematics education in the west. It suggests that students should progress from concrete (manipulating physical objects) to representational (using visual models) and then to abstract (working with numbers and symbols) stages of learning. Using manipulatives and visual aids aligns with this approach and helps students build a solid foundation before moving to abstract math concepts.

Encourage Problem-Solving

and Critical Thinking

←Students' assignments, swipe for more→

At Harrow, teachers always promote problem-solving skills by presenting math challenges that require logical reasoning and critical thinking. Good math teachers normally encourage students to think through problems, break them down into smaller parts, and apply different strategies to find solutions. This approach fosters analytical skills and boosts confidence in tackling math problems and beyond.

Hmelo-Silver, C. E. suggested that a problem-based learning approach focuses on presenting students with real-world problems and encouraging them to find solutions through critical thinking and problem-solving. By incorporating problem-solving activities, teachers may engage students in higher-order thinking skills and promote a deeper understanding of mathematical concepts.

Individualized Instruction and Support

Harrow Zhuhai recognizes that each student has unique learning needs and abilities. Our Close Personal Tutoring system provides personalized attention and support to young learners by tailoring instruction to their skill level. Particularly with Math, our teachers provide scaffolding to slow learners, while offering additional practice or more challenging problems for fast learners. Math team also aim to organize small-group activities or one-on-one sessions to address individual difficulties and provide extra guidance.

As supported by Tomlinson’s theories, differentiated instruction recognizes that students have diverse learning styles, abilities, and needs. By providing individualized instruction and support, you acknowledge these differences and create a learning environment that meets the unique needs of each learner. This approach enhances engagement and maximizes learning outcomes.

Comments from Experts

Sera He

Head of Mathematics

at Harrow Zhuhai

“Effective mathematics teaching involves purposeful questioning to assess and advance students' reasoning and understanding. It is important for teachers to ask questions that prompt students to explain their thinking and make connections. Building procedural fluency is emphasized, ensuring that students understand the concepts behind procedures and can apply them in different situations. Supporting productive struggle encourages students to delve deeper into mathematical ideas and relationships. Our ultimate aim is to develop their mathematical mind.”

The international approach of Learning of math may be quite different from the conventional approaches

Not so much memorization of formulas and stacking of test questions

But as the famous statistician and Harrow alumnus Ronald Fisher says

"The greater the departure from the normal, the more likely a significant result becomes."

——Ronald Fisher

Harrow Education focuses on developing a learning mindset and approach

Through carefully designed curriculum and hands-on practice

We inspire and motivate children for active learning

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