幼教权威解读：数学启蒙，始于数字却不止于数字
为什么许多孩子对数学有畏难情绪？
学好数学，孩子天分＞后天培养？
数学=算数+解公式=枯燥乏味？
是时候打破这些刻板印象
来听听AISL哈罗幼教专家分享
如何通过生动有趣的方式，引导孩子
探索“数字王国”，在日常生活中培养
数学思维与实践应用能力
让孩子不怕数学，探索数学，善用数学
为未来学业奠定先机
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“数学”无处不在，它的概念、元素和应用，存在于我们的日常生活、周遭环境，以及我们的思维和行动中。
清晨，我们从长方形的床上醒来；拉开窗帘，看到形状各异的窗户；到卫生间刷牙（两分钟），接水与牙膏的量也有讲究；冲一杯咖啡（ 需要多少水/牛奶/糖才能在我们最喜欢的几何花纹杯子里冲出一杯理想的咖啡）或准备早餐（需要在麦片里加多少牛奶才恰到好处）；整理背包去上班或上学（包有点轻，什么东西忘记装了？）。
洗澡时，我们会按顺序清洗，同时记下时间。穿衣时，我们会摸到衬衫或上衣有几颗纽扣（节后有没有感觉衬衫变小了？）。在做每日规划时，我们会预测从早到晚分别要做些什么，并从中找出辨别出熟悉的模式和事件。
Maths is everywhere; in our daily lives, the environment around us, in our thinking and our actions.
From the moment we wake up in our rectangular beds, opening the curtains covering our windows of varying shapes, and heading to the bathroom to clean our teeth (for two minutes) noting how much toothpaste and water we need to complete the job properly, to making our coffee (how much water / milk / sugar do we need to produce our ideal cup in our ideal cup – our favourite because we like the geometric pattern best) or breakfast (how much milk do we add to our cereal to make it just right), and packing our bags for work and school (is the bag feeling lighter – what have we forgotten to pack?).
As we shower, we sequence the order of cleansing, whilst we note the time. As we dress, we feel the number of buttons on a shirt or blouse (does this shirt feel a little smaller after the recent festivities?), and consider the day ahead, predicting the flow of the day and recognising familiar patterns and events.
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我们掌握了时间、日期、月份和年份的概念，知道日历上的哪些事件已经发生，哪些即将发生（别忘记母亲节快到了......）。我们回忆昨日，期盼明天的各种可能性。
在通勤路上，我们会计算距离、轮渡时间、地铁站点和换乘，确认站点并计算还有多远（已走五站，还剩三站）才能在规定时间内到达目的地（准时、提前还是迟到？） 。
在地铁上，我们会看书，并确定距离章节结尾还有多少页，或者全书还剩下多少章节。我们可能会选择解一个数独谜题，或者将最喜欢的杂志翻到第30页，因为那里有我们最喜欢的专题。
在道路上行驶时，我们被形状大小不一、以不同速度行驶的车辆包围，被大量的车牌、路标和出口标识环绕着——所有这些都是数学语言的组合，它们为我们每天的生活和出行指明方向，确保我们在某个时刻到达我们需要到达的地方。
所有这些日常习惯所需技能的显现并非偶然，而是通过学习养成的。
购物时，我们会计算要花多少钱，并考虑放进购物车里的食物能否通过适当分配做成一顿饭。烘焙时，我们会计算度量（有的人通过称量配料，有的人则通过估算）和时间。
烹饪时，我们会尝一尝味道，然后决定添加更多香料、加入另一种香草或减少水量。每次清点冰箱和橱柜里的食材时，我们都会对食材进行分组和比较（六袋意大利面，但只有三罐酱汁，其中一罐我们不还太喜欢，西兰花也不够一顿的量了）。
生活无处不数学。作为成年人，我们早已对生活中的数学习以为常，不太会注意到它。然而，它确实存在。数字、数字运算、形状、度量和时间无时无刻不围绕、影响、指引着我们——无声无息，却蕴藏着巨大的力量。
儿童需要发展扎实、稳固的数学理解能力，这是他们运用技能素养与世界进行互动，并理解周遭环境的重要前提。
生活离不开数学知识，它为交流和理解提供了一种通用语言。在学习熟练掌握数数、测量、理解几何图形、形成时间观念和图形观念所需的单项技能的同时，孩子们还需要知道如何学以致用，将它们与日常生活经验联系起来。
数学学习具有由浅入深递进式发展的特点，随着技能和知识的不断增长，孩子们会对自己充满信心，并能随时运用它们来支持对不同知识和概念的自主探索和演练。
数学发展包括掌握技能、理解概念和获得各领域的事实性知识。它还包括在概念之间建立联系，例如将数字“3”与三个物体联系起来。
儿童还需要发展推理能力，如逻辑思维、预测能力和交流想法的能力。关于儿童如何学习数学的大量研究表明，数学学习是非常复杂的。数学素养的发展速度取决于具体的数学知识和其他技能，包括:
执行功能 ——例如工作记忆，即在大脑中暂时储存信息并对其进行加工的能力
建立牢固的早期数学概念需要时间。即使孩子看似可以成功地参与数学活动，他们也不一定完全掌握基本概念。例如，他们也许可以正确地说出一个数列，但却不理解其中数字的含义。在某种情境下，他们看似掌握了某个概念，但换到另一个情境下，却无法表现出对该知识点的掌握。
*改编自：
早期数学启蒙：支持幼儿数学素养的方法和实践
英国教育捐赠基金会
https://educationendowmentfoundation.org.uk/
因此，幼儿教育工作者（包括家长）的职责是为幼儿学习者提供一个良好的学习环境和条件，让孩子和大人们进行有效的互动，最大限度地增加数学学习的机会，从而确保通过引导、启发和强化，所有孩子都能自信地掌握多样化的、必要且作用巨大的数学语言。
We know the time, the date, the month and year. We know what calendar events have happened and which are upcoming (don’t forget that Mother’s Day is approaching…). We appreciate what happened yesterday and consider what might happen tomorrow.
