A Japan has a significantly better record in terms of average mathematical attainment than England and Wales. A 日本在数学上的平均成就比英格兰和威尔士更好。 Large sample international comparisons of pupils' attainments since the 1960s have established that not only did Japanese pupils at age 13 have better scores of average attainment, but there was also a larger proportion of 'low' attainers in England, where, incidentally, the variation in attainment scores was much greater. 从 20 世纪 60 年代起，就有了大量针对小学生的国际化抽样对比，结果显示，不仅 13 岁的日本小学生在各项数学成就上有更好的成绩，而且在英格兰有大部分的“低”成就者，其成绩的变化更大。 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? 在这两个国家，教育占国内生产总值的比例是相近的，那为什么在数学领域，日本有更高的且始终一致的成就?

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B Lower secondary schools in Japan cover three school years, from the seventh grade (age 13) to the ninth grade (age 15). B在日本，初中包括三个学年，从七年级（13 岁）到九年级（15 岁）。 Virtually all pupils at this stage attend state schools: only 3 per cent are in the private sector. 几乎所有在这个阶段的小学生都进入国立学校：只有 3% 进入私立学校。 Schools are usually modern in design, set well back from the road and spacious inside. 学校的设计通常都很现代化，远离公路，内部宽敞。 Classrooms are large and pupils sit at single desks in rows. 教室很大，每一排的小学生都有单独的座位。 Lessons last for a standardised 50 minutes and are always followed by a 10-minute break, which gives the pupils a chance to let off steam. 每个标准的课程持续 50分钟，课间休息 10 分钟，能让小学生有放松的机会。 Teachers begin with a formal address and mutual bowing, and then concentrate on whole-class teaching. 老师们都以正式的致辞和与学生相互鞠躬致意来开场，随后专注于整堂课程。

Classes are large - usually about 40 - and are unstreamed. 班级很大——通常在 40 人左右——并且不是按智力分班级的。 Pupils stay in the same class for all lessons throughout the school and develop considerable class identity and loyalty. 在整个学校生涯中，小学生们待在同一个班级学习所有的课程，因此培养了广泛的班级归属感和忠诚度。 Pupils attend the school in their own neighbourhood, which in theory removes ranking by school. 小学生们都就近上学，这从理论上排除了学校的排名制度。 In practice in Tokyo, because of the relative concentration of schools, there is some competition to get into the 'better' school in a particular area. 事实上在东京，由于学校的相对集中，为了能够进入某个区域的“更好”的学校，还是会有一些竞争。

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C Traditional ways of teaching form the basis of the lesson and the remarkably quiet classes take their own notes of the points made and the examples demonstrated. C 传统的教育方式奠定了课程的基础，整个班级非常安静，都在记录重点和列举的例子。 Everyone has their own copy of the textbook supplied by the central education authority, Monbusho, as part of the concept of free compulsory education up to the age of 15. 每个人都有自己的课本拷贝件，这些课本由中央教育机构——文部省提供，作为 15 岁之前的免费义务教育概念的一部分。 These textbooks are, on the whole, small, presumably inexpensive to produce, but well set out and logically developed. 这些课本整体上来说很小，并且生产起来也不昂贵，但被很好地组织并合理地开发出来。 (One teacher was particularly keen to introduce colour and pictures into maths textbooks: he felt this would make them more accessible to pupils brought up in a cartoon culture. （有一个老师特别渴望将颜色和图片放入数学书中：他觉得这样能更好地使在卡通文化背景下长大的小学生接受数学教学。 ) Besides approving textbooks, Monbusho also decides the highly centralised national curriculum and how it is to be delivered. ）除了令人满意的课本，文部省还决定了高度集中化的国民教育课程以及这些课程的实施方法。

