本文论述了数学抽象的特点，探讨了如何培养数学抽象能力的问题。
This paper discusses the characteristics of mathematical abstraction, and considers how to train the ability of mathematical abstraction in mathematics teaching.
韩礼德经研究发现儿童语言的告知功能是在两岁以后出现的，它标志着抽象能力的形成，域重合开始出现。
Halliday discovered that children's language informing function occur at the age of two, symbolizing the formation of their abstraction ability, that means the occurrence of domain conflation.
由于我们能将对象看成是实体在计算机中的表示，因此面向对象的方法可让我们将注意力集中在这些实体上并构造那些具有相同抽象能力的计算实体。
Because we can regard objects as entities' representation for computer, we can pay our attention to these entities and construct some computable entities that are as abstract as these entities.
没有什么比传达抽象想法的能力更能定义人类，无论这些想法是有关宇宙、心灵、爱情、梦想，还是点一杯饮料。
Nothing defines humans so much as our ability to communicate abstract thoughts, whether about the universe, the mind, love, dreams, or ordering a drink.
长期以来，舍伦贝格一直质疑科学研究所支持的这一说法：音乐教育提高儿童的抽象推理、数学或语言能力。
Schellenberg had long been skeptical of the science supporting claims that music education enhances children's abstract reasoning, math, or language skills.
他断言，在理解冗长且完全抽象的一系列观点方面，他的能力非常有限，因此他深信自己在数学上永远不会成功。
He asserted that his power to follow a long and purely abstract train of thought was very limited, for which reason he felt certain that he never could have succeeded with mathematics.
研究表明，学龄前儿童具有抽象思维的能力。
The research shows that preschool children are capable of thinking in abstract terms.
最重要的一点是，智力是通过你解决复杂问题的能力来衡量的；一定的读写和计算能力；能快速解出抽象方程。
At the top of the list is the notion that intelligence is measured by your ability to solve complex problems; to read, write and compute at certain levels; and to resolve abstract equations quickly.
能力件从另一个抽象层次来看待这些问题。它们能够看到组织的稳定、组件部分，无需操心它们的工作方式。
Capabilities bring another level of abstraction to the table; they allow to look at the stable, component parts of the organization without worrying about how they work.
尤其是在液化智力(即解决新问题和抽象思维的能力)测试中，他们的表现有大幅度提升。
Specifically, they improved their performance on tests of so-called fluid intelligence, the ability to solve new problems and reason abstractly.
对于应用程序架构师来说，另一个重要技能是，具有为特定的需求(删除细节，并将其映射为更普通的问题类别)创建抽象的能力。
Another critical skill for application architects is the ability to create abstractions around the particular requirements that remove specifics and map to a more generic class of problems.
我们是应该信任抽象理论推理的能力呢，还是应该依赖更加直接的情感反应？
Should we be putting our faith in our capacity for abstract theoretical reasoning, or should we be relying on our more immediate emotional responses?
而是使用相同的设备能力抽象来推断出应该如何处理某个视图。
Rather, they use the same device capabilities abstraction to infer how a particular view should be rendered.
定义接口的能力意味着访问者抽象于操作的具体实施操作以外。
The ability to define an interface means that the caller is abstracted away from the implementation of the operations.
抽象的能力会让它达到最好的状态！
影响分析就是分析潜在变更在整个抽象层以及抽象的每个层面对一个系统的影响的分析能力。
Impact analysis is the ability to analyze the potential impact of a change to a system through all levels of abstraction, as well as within each level of abstraction.
通过组装一个或多个IT服务来定义业务服务的能力提升了重用的抽象层次，这是SOA的主要优势之一。
The ability to define a business service that can be realized through a composition of one or more IT services raises the level of abstraction of reuse - one of the main advantages of SOA.
下一阶段，具体运算阶段，七到十二岁，儿童可以解决守恒问题，但儿童的抽象推理能力仍然有限。
The next phase, concrete operations, from seven to twelve, you can solve the conservation problem, but still you're limited to the extent you're capable of abstract reasoning.
例如，通过睡眠处理的记忆能帮助人们在平时提升洞察力，自我推断能力，还能培养抽象思维。
For example, sleep-enabled memories may help people produce insights, draw inferences, and foster abstract thought during waking hours.
爬出洞穴外的探寻者是那些有能力在抽象和概念化的关系中游刃有余的人。
Learners who manage to climb out of the cave are persons who have become empowered to move freely and with ease among abstractions and conceptual relations.
大脑新皮层同时也提高了灵长类动物的抽象思维和问题解决能力，并增强了它们在控制冲动和社交技巧方面的灵活性。
It also enables more abstract learning and problem-solving, as well enhanced flexibility in impulse control and social skills.
这要求具有某种形式的抽象思维(而不再是代码的细节)，这种思维能力可能较难形成。
This requires a form of abstract thinking (beyond the bits and bytes of code) that can be difficult to master.
X Forms在表单数据模型及其表示之间增加了一层新的、功能强大的抽象，并提供了在多个不同提交动作之间使用一个表单的能力。
The XForms standard adds a powerful new abstraction between a form's data model and its presentation, as well as providing the ability to use a single form with several different submission actions.
最后要说一点，不可变类最酷的一个地方是，它们融合到复合（composition）抽象中的能力是如此之强。
Finally, one of the best features of immutable classes is how well they fit into the composition abstraction.
Gershenfeld指出，维持这种抽象要求不断增加的能力以及复杂的编程，要把这些装进它的脑袋。
Gershenfeld, noting that maintaining that abstraction requires increasing amounts of power and complex programmning, wants to turn this on its head.
在本文中，您将看到关于低层能力的一些相对完整的示例，而对大部分高层次能力将只是进行简单抽象的描述。
In this article, you'll see some relatively fleshed-out examples from the lower-level capabilities, but most of the higher-level capabilities will be simply described abstractly.
根据弗林的观点，一代代人IQ的提升是由不断增强的抽象逻辑能力所引起。
According to Flynn, generational rises are prompted by increased exposure to abstract logic.
这培养了在不同的抽象层次上同时工作的能力，根据手边的情况和任务或多或少地着重于细节。
This fosters the ability to work simultaneously at different levels of abstraction, focusing on more or less detail according to the situation and task at hand.
这培养了在不同的抽象层次上同时工作的能力，根据手边的情况和任务或多或少地着重于细节。
This fosters the ability to work simultaneously at different levels of abstraction, focusing on more or less detail according to the situation and task at hand.
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