As we travel to work, we calculate distance, ferry timings, MTR stops and changes, acknowledging the stations and calculating how far we have to travel in the time we have (five stations done, three to go), in order to get where we need to be by a certain time (will you be on time, be early or be late?).
Photo credit: MTR Corporation Limited
On the MTR, we read our book and determine how many pages until the end of the chapter, or how many chapters are left in the book. We may complete a sudoku puzzle or turn to page 30 of our favourite magazine because that is where our much-loved feature is.
On roads, we are surrounded by vehicles of different shapes and sizes, moving at different speeds with a vast quantity of licence plates, road signs, exits around us – all a combination of mathematical language which inform our lives and the direction we take each day to get where we need to be at a particular moment in time.
The skills required to undertake all these daily habits did not happen by accident. They were learned.
When we shop, we calculate money. With food items in our shopping cart, we consider whether they can be shared appropriately to make a meal. When we bake, we calculate measure (some of us by forensic weighing of ingredients, others by estimation) and time.
When we cook, we taste and make decisions on adding more spice, another herb or reducing liquid. Each time we assess what we have in the fridge and the cupboards, we are grouping and comparing what we have (six bags of pasta but only three jars of sauce, and one of these we don’t really like, and not enough broccoli to make one meal).
Maths is everywhere and as adults it becomes so implicit and discrete within our lives that we don’t necessarily acknowledge it. It is there, nonetheless. Number, number operations, shape, measures and time continually surround us, influence us and direct us – silently, yet with great power.
Children need to develop a secure and well-established mathematical understanding as a vital prerequisite for engaging with and comprehending technical aspects of the world. The need for mathematical knowledge surrounds us and enables us to communicate and understand in a common language.
The discrete technical skills required for developing proficiency in counting, measuring, understanding geometric shape, a sense of time and patterns need to be learned alongside, and within a context of, how these can be utilised and relate to everyday life experiences.
The sequential and developmental nature of mathematical learning will enable children to gain confidence in their increasing skills and knowledge and be able to readily apply this to support their own exploration and rehearsal of different knowledges and concepts.
Mathematical development involves acquiring skills, understanding concepts, and gaining factual knowledge across a range of areas. It also involves forming connections between concepts, for example connecting the numeral ‘3’ with three objects.
Children also need to develop reasoning skills such as logical thinking and the ability to predict and communicate their ideas. A large amount of research on how children learn maths has revealed how complex it is. The rate of mathematical development relies on specific mathematical knowledge and other skills, including:
Executive functions – such as working memory, which is the ability to hold information in your mind and manipulate it
Language and motor skills
Children’s prior mathematical experiences
Children’s interests, enjoyment, and attitudes towards maths
Developing a secure grasp of early mathematical ideas takes time. Even if a child appears to be engaging successfully in mathematical activities, they may not have a full grasp of the underlying concepts. For example, they might be able to say the count sequence correctly but not understand the meaning of numbers within it. Children may also appear to have grasped an idea in one context but then not show that knowledge in a different context.
*Adapted from:
Early Mathematics: Approaches and practices to support mathematics in the early years
Education Endowment Foundation
https://educationendowmentfoundation.org.uk/
Therefore, the role of the early years educator (parents included) is to offer young learners an environment and provision that, alongside impactful adult interactions, maximise the opportunities for mathematical learning thereby ensuring that through invitations, provocations and enhancements, all children become confidently conversant in the vibrant, essential and powerful language of mathematics.
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