基于数学核心素养的小学数学教学模式研究
——以人教版小学数学二年级下册《两位数减两位数》为例
原文作者 丹尼尔·坦纳
摘要：每一种书面记载的历史,无论是关于一个事件、一个专业领域、一个种族、一个国家或者整个世界,都需要将各种事件加以记载、组织、阐释和描述。在查明会发生什么和揭示使事件可能发生的条件时,科学的方法是至关重要的。
关键词：学校； 课程史
每一种书面记载的历史,无论是关于一个事件、一个专业领域、一个种族、一个国家或者整个世界,都需要将各种事件加以记载、组织、阐释和描述。在查明会发生什么和揭示使事件可能发生的条件时,科学的方法是至关重要的。虽然绝对的真相永远不可能被了解,但历史学家却坚信关于历史的运动变化有许多是能够被了解的。于是,历史学家就以这种态度将研究的结果展示给其他研究者。由于新的见解根据学术的客观性不断地被揭示,历史需要—总是必须—改写。从这种意义上讲,所有严肃的历史均是一种重构物( reconstructions)
不过,从学术探究的角度看,单纯的历史事实和事件并不能构成一部历史。为了将发现历史的激动人心过程传递给读者,它们必须加以选择解释和整理。当然,课程史的读者除了关心事件本身之外,还需要关心事件所发生的原因。如果历史能对洞察目前关注的问题有所贡献的话,关心事物发生的原因对于教育者来说就是至关重要的。
塔奇曼( Barbara Tuchman)是著名的美国历史学家。她相信人们必须首先查明发生过什么,然后按某种序列对重要人物、事件、日期和文献(“确切地说,是用句子、段落和章节”)进行整理安排。她告诉我们将事实如何转变为一种叙事的过程即是“透过事实的现象去揭示它的原因”。人们并不是从一个命题出发,然后去选择那些适合自己体系的事实。塔奇曼写道,所发生的事件的原因“将不期而遇,但是如果人们尚未了解曾发生过什么,从一开始就追逐事物的原因,那么情况就不是如此了,它将使人们永远陷于困惑之中”。
20世纪六七十年代,教育领域里激进的修正主义者始于如下命题:进步教育在意图和结果上均是保守的。在书写历史时,他们忽视了这一矛盾。2这是最近干扰课程史的编写的事件之一。这里的要点是,历史的目的是为了查明发生过什么,以及为什么会发生。正如塔奇曼所坚持的,“因为一些事件不合口味就加以遗漏,那是在写小说,而不是在写历史。”
历史学家同任何其他人没有什么两样,他们从自己的角度来看待事物,这种角度决定了他们所需要的相关事件。不论所做的学问多么微观,在历史学家的心目中都存在着一种决定着他们对事实的选择和处理的历史观。正如比尔德在1933年就任美国历史协会会长所作的致词中所指出的如果历史学家否认存有一个参照系,导致它以隐蔽的方式发生作用,这种情形是致命的。尽管研究者代表了一种客观的形象,实际上那种支配他或她的思想和决定事件的选择与处理的价值观却被掩饰了。
按照比尔德的意见,为了避免偏见,历史学家必须意识到自己的历史观,并且不能回避它。的确,比尔德告诫该协会成员,历史学家应当“不断审视他自己的参照系,澄清它,扩充它hellip;hellip;并且通过尊重历史上巨大变迁所蕴含的思想和利益的性质作出深思熟虑的猜测,给予历史以结构的连贯性”。换言之,历史学家应当袒露自己如何运用历史观来发展历史知识。在这样做的过程中,历史学家也同时避免了隐性(甚至对历史学家本人也是隐性的)偏见所设下的陷阱。
在1933年的全美历史协会的大会上,比尔德主张只有三种历史观是可以接受的:“第一,历史是混沌无序的,每一种用别的方法解释它的企图都是幻想;第二,历史是一种周期性的循环运动;第三,历史按线性的方式运动,要么是直线上升要么是螺旋上升,而且是按某种方向运动的。”7在他的演讲词的结束语中,比尔德表明了他自己的历史观是发展性的――即整个世界正向着更美好的未来逐步前进,历史学家的作用就是加速这个完善的过程,即增进我们对过去的理解以利于现实的改进。对于比尔德来说,历史学识有一种实用性的目的,即通过帮助改革者了解过去发生的种种陷阱与失败并理解其原因,以期避免它们,并且通过了解和解释思想观念的巨大变迁,帮助改革者建立一种更加美好的未来。
康马杰( Henry Steele Commager)告诉我们,“历史,包含着所有被历史学家人为地放在一起的东西”8。这里,康马杰以极简单的形式谈论历史,历史不是一种编年史叙述,而是一种过去的重构物。历史不可避免地是解释性的。人类的许多宣言和成就已经远逝,巨大数量的文献和其他原始资料必须被转译成一种可理解的过去。“如果历史学家期望他的读者弄懂这些宣言的某些意义,他就必须对之加以解释,”康马杰写道,“一旦历史学家开始解释这些官言,他就被迫对历史进行重构。”历史学家是在当今的主导性思想的控制下重构历史的,即在教育机会的扩张或新闻媒体权力发展的控制下重构历史。当历史学家向历史记录注入生命并且赋予历史以意义时,他或她就正在重新创造历史。但是,如康马杰所强调,“历史所呈现的并不是过去,而是对过去的一种选择、组织和解释。
课程史是有用的,因为许多古老的思想具有不朽的特征。问题探究法( problem method of investigation)作为一种课堂活动经历了从杜威到现代教师的发展历程。而教师应成为专业人员(课程编制者)而不是技工的观念甚至更为古老,向前可追溯到19世纪60年代的实物教学( objectteaching)。课程领域的核心思想必须代代相传,课程史理应履行这种职责。
课程史是课程领域的全部记忆。没有它我们就不可能对当代的问题有个全面的了解;如果没有人能够查明从前发生的事情,我们只好重新发明教育之轮( pedagogical wheel),而无法认识到过去已有的成功与不成功的教育模式。但是,仅仅将我们的经验记载下来并不能保证这些记载被当代的课程改革者所查询。确实,我们有着革新文化的嗜好,但常常忽视了来自最近和遥远过去的相关事件及教训。与此同时,在相继的时期中,社会政治的更替迫使学校取消在前一阶段强加于它们的改革,或者重新组织它们早些时候被迫放弃的改革。一个时期内,我们开设“新数学”和学科中心课程( discipline- centered curriculum),而另一个时期内,我们设立开放课堂( open classroom)和学生中心课程( learner-centered curriculum);一个时期内,我们的课程大大扩张,而在接下来的时期内,我们又缩减课程“回到基础”( back to basics)。“新的”局部性改革是作为前一段时期实施的局部性改革的矫正而推行的。
过去的记载表明,局部的改革方法必定走向失败,因为它们产生课程失衡问题以及丧失了课程的衔接性。周期性地,人们总是不断发现有必要保持课程的连贯性以及除综合课程以外的核心课程。但是,当我们没有从早期实现课程平衡和综合的努力中汲取经验教训时,问题就会产生。同样,人们也会周期性地不断发现进行反省思维的必要,而与此同时,人们又忘记了汲取过去的经验教训,这种思维的发展需要将那些超越了学科界限的思想和问题解决方法注人到课程之中去。可以说,孤立的研究是一个长期存在的课程问题。
课程史还有另一种功能:它帮助我们理解那些限定我们专业和个人生活的各种传统。这种功能不仅仅是一种实用的东西―它还是一种情感上的事情。我们以此发展一种对我们祖先的责任感,而且也许我们会激起种抱负去继续他们的事业。历史提供各种典范,不管我们正在谈论的是五年级学生对林肯总统的崇拜以及对其童年时代的兴趣,还是专业教育人员对贺拉斯・曼( Horace mann)(他是首次主张教学应成为专门职业的人之一)的受惠感。
外文文献出处：《HISTORY OF THE SCHOOL CURRICULUM》
附外文文献原文
Every written history-of an event, a professional field, a race, a nation or the entire world-requires that events be recorded, organized, interpreted, and presented. The scientific method is essential in finding out what happened and in revealing the conditions that made the events possible. Although the absolute truth can never be known, the historian is guided by the conviction that more can be known about the movement of history The historian then chooses the manner in which the results of the research aregiven to Others. Since new insights are continually being revealed bv school-arly objectivity, history is-and always must be--rewritten. In this sense, all rious histories are reconstructions However scholarly the inquiry historical facts and events alone do not produce a history. They must be selected, interpreted, and arranged in order to communicate to the reader the excitement of discovery about what happened. Of course, readers of curriculum history are concerned about the why of what happened as well as the events themselves. The why is important if the history is to contribute insights into problems of present concern to educators