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D Lessons all follow the same pattern. D课程都有相同的模式。 At the beginning, the pupils put solutions to the homework on the board, then the teachers comment, correct or elaborate as necessary. 开始的时候，小学生们将家庭作业的答案写在黑板上，随后老师评论、纠正，或在必要时详细解释。 Pupils mark their own homework: this is an important principle in Japanese schooling as it enables pupils to see where and why they made a mistake, so that these can be avoided in future. 小学生给他们自己的作业评分：在日本学校，这是一条很重要的规则，因为它能使小学生们知道自己错在哪里以及为什么犯错，以此来避免以后再犯错。 No one minds mistakes or ignorance as long as you are prepared to learn from them. 没有人介意错误和无知，只要你准备好从中吸取教训。 After the homework has been discussed, the teacher explains the topic of the lesson, slowly and with a lot of repetition and elaboration. 讨论完回家作业后，老师缓缓地、重复且仔细地讲述这堂课的主题。 Examples are demonstrated on the board; questions from the textbook are worked through first with the class, and then the class is set questions from the textbook to do individually. 老师在黑板上举例；然后和整个班级的学生先一起解决课本上的问题，随后整个班级的学生被要求独立完成从课本中提出的问题。 Only rarely are supplementary worksheets distributed in a maths class. 数学课上几乎没有补充的习题。 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 sheets unnecessary. 令人印象深刻的是，课本的逻辑特性，综合性地覆盖了不同的例子，加上班级的相同性，抵消了不必要的功课。 At this point, the teacher would circulate and make sure that all the pupils were coping well. 在功课这点上，教师会循环教导直到所有的学生都会了。

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E It is remarkable that large, mixed-ability classes could be kept together for maths throughout all their compulsory schooling from 6 to 15. E 值得注意的是，大的、多功能化的班级里的学生，在他们 6 到 15 岁的义务教育学年内，为了数学聚集在一起。 Teachers say that they give individual help at the end of a lesson or after school, setting extra work if necessary. 教师们说他们会在课后或放学后给予个别帮助，有必要的话还布置额外的功课。 In observed lessons, any strugglers would be assisted by the teacher or quietly seek help from their neighbour. 在公开课上，任何有困难的学生都会得到老师的帮助，或者悄悄地问他们周围的同学。 Carefully fostered class identity makes pupils keen to help each other - anyway, it is in their interests since the class progresses together. 精心培养的班级归属感使得学生们都乐于互相帮助——不管怎么说，自从整个班级一起学习后，这就成了他们的共同兴趣。

This scarcely seems adequate help to enable slow learners to keep up. 这些帮助似乎并不足以使学习慢的人赶上进度。 However, the Japanese attitude towards education runs along the lines of 'if you work hard enough, you can do almost anything'. 然而，日本人对待教育的态度一直基于这样的原则“如果你足够努力，你就能完成几乎任何事情”。 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 encouraging them to work harder. 父母会时刻被通知他们子女的学习进度，并且督促孩子赶上学习进度，如果有必要，父母还送孩子去“Juku”（私人的晚上辅导班），鼓励他们努力学习。 It seems to work, at least for 95 per cent of the school population. 这似乎对学校 95% 的学生都是行得通的。

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F So what are the major contributing factors in the success of maths teaching? F那么，什么才是成功的数学教学的主要因素? Clearly, attitudes are important. 显然，态度是很重要的。 Education is valued greatly in Japanese culture; maths is recognised as an important compulsory subject throughout schooling; and the emphasis is on hard work coupled with a focus on accuracy. 在日本文化中，教育被认为很重要，数学在义务教育中被认为是一门重要的学科，并且重点是在努力学习和关注准确性上。

Other relevant points relate to the supportive attitude of a class towards slower pupils, the lack of competition within a class, and the positive emphasis on learning for oneself and improving one's own standard. 另外一些观点，和整个班级积极帮助落后的学生有关，如同一个班级中的竞争缺失，以及积极强调自我学习和自我提高。 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. 有些被引用的观点认为，日本的课堂强调重复单调的教学，凭记忆学到事实，这些观点可能是不公平也非正义的。 No poor maths lessons were observed. 大家所见到的数学课没有差劲的， They were mainly good and one or two were inspirational. 且大多是好的，有一个甚至两个是励志的。