青少年的数形结合能力外文翻译资料

本科毕业设计（论文）

外文翻译

青少年的数形结合能力

作者：丹·莫顿

国籍：英国

出处：《British journal of Educational Psychology》

中文译文：

1.调查的目的和调查的范围。

接下来的调查的主要目的是寻找数形结合能力的存在是否与算术能力的任何显著程度相关。在执行算术操作时，没有必要假设它们的拥有者使用数形结合；因为它们可以独立于算术能力发展，但在相同的条件下。例如，如果数形结合能力和算术能力都依赖于智力（这是可能的），那么它们将在一定程度上倾向于共存，尽管两者之间可能完全没有影响。

我们希望回答的问题是：（1）在完全没有被任何社会或智力质量所选择的儿童中，数形结合能力发生率是多少？（2）儿童的数形结合能力与成人的数形结合能力不同吗？（3）在数形结合的发生率方面，性别之间是否有显著差异？（4）数形结合能力是否与算术能力相关，如果是，相关的程度如何？

2.研究对象

从Aberdeen参加日间学校的867名学生中获得了关于数字图像和数字表格的信息。在这四所学校的校长的支持下，我们能够亲自进行所有的调查。选择班级是为了形成年龄的统一群体，孩子的社会地位是大城市学校的绝大多数学生，即工人阶级、上层工人阶级和下层中产阶级。穷人的代表很少，富人的代表也同样很少。几乎所有的学生都在高年级（小学后）课程的第一年，不在第一年的学生在第二年级。从年龄和受教育程度的角度来看，这个群体是一个相当统一的群体。孩子们进入高级班的事实可以被认为是他们被选中的证据。在某种意义上，他们确实是被选中的。控制考试阻碍少量，那些智力低下和那些非常不幸的在他们的学校，而非常优越的部分同样比集团略小于我们通常应该发现，由于一定数量的优秀的这个年龄段的学生去了中学。因此，这个群体可能被认为是一个正常的智力群体，只因为在极端情况下的选择而略有减弱。

这两个实验组里面，男孩（427）和女孩（440）在年龄方面几乎是相同的：唯一的显著差异是在14岁的组中有更多的男孩，这一事实略微提高了他们的平均值，数字增加了最后一个四分位数。整个组的平均年龄为13岁。16个月，其中86%-6%的人年龄在12岁至14岁之间。

3.数据收集

所有的信息都是以回答问题的形式收集起来的。每一节课都要和其他班级一样，提出同样的问题，同样的顺序。每个班的时间约为四分之三，平均约30名学生。

选择合适的问题显然是一个困难。如果不对任何一个孩子，甚至是最聪明的孩子说，“你有一个数形结合的能力，如果有，尽可能仔细地描述它。”因为内省的习惯在青春期发展得最快，事实上在许多情况下只发展到非常轻微的程度。对于孩子们来说，他们的词汇量和描述能力还不足以令人满意地应付自发地描述他们的意象这一困难的任务。因此，我认为，鉴于这些问题的不成熟和缺乏经验，应该采取一些更迂回的方法。因此使用了大量的问题，因此取消了几个理想的目的。也许最重要的是，通过考虑对一些较简单的问题的答案，可以获得对更重要的问题的证实。因此，每门课总共有30个问题。但从调查的角度来看，许多都是无关紧要的，而另一些则与此只有轻微的联系。我建议有充分的理由忽略从大多数问题中得到的结果。

4.算术能力测试

调查的第二部分包括测试这867名儿童的算术能力。不幸的是，在其中一所代表150名学生的学校，没有进行明确的算术测试。因此，比较基础仅限于其余的717个小学生。对于机械算法的测试，使用了Ballard的《新考官》第190页中给出的测试。允许的时间是30分钟，而不是50分钟；这只是为了方便参加考试的老师（因为在这里，老师进行了考试并批改试卷，然后交给我查看）。

本测试结果为：平均评分=29.46

u=8.9

5.计算关联性

寻找数字表单是否与算法（1）的表单组，编号17，那些有数字表单。（2）无形式组，编号700，那些没有。我们找到了表格组中17名学生的个人得分，下表显示了他们在完整算术中的分布情况，717名学生被分为两组：717组。

因此，17人中有13人在整个组的前四分之一，而在前八分之一的组中有8人，即有表格的47%。这似乎表明，有数字形式的孩子通常都擅长机械运算。为了衡量这种相关性，所采用的公式是：

