本文是数学专业的留学生作业范例，题目是“Mathematical Learning in the Early Years(早期的数学学习)”，这是一个众所周知的事实，即儿童生命的早期对于他们的情感和社会发展，他们的总体健康以及智力、情感和身体的成长都非常重要。几乎所有的孩子都以不同的速度发育，他们在三到五岁的时候就开始学习了。家庭环境对儿童早期的发展非常重要。大多数人认为这是一个孩子准备好和开放的学习经验和高质量的照顾的时候。政府已经制定了一项早期政策，特别侧重于为儿童，尤其是非常年幼的儿童提供全面的服务。
Introduction介绍
This is a well known fact that the early years of a child’s life are very important in terms of their emotional and social development, their general well being and their intellectual, emotional and physical growth. Almost all the children develop at different paces and what they learn takes place in the first three to five years of life. The environment of home is very important in the development of a child in the early childhood. Most of the people think that this is a time when children are most ready and open to learning experiences and a high quality care. The government has developed a policy for the early years that especially focuses on providing a comprehensive range of services for children, specially the very young ones. The policy involves the integration of early years with childcare provision. This policy enables children to build on throughout their entire life and it provides a positive foundation for children’s early development. The high quality care provision in the early years also provides parents with peace of mind and allows them to balance work and family life. This paper will outline the most important elements in the education, training and development of a child the early years of his life. Beginning with a general overview of the early years sector role modeling, pedagogy’s of play and inclusive practice will be examined as elements that are vital to the education, training and development of those wishing to work in early years education. The Labour Government which was formed in 1996 used as its pre election catch-phrase the words ‘education, education, education. Since that time things have improved in some areas. In 1996 the labour government policy has been promoting a series of educational reforms. As a result in 1998 the National Childcare Strategy was launched. Four year old children, whose parents require it, the course is very vital in the early years of education. There has also been a growth in the proportion of two year old children in part-time early years education. These places are available in centers of primary schools in a number of settings through pre-school to authority nurseries settings like the one offered by the Pre-School Learning Alliance. In 1998 Early Years Development set up in each local authority to promote the expansion of early years education.
Numeracy计算能力
Literacy is to language as numeracy is to mathematics. They both represent a different means of communication which is very important to our civilized life. Both literacy and numeracy are on the decline in the United States of America. There are a lot of differences in form and structure; both in natural language and mathematical language are very powerful tools for representation, description and communication. The use of numeracy is very important for a nation expecting to compete in a global economy.
识字之于语言，犹如算术之于数学。他们都代表了一种不同的交流方式，这对我们的文明生活非常重要。在美利坚合众国，读写和计算能力都在下降。在形式和结构上有很多不同;自然语言和数学语言都是非常强大的表示、描述和交流工具。对于一个希望在全球经济中竞争的国家来说，计算能力的使用是非常重要的。
On the other hand the natural language is ambiguous, redundant and concrete and the mathematical language is abstract, precise and concise, precise, and abstract. Full expression of vision and thoughts and visions requires the richness of both mathematical language and the natural. Yin and yang, literacy and numeracy are the example of human communication. Mathematics very basic and core subject in child education. All over the world the I Q tests include an assessment based on the system of numeracy and therefore it is very important component of our lives.
Mathematical Learning in the Early Years早期的数学学习
Learning about numbers in early years of our life is very important in developing positive attitudes about mathematics at an early age. Special methods will assist children to develop early numeracy skills. These methods will need to include the use of engaging and motivating materials that children can manipulate. Young children need to experience a lot of doing before written numerals will make sense.
在我们生命的早期学习数字对于从小培养对数学的积极态度是非常重要的。特殊的方法将帮助孩子们发展早期的计算技能。这些方法将需要包括使用儿童可以操纵的引人入胜和激励的材料。年幼的孩子需要经历很多，才能理解书写的数字。
As early as 1 year of age, many children will start saying the words ‘one’, ‘two’ and ‘three’, etc. But they do understand that the number refers a set of items or just an item At this stage, children do not have number correspondence.