Barbara Tuchman, a distinguished American historian, believed that(ne must first find out what happened and arrange the personalities, events,dates and documents in some seguence to be exact, in sentences, para-graphs and chapters. She told us that the process of transforming facts intoa narrative forces the why to the surface. One does not begin with a thesisand select the facts that suit ones system Tuchman wrote that the why ofwhat happened will suddenly appear and tap one on the shoulder, but notif one chases after it first, before one knows what happened. Then it willelude one forever
In the 1960s and 1970s, radical revisionists in the field of education began with the thesis that progressive education was conservative in intentand outcome. In writing histor they left the contradictions out. This is one of the disturbing developments that has recently influenced the writing ofcurriculum history. The point of importance here is that the purpose of history is to find out what happened and why. As Barbara Tuchman maintained,Leaving things out because they do not fit is writing fiction, not historyConceptions of History
Historians are no different from anyone else, they see things from theirown perspectives, which determine for them the events that are related However meticulous the scholarship, there is in the historians mind
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Every written history-of an event, a professional field, a race, a nation or the entire world-requires that events be recorded, organized, interpreted, and presented. The scientific method is essential in finding out what happened and in revealing the conditions that made the events possible. Although the absolute truth can never be known, the historian is guided by the conviction that more can be known about the movement of history The historian then chooses the manner in which the results of the research aregiven to Others. Since new insights are continually being revealed bv school-arly objectivity, history is-and always must be--rewritten. In this sense, all rious histories are reconstructions However scholarly the inquiry historical facts and events alone do not produce a history. They must be selected, interpreted, and arranged in order to communicate to the reader the excitement of discovery about what happened. Of course, readers of curriculum history are concerned about the why of what happened as well as the events themselves. The why is important if the history is to contribute insights into problems of present concern to educators
Barbara Tuchman, a distinguished American historian, believed that(ne must first find out what happened and arrange the personalities, events,dates and documents in some seguence to be exact, in sentences, para-graphs and chapters. She told us that the process of transforming facts intoa narrative forces the why to the surface. One does not begin with a thesisand select the facts that suit ones system Tuchman wrote that the why ofwhat happened will suddenly appear and tap one on the shoulder, but notif one chases after it first, before one knows what happened. Then it willelude one forever
In the 1960s and 1970s, radical revisionists in the field of education began with the thesis that progressive education was conservative in intentand outcome. In writing histor they left the contradictions out. This is one of the disturbing developments that has recently influenced the writing ofcurriculum history. The point of importance here is that the purpose of history is to find out what happened and why. As Barbara Tuchman maintained,Leaving things out because they do not fit is writing fiction, not historyConceptions of History