当一个尺度上的数据只分为两个类别（例如，好或坏，存在或不存在等）时，就使用这个二分r公式。

6.结论：

（1）通过对867名12-14岁的学生进行问卷调查，发现整个组的人数比例为1/43。女孩拥有它们的程度似乎略高于男孩，她们的频率分别为1/40，而这些频率为1/47：但他不能接受这种差异超出了抽样误差的限制。

（2）儿童的数形结合能力比成年人的数量形式要基本得多，如梨的回忆和遗忘，或高尔顿对人类面貌的调查中所描述的那样。

（3）有明确的迹象表明，虽然他们没有数形结合能力，但许多儿童有他们后来可能发展的基础：例如，对许多儿童来说，数字似乎向右发展；较小的数字似乎更接近；数字线在10、12等处弯曲或转弯。

（4）那些有数形结合能力的儿童，作为一个群体，在机械运算方面能力优越，17人中有13人，或76.4%，在所有接受算术测试的儿童中处于上四分之一。

67名儿童，男女，BGDS在上午12：00至14：00被安置。二十个问题中的一个，都是关于与数字相关联的图像；这些问题中有两个很好地处理了数字的图像。发现数字的图像存在于整个组中的1个SIIR 43中。女孩的比例略低于男孩（40人中有1人，47人中有1人）。然而，这种显著的差异并没有显示出统计上的有效性。除了152个外，整个小组都被应用了一个标准化的算术测试，结果发现那些把图像和数字联系起来的人在这个测试中获得了相对更好的分数。最上面的四分之一。算术能力。包括76%将图像与数字联系在一起的人。这一事实表明，这些图像的存在与机械算术的能力之间存在着某种联系。计算得出的相关系数为67。

向567名年龄在12岁至14岁之间的男女儿童提出了20个问题中的一个，所有这些问题都涉及心智问题：其中两个问题特别涉及心智问题。在整个组中，43人中有1人出现数字组，女孩的出现率略高于男孩（40人中有1人，47人中有1人）。虽然观察到的差异在统计上是不正确的。除了152个之外，整个小组都接受了标准的计算测试，发现那些有数字分组的人在计算测试中的表现相对较好：前四分之一的计算能力占那些有数字分组的人的73%。（2）在计算能力的前四分之一，有数字分组的人的计算能力的前四分之一，有数字分组的人的计算能力的前四分之一，有数字分组的人的计算能力的前四分之一，有数字分组的人的计算能力的前四分之一。这表明数字分组的存在与机械计算的优越能力之间存在一定的相关性。对于这种相关性，系数为67。

附：外文原文

NUMBER FORMS AND ARITHMETICAL ABILITY

IN CHILDREN.

By DAN M. MORTON.

L——References to earlier work.

1. —The aim and scope of the investigation.
2. —The subjects of the investigation,
3. —The collection of data.
4. —The reactions of the subjects.
5. —The arithmetic test.
6. —The calculation of the- correlation.
7. —Conclusions.
8. —Examples of children^ number forms.

I,—References to earlier work.

Galton states¹ that number forms are io be found in one in twenty of the general population (adult) with considerable differences (one in thirty as compared with one in fifteen)² between men and women. This difference he takes to be a particular instance of the general law that womens powers of imagery are greater than mens. Pear in his book. Remembering and Forgetting, for the most part quotes the figures, and summarizes the results obtained by Calkins and Pear, but makes some suggestions which it is the object of this investigation to test, viz., that many people who have no number forms, nevertheless possess some of the rudimentary imagery from which they are built up.⁴

There are few references dealing with number forms in children. Galton suggests⁵ on the ground that vivid imagery is characteristic of children, as it is of women, that the incidence in children will be greater than it is in adults, and he states that these number forms are neither so well defined nor so ” ell developed as those of adults. He obtained some information from masters in Winchester and Charterhouse schools, and gives the figures one in twenty as the probable incidence for children.⁷

That number forms axe useful to their owners is a point on which Galton was not able to come to a definite conclusion ; but he is inclined to believe that they are developed because they are useful,⁸ and he states

¹ and 2 Galton, Inquiries (Everyman Edition), p. 82.

3 Ibid._t p. 69.

• Pear, Remembering and Forgetting, pp. 189-190.