Concepts That Help Young Children帮助幼儿的概念
Children should be engaged in a variety of measurement concepts which is a great beginning. Children enjoy telling us that they are elder than their brother or sister or taller than the cupboard. Young children will also develop thinking that they have more in their cup because the fact that their cup is taller. We all should support this language because it needs to be promoted and children need parental guidance to help with the misconceptions of these concepts through experimentation.
孩子应该参与各种测量概念，这是一个很好的开始。孩子们喜欢告诉我们他们比他们的兄弟姐妹大，或者比橱柜高。年幼的孩子也会认为他们的杯子里有更多的东西，因为他们的杯子更高。我们都应该支持这种语言，因为它需要推广，儿童需要父母的指导，通过实验来帮助消除对这些概念的误解。
You can start from a bathtub which is a great starting point, using different types of plastic cups and containers. At this age, perception will guide the child and they do not have any other strategies to guide them in determining which is heavier or lighter or has more or less etc. through playing techniques a day care provider or a parent can provide great learning experiences to assist young children’s misconceptions.
The Impact of Mathematics on our daily lives数学对我们日常生活的影响
If someone don’t know about how to change and understand completely then it means he or she is not fit to learn anything. Whatever profession you choose in our lives we have to learn mathematics because we all need it to excel in our daily lives. You must have it to get a high paying job. For example cooking, you have to measure different ingredients and pour them in correctly. It requires you to measure lengths and draw them. Pressing the numbers on the cute and tiny toy that our mother had bought for us through good experience, if you are going on shopping or just doing math problems you have to use mathematics everywhere you go, to make sure that you are using the right measuring unit. When we look around ourselves we see that Math is everywhere in our daily lives. If you don’t then you might mess up your project that you are cooking. Like dessert, using Math does a body good. Math is all around us and that we do need it in our daily lives.
如果一个人不知道如何改变和完全理解，那么这意味着他或她不适合学习任何东西。无论你在生活中选择什么职业，我们都必须学习数学，因为我们都需要它在日常生活中出类拔萃。你必须拥有它才能得到一份高薪的工作。例如烹饪，你必须测量不同的食材，并正确地倒进去。它需要你测量长度并画出来。按下妈妈给我们买的可爱的小玩具上的数字，如果你去购物或做数学题，你必须在任何地方使用数学，以确保你使用的是正确的计量单位。当我们环顾四周，我们发现数学在我们的日常生活中无处不在。如果你不这样做，你可能会搞砸你正在做的项目。就像甜点一样，使用数学对身体有好处。数学无处不在，我们在日常生活中确实需要它。
Social and Cultural Factors Affecting Child’s Learning影响儿童学习的社会和文化因素
All the children born and live not only in a society but also in a specific part of it, and are therefore, influenced by particular subcultures of race, religion, and class, as well as by specific groups such as friends and family. Almost all the children during their lifetime, they continually encounter changing or new things and conditions, both social and personal , and must learn to handle all the changes. The most important socialization occurs during infancy and childhood, when the foundations of later personality are laid. Whether a child shy or ongoing, average or intellectually advanced, or depends on many unique influences effects are difficult to predict at the child’s birth.
所有的儿童不仅出生和生活在一个社会中，而且生活在这个社会的特定部分，因此，受到种族、宗教和阶级等特定亚文化的影响，也受到诸如朋友和家庭等特定群体的影响。几乎所有的孩子在他们的一生中，他们不断地遇到变化或新的事物和条件，无论是社会的还是个人的，并且必须学会处理所有的变化。最重要的社会化发生在婴儿期和儿童期，这是后来人格形成的基础。一个孩子是害羞还是发育良好，是平均水平还是智力先进，还是取决于许多独特的影响因素，在孩子出生时很难预测。
There are many different factors that influence child development. It includes every aspect of cognitive, physical, emotional and personality development. Peer groups or family members, the community and the school environment, influence deeply on how the child will socialize, think and become self aware. In many parts of the world the impact of socio-cultural factors on the personality development of adolescents.