Historians are no different from anyone else, they see things from theirown perspectives, which determine for them the events that are related However meticulous the scholarship, there is in the historians mind a viewof history that controls the selection and arrangement of facts. As charlesBeard pointed out in his presidential address before the American HistoricalAssociation in 1933, it is when the historian denies having a frame of reference. so that it comes in through the back door that we have a pernicious situation.Although conveying an image of objectivity the researcher masks the valuations that have dominated his or her thinking and have determined the selection and treatment of events In attempting to avoid bias, according to beard, the historian must be aware of his or her conception of history and not run away from it Indeed Beard told the association, the historian should'proceed to examine his own frame of reference, clarify it, enlarge it. and give it consistency of structureoy a deliberate conjecture respecting the nature of the vast movements of ideas and interests called historv. In other words, the historian should expose and use his conception of history to advance historical knowledge. Inso doing, the historian is also avoiding the trap of hidden bias(hidden perhaps even to himself)
Historians are no different from anyone else they see things from their own perspectives, which determine for them the events that are related However meticulous the scholarship, there is in the historians mind a view of historv that controls the selection and arrangement of facts. As Charles Beard pointed out in his presidential address before the american Historical Association in 1933, it is when the historian denies having a frame of reference. so that it comes in through the back door, that we have a pernicious situation.Although conveying an image of objectivity the researcher masks the valuations that have dominated hi the selection and treatment of even s or her thinking and have determined In attempting to avoid bias according to beard, the historian must be aware of his or her conception of history and not run away from it Indeed Beard told the association, the historian should 'proceed to examine his own frame of reference, clarify it, enlarge it. and give it consistency of structure by a deliberate conjecture respecting the nature of the vast movements of ideas and interests called history. In other words, the historian should expose and use his conception of history to advance historical knowledge. In sO doing the historian is also avoiding the trap of hidden bias(hidden perhans even to himself Three Views At the association meeting of 1933, Beard argued that only three conceptions of history were possible History is chaos and every attempt to interpret it otherwise is an illusion History moves around in a kind of cycle. History moves in a line, straight or spiral, and in some direction In the closing lines of his address beard indicated that his own view of history was developmental-that the world is moving progressively toward a better future and the historian s function is to accelerate the improvement to improve our understanding of the past in the interest of improving the present. For Beard, historical scholarship has a pragmatic purpose-to help reformers avoid the pitfalls and defeats of the past by helping them to under
stand why they happened, and to build a better future by knowing and ex-plaining the vast movements of ideas Making History. History, Henry Steele Commager tells us, ' embraces all that is put together artificially by the historian Here Commager is not talking
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