⁸ Galton, ibid., p. 69.

• ⁷ and ⁸ Galton, ibid., p. 87.

explicitly⁹ that they are an aid to remembering. Muller deals at some length with t

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NUMBER FORMS AND ARITHMETICAL ABILITY
IN CHILDREN.

By DAN M. MORTON.

L——References to earlier work.

1. —The aim and scope of the investigation.
2. —The subjects of the investigation,
3. —The collection of data.
4. —The reactions of the subjects.
5. —The arithmetic test.
6. —The calculation of the- correlation.
7. —Conclusions.
8. —Examples of children^ number forms.

I,—References to earlier work.

Galton states¹ that number forms are io be found in one in twenty of the general population (adult) with considerable differences (one in thirty as compared with one in fifteen)² between men and women. This difference he takes to be a particular instance of the general law that womens powers of imagery are greater than mens. Pear in his book. Remembering and Forgetting, for the most part quotes the figures, and summarizes the results obtained by Calkins and Pear, but makes some suggestions which it is the object of this investigation to test, viz., that many people who have no number forms, nevertheless possess some of the rudimentary imagery from which they are built up.⁴

There are few references dealing with number forms in children. Galton suggests⁵ on the ground that vivid imagery is characteristic of children, as it is of women, that the incidence in children will be greater than it is in adults, and he states that these number forms are neither so well defined nor so ” ell developed as those of adults. He obtained some information from masters in Winchester and Charterhouse schools, and gives the figures one in twenty as the probable incidence for children.⁷

That number forms axe useful to their owners is a point on which Galton was not able to come to a definite conclusion ; but he is inclined to believe that they are developed because they are useful,⁸ and he states

¹ and 2 Galton, Inquiries (Everyman Edition), p. 82.

3 Ibid._t p. 69.

• Pear, Remembering and Forgetting, pp. 189-190.

⁸ Galton, ibid., p. 69.

• ⁷ and ⁸ Galton, ibid., p. 87.

explicitly⁹ that they are an aid to remembering. Muller deals at some length with their possible usefulness. He adopted a second method of investigation in addition to the mere questioning of the subjects : he set them material to learn, and thus obtained information regarding the development and utility of the various types of imagery that arose in the process of learning. Calkins, as a result of investigations with 525 students among whom she found 65 number forms, an incidence of one in eight, states¹⁰ that almost exactly one-half of those with number forms found them useful. She also suggests that there is a strong inherited tendency in some people to have number forms. Pear, discussing their utility, quotes figures¹¹ to show that only a minority of those possessing number forms are convinced of their utility for computation, etc.

Muller,s account¹² ?s the most exhaustive ; he deals with number forms only as examples of the larger class of imagery that arises in learning any kind of systematized knowledge. It seems to be his opinion that such imagery is essentially useful, and he suggests that teachers could with advantage appeal to this to produce useful imagery in the learning of almost any body of material. About number forms in particular he makes the following statements : that the majority go up only to 100 : that beyond 100 number forms become vague and ill-defined : that when they change their direction they do so most often at frequently used, important numbers such as 10, 12, 20, 100, etc. ; and that number forms do not remain fixed in all particular details, the general shape alone remaining constant.

There is little doubt but that number forms as described by Galton¹³ are instances of eidetic imagery as described by Jaensch.¹⁴ Galton makes it clear that many of his subjects actually saw their number forms. This, however, is by no means the rule. Muller also, in. dealing with their localization, gives definite indications that in at least some cases they satisfy the criteria of eidetic imagery. If they are a phenomenon identical with, or closely allied to, eidetic imagery, we should expect to find them to be very common in children. (Jaensch gives 65 per cent as the proportion of children who have eidetic imagery.)

These accounts of number forms have been almost all descriptive. The subjects have not in general been an unselected section. of the general population, having been for the most part friends and acquaintances of

⁸ Galton, ibid., p. 89.

1. Calkins, Amer. Jour, of Psy., 1892-93.
2. Pear, ibid., p. 196.
3. MCller, Leipzig, 1913, Part IH, pp. 72-.131.
4. Galton, ibid., p. 79, et seq.
5. Jaensch, Eidetic Imagery, passim.

6o Arithmetical Ability in Children

the investigators, or students, or public school boys, who were probably superior to the average, both socially and intellectually. Very few references have been made to childrens number forms, and while much has been said regardin

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