After studying major socio-cultural factors that affect the children personality we came to know the factors which are identified as important determinants of child personality are parents education, their economic conditions , family structure and family size, peer group, children’s socialization level, school environment, parent’s involvement level in extra curricular activities and children’s day to day activities and government policies. There are many recommendations that are proposed which focus on parents reasonability towards child education, governments role in providing equal quality education to all classes of children compared emphasizing on improving parent, teacher and children relationships. This study also highlighted and suggested areas of further research. Subject having potential to be studied individually. Moreover, the role of media and other new emerging sources of mass communication should also be investigated. More studies on children’s psychology gives understanding to better personality development of children. Nurturing children in the best way is the key to attain broader objective of building an educated, well behaved society and nation and this objective can be achieved through conducting research on children psychology.
The Use of Calculators in Schools
In our country, students use calculators for their schoolwork. But many people oppose this idea because they believe that the child’s basic arithmetic skills would suffer badly. This remains they major disagreement about the importance of the ability to perform calculations. Some curricula restricting calculator use until a certain level of proficiency has been obtained, on the other hand some experts concentrate more on teaching problem-solving and estimation techniques. According to this research suggests that inadequate guidance in the use of calculating tools can restrict the kind of mathematical thinking that students are engage in. One theory says that calculator use can even cause core mathematical skills to atrophy, or that such use can prevent understanding of advanced algebraic concepts.
There are some other concerns also, for instance, a pupil can use the calculator in the wrong manner but he thinks that the answer is correct because that was the result given by a calculator. Teachers try to counter this by encouraging all the students to learn to make an estimate of the result manually and ensuring it roughly, after that they can agree with the calculator’s result.
Rote Learning死记硬背
Rote learning is the way of learning in a very short time; for example, when learning the Arabic alphabet or lists of words. In the same manner when learning the conjugation of irregular verbs, the morphology is often too subtle to be learned explicitly in a short time. However, as in the alphabet example, learning where the alphabet came from may help one to grasp the concept of it and therefore memorize it.
死记硬背是在很短时间内学习的方法;例如，在学习阿拉伯字母或单词列表时。同样的道理，在学习不规则动词的变位时，动词的形态往往过于微妙，短时间内无法明确地掌握。然而，在字母表的例子中，学习字母表的来源可以帮助一个人掌握它的概念，从而记住它。
Rote Learning and Mathematics
Teaching mathematics by rote learning method is an ineffective and outdated way of teaching. Rote learning completely relies on learners remembering and reciting lists of information. The thing which is not taught in rote learning is the full rounded understanding of the subject. That is the reason why you should never use rote for learning mathematics. If you are unfamiliar with the term rote learning it is embodied in the chanting’ of facts that used to occur in classrooms: 13=3. 25=5. 37=7 and so on. Some times we see that the children these facts smoothly and perfectly. But the fact is that if you took the numbers out of order or changed them around it became clear that the understanding of what these numbers actually mean has not been learned. For instance, if a child had just learnt their three times table they would know that 94=28 but if asked what 39= they would often say they had not done their 9 times table yet. This shows that the words had been learned but understanding had not been achieved.
That is the main reason that children should never go for rote learning. If your children’s teacher or school is teaching in this way you should question it. It is not good for children’s leaning and will not inspire them to want to learn more. The ideal teaching session should leave learners wanting to know more, inspired and interested. Rote learning is more likely to lead to boredom frustration and inadequate knowledge of the subject.
Contextual and Categorical Thinking in Young Children
The circular thinking in children facilitates educational choices and supports collaboration. But it makes the disability categories difficult to understand especially when taken out of context. Today we know that the disability categories are mainly the products of social process. Some times being identified as belonging to a category and thus receiving additional resources which can also mean discrimination.
儿童的循环思维促进了教育选择，并支持合作。但这使得残疾类别难以理解，尤其是在断章取义的情况下。今天，我们知道，残疾类别主要是社会进程的产物。有时被确定为属于某一类别，从而获得额外资源，这也可能意味着歧视。
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