A 就数学的平均成绩而言，日本的纪录要比英格兰和威尔士好得多。20世纪60年代以来，就学生数学成绩所做的大量国际样本比较研究证实，13岁的日本学生平均分数更高，同时也证实了英国表现“不佳”的学生比例更大，而且，顺便说一句，英国学生分数的变化也比日本学生大得多。两个国家在教育上的国民生产总值比例十分相近，那日本是如何实现这一更高、更稳定的数学成绩的呢?

AJapan has a significantly better record in terms of average mathematical attainment than England and Wales. Large sample international comparisons of pupils` attainment since the 1960s have establish that not only did Japanese pupils at age 13 have better scores of average attainment, but there are also a larger portion of `low` attainers in England, where, incidentally, the variation in attainment scores was much greater. The percentage of Gross National Product spent on education is reasonably similar in the two countries, so how is this higher and more consistent attainment in maths achieved?

B 日本的初中教育为时三年，从7年级(13岁)到9年级(15岁)。几乎所有这个阶段的学生都选择国立学校：只有3％在私立机构就读。学校通常都设计得很现代化，远离马路，占地面积也很大。教室空间很大，学生使用的是成排的独立课桌。每堂课的持续时间是标准化的50分钟，然后是10分钟的休息时间。可以让学生们放松一下。教师上课以正式的问候和互相鞠躬开始，之后注意力就集中在整堂课的教学上了。

上课的班级较大——通常约40人——且不根据智力水平分班。学生在校期间的所有课程都在同一个班级，因此他们有相当强烈的班级认同感和忠诚意识。学生在自己的社区上学，从理论上排除了学校排名。实际上在东京，因为学校相对比较集中，在某些特定区域会存在一些进入“更好的”学校的竞争。

Classes are large – usually about 40 – and are unstreamed. Pupils stay in the same class for all lessons throughout the school and develop considerable class identity and loyalty. Pupils attend the school in their own neighborhood, which in theory removes ranking by school. In practice in Tokyo, because of the relative concentration of schools, there is some `competition` to get into the `better` school in particular area.

C 传统的教学方式是课堂的基础，学生们安安静静地对老师指出的重点和给出的示例做笔记。每个学生都有自己的课本，由中央教育机构文部省(Monbusho)提供，这也是15岁以下的公民享有免费义务教育理念的一部分。总体来说，这些课本体积较小，制作成本可能比较低，但排版精美，结构合理。(有一位老师特别热衷于在数学课本中引入色彩和插图：他觉得这样的课本更容易被在卡通文化背景下长大的学生所接受。)除了批准使用课本，文部省还负责制定高度集中化的全国统一课程及其执行方式。

D 所有的课堂都遵循相同的模式。一上课，学生先把家庭作业的答案写在黑板上，然后由老师讲评、纠正，必要时进行详细解释。学生自己批改作业：这在日本的学校教育中是一条重要原则，因为这样做可以让学生认识到自已在哪里犯了错误，为什么会犯错误，从而避免今后再犯同样的错误。没有人在意你的错误或者无知，只要你能从中有所收获。

讨论完家庭作业之后，教师就开始讲解本堂课的主题，速度很慢，有很多重复和详细解释。所有例子都在黑板上演示；课本上的一些问题先在课堂上由大家一起完成，另外一些问题随后再单独布置给每个学生。数学课上，老师只在极少数悄况下才会发一些额外的练习册。给人的印象是，课本的逻辑性，其中对各种例子的全面涵盖，再加上学生水平整齐划一，使得练习册无用武之地。布置完作业，教师就会在教室里转一转，以确保所有学生都没有进一步的问题。

After the homework has been discussed, the teacher explains the topic of the lesson, slowly and with a lot of repetition and elaboration. Examples are demonstrated on the board; questions from the textbooks are worked though first with the class, and then the class is set questions from the textbooks to do individually. Only rarely are supplementary worksheets distributed in a maths class. The impression is that the logical nature of the textbooks and their comprehensive coverage of different types of examples, combined with the relative homogeneity of the class, renders work sheet unnecessary. At this point, the teacher would circulate and make sure that all the pupils were coping well.

E 值得注意的是，在从6岁到15岁的整个义务教育期间，学生可能都是在能力不一的大班里一起学习数学。教师们说他们会在课堂结束时或者放学后给学生个别辅导，必要的话还会额外再留作业。在被观摩的课堂上，任何有困难的学生都能得到老师的帮助，或者他们会悄悄请同桌帮助。精心培养出的班级认同感让学生热衷于互相帮助——无论如何，班级的共同进步与他们休戚相关。

这样的帮助似乎并不能让后进的学生跟上班级进度。但是，日本人对待教育的态度所遵循的原则是“只要你足够努力，你就几乎无所不能”。父母能够及时了解到孩子的进步，在帮助孩子跟上班级进度方面起了不少作用，必要时他们会把孩子送到“聚酷(私立夜校补习班)”，并鼓励他们刻苦学习。这种做法好像至少对95％的在校生都能起到作用。

This scarcely seems adequate help to enable slow learners to keep up. However, the Japanese attitude towards education runs along the lines `if you work hard enough, you can do almost anything`. Parents are kept closely informed of their children`s progress and will play a part in helping their children to keep up with class, sending them to `Juku` (private evening tuition) if extra help is needed and encourage them to work harder. It seems to work, at least for 95 percent of the school population.

F 那么什么是日本数学教学成功的主要因素呢?显然，态度是很重要的。在日本文化中，教育极受重视；数学被视作整个学校教育过程中一门重要的必修科目；刻苦努力和精益求精是重中之重。

其他关乎成功的因素包括班级对后进生的支持态度，班级内没有竞争，积极强调为自己而学习以及提高自身的水平等。“重复乏味的课堂和死记硬背事实性知识”不时被引用来描述日本的课堂，这种观点也许是不公平也不公正的。观摩中并没有看到糟糕的数学课，基本上都不错，且其中一两堂课还让人感到很有启发性。

Other relevant points relate to the supportive attitude of a class toward slower pupils, the lack of competition within a class, and the positive emphasis on learning for oneself and improving one`s own standard. And the view of repetitively boring lessons and learning the facts by heart, which is sometimes quoted in relation to Japanese classes, may be unfair and unjustified. No poor maths lessons were observed. They were mainly good and one or two were inspirational.