JEAN PIAGET IS A SWISS PSYCHOLOGIST who began to study intellectual development (Dembo, 1994). His Cognitive Theory is influential in both education and psychology fields. He proposed that the thinking process will develop through each of the stages until a child can think logically. Understanding cognitive development helps us arrange appropriate lessons and learning environments. An instructor should assess a child’s current level of maturity before beginning the instructional design process. The following are four of Piaget's developmental stages:

皮亚杰是一位瑞士心理学家,他开始研究智力发展(Dembo,1994) 。他的认知理论既在教育领域又在心理学理论有影响。他提出思维过程是通过不同阶段来发展的，直到儿童能够进行逻辑思考。理解认知发展帮助我们适当地安排课程和学习环境。一位教育者在开始教学设计过程前应该评估儿童当前成熟的水平。下面是皮亚杰思维发展的四个阶段。

Even though Piaget was opposed to applying age norms to the stages, most researchers consider approximately the first two years of life to be the Sensorimotor Stage (McCormick, 1997). Infants mainly make use of senses and motor capabilities to experience the environment. For instance, if infants cannot see or touch an object, they stop trying to find it. Once infants develop the capability to recognize that a hidden object still continues to exist, they start searching for it.
The characteristic limitation of this stage is ‘thinking only by doing’. The Sensorimotor infant gains physical knowledge.

感知运动阶段（出生-2岁）

即使皮亚杰反对划分年龄阶段的标准，大多数研究者大概把生命头两年考虑为感知运动阶段（McCormick,1997）。婴儿主要运用感官和运动能力来感知环境。例如，如果婴儿不能看到或触摸到一个物体，他们就停止尝试着找到它。一旦婴儿发展这种能力——认识到一个隐藏的物体仍继续存在，他们会重新开始寻找它。

The second stage in Piaget’s theory of development coincides the preschool years. Children start to use symbols such as language to represent objects. For instance, the child understands the word “apple” although a real apple is not seen. However, the Preoperational child still learns from concrete evidence while adults can learn in abstract way. The Preoperational child is also unaware of another person’s perspective. They exhibit egocentric thought and language.

Here are some limitations of Preoperational thought. To begin with, the Preoperational child lacks the concept of conservation. As shown in Image 1, a child is presented with two rows of apples that contain the same number of apples. While one row is lengthened without any change in the number of apples, the Preoperational child states that the rows are not equivalent. The appearance of the objects gives the wrong impression about them. Children’s decisions are dominated by their perceptions.

Image 1: The Preoperational child lacks the concept of number conservation.

Conservation does not happen simultaneously in all subject areas. Children can understand conservation of numbers around age 5-6, and understand conservation of substance, or mass around age 7-8.
Additionally, the Preoperational child is likely to center on only one dimension of an event and ignore other important details. Also, children concentrate more on the static features of an event than on the transformations from one state to another.
Last, children in the Preoperational period at times will see some relationships between particular cases while in actuality there is none. For instance, a child might say, “If an apple is red, then a green fruit is not an apple.”

前运算阶段（2-7岁）

    皮亚杰认知发展的第二阶段与学龄前一致。儿童开始使用符号如语言来表示物体。例如，尽管在看不到真实的苹果，儿童也能理解苹果这个单词 。可是，前运算的儿童仍需要依靠具体事物来学习，而成人能够用抽象的方式来学习。处在前运算阶段的儿童还不能意识或察觉到别人的观点，他们展示的是以自我为中心的思维和语言。

    下面是前运算阶段思维的局限。首先，前运算阶段的儿童缺乏守恒的概念。如图1所示，向一个儿童呈现两行苹果，每行含有相同数量的苹果。当不改变苹果数量而加长一行时，前运算阶段的儿童说两行不相等。事物的外观给出关于它们的错误印象。儿童的判断受他们的看法控制。

图1:前运算阶段儿童缺乏数量守恒的概念

     守恒不同时发生在所有主题领域。儿童能够理解数量的守恒大约在5-6岁,理解物体的守恒，或群体的大约在7-8岁。

       其次,前运算阶段的儿童可能以一个事件的一方面为中心而忽视其它重要的细节.同样,儿童更多的集中在一个事件的静态特征而忽视事件从一种状态转换到另一种状态的特征。

       最后，在前运算阶段的儿童经常看到特别事例的一些关系，而事实上有些并不存在。例如，一位儿童可能说，如果苹果是红颜色，那么绿色的水果就不是苹果

The next stage generally represents the elementary grade years. The concrete operational child begins to think logically. Operations are associated with personal experience. Operations are in concrete situation, but not in abstract manipulation.

Image 2: The concrete operational is capable of reversible thought only if they operate physical objects.

Concrete operations allow children to classify several classes into a bigger group or to combine a number of classes in any order. Although objects are moved or reordered, no change takes place.

具体运算阶段(7-11岁)

下一阶段一般表示小学基础阶段。具体运算阶段的儿童开始逻辑思维。操作与个人的经历有关。操作发生在具体情境下，但不能进行抽象处理。

图2：具体运算阶段能胜任逆向思维，只要他们操作物理对象

具体操作允许儿童将几类归类进更大的群组里或以任意顺序组合一些类。不管对象被移动或重新排序，没有变化发生。

After roughly 11 years old, students have the ability to consider many possibilities for a given condition. They are able to deal with propositions that explain concrete facts. They have the ability to use planning to think ahead.
Most importantly, students at Piaget’s final stage of cognitive development increase their ability to think abstractly. They can solve complex and hypothetical problems involving abstract operations.
Formal operational thinkers can recognize and identify a problem. They can state several alternative hypotheses, execute procedures to collect information about the problems to be studied, and test the hypotheses.

形式运算阶段（11岁及以后）

大概11岁后，学生具有在给定条件下考虑多种可能性的能力。他们能够处理命题，这些命题用来解释具体事实。他们具有提前计划的能力。

最重要的是，处于皮亚杰认知发展阶段的学生增加了他们抽象思考的能力。他们能解决复杂的和假设性的问题，而这些问题涉及到抽象操作。

形式运算阶段的思考者能认识和识别一个问题。他们能陈述几个可替代的假设、执行过程来收集信息，这些信息是关于要研究的问题的。并且验证假设。

Shu-wan Lin