在课堂实践中到底应该什么做,这个创造空间应该还给学生,教师不用去做那么细致的规定,第一步干什么,第二步干什么,教师完全可以从当时的情景、学生的感受、学生的一些想法去做起。并强调,我们在数学课堂上不是要给学生一个模式,我们是要学生有这样的创造的冲动,要学生生长出智慧来,要学生越来越觉得自己是一个可以主动地、自主地创造的人。我在一个教学班做了这样一个教学片段尝试:
教学片段:列方程(组)解应题
方程思想是贯穿于初中阶段的重要数学思想之一,通过灵活运用,可以得出多种解题方法。
![](data:image/png;base64,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)
以方程为工具分析问题,解决问题、即建立方程模型是重要的数学知识之一,列方程中蕴含了“数学建模思想”和解方程中蕴含的“化归思想”,是非常重要的数学思想。
上述教学过程,成功的地方有两点:(1)能将题目进行一题多解,让知识和解题方法深化,使解题思想升华。(2)让出讲台,让学生在讲台充分展示个人的解题思维,能激活课堂学习氛围,提升学生学习数学兴趣,同时激发学生创造思维,提升学习自信。在时间上比我原定的教学设定时间多出了5分钟。这是一个矛盾点,但总体来说收获比失去的多。
从实践中可以看出,数学课堂教学的预设与偶然生成是相辅相成,又存在矛盾,但两者缺一不可。教学更多强调的是人的发展,教学要重视知识学习的逻辑和效率,更要注重生命体验的过程和质量,课堂生成更能体现人的发展。因此,作为教师,要认真处理预设与生成的关系,使两者相辅相成、相互促进。
一、精简课堂教学预设,提高偶然生成的创造空间
对数学教师而言,首先要认真钻研教材,弄懂教材的本意和新意,尊重教材的价值取向,把握教材的重点和难点,精简知识结构,因材施教。其次要拓宽知识面,丰富背景知识,以有效应对课堂偶然生成所产生的新问题,让偶然生成为教学预设服务,做到“不离主题”,这是教师在课堂中有效地激发生成、引领生成和调控生成的基础。课堂生成是师生的“即兴创造”,是“突然觉悟”,它犹如天马行空,不期而至。为此,立足课堂教学预设的基础,教师要尽可能提高偶然生成的创造空间,引领学生发展创造性思维。预设要有弹性和开放性:给生成腾出时间和空间。教师要确立课堂生成的意识,要深入思考课堂教学的大方向,大环节和关键性内容,把提课堂教学的整体思路和目标指向,为学生的自主活动提供必要的时间。在教学中,我们应多说引导创造发展的话:如“还有别的做题方法吗?、“你还知道什么?”、“他做得对吗?说说你的看法。”等等。给学生提供思考空间,课堂目标自然实现。
二、数学老师在教学实践中改变教学观念,重视课堂生成。
传统教学把丰富复杂、变化不定的教学过程,简约化为特殊的程序化的单一的认识活动,把它从整体的生命活动抽象、隔离出来,是传统教学观最根本的缺陷。许多教师习惯于把课堂上的一切都算计在内,把“意外情况”、“节外生枝”都视为“扰乱课堂”而加以排除,课堂生成自然也就无了立锥之地。它导致课堂教学的机械、沉闷和程序化,缺乏生气与乐趣,缺乏智慧挑战和对好奇心的刺激,使师生的生命活力在课堂上不但得不到充分的发挥,而且受到压抑和制约,从而导致师生厌教,学生厌学。
课堂生成的是动态的,意味着老师上课不是执行教案的过程而是教案再创造的过程:不是把心思放在教材、教参和教案上,而是放在观察学生、倾听学生、发现学生并与学生积极互动上。这要求教师在课堂教学活动中不能拘泥于课前的预设,重视课堂生成,要根据实际情况,随时对教学作出有把握的调整、变更。重视课堂生成,能让学生有这样的创造的冲动,要让学生长出智慧来,要让学生
越来越觉得自己是一个可以主动地、自主地创造的人。
三、课堂生成的需要数学老师的智慧
当学生精力不振时,你能否使他们振作?当学生过度兴奋时,你能否使他们归于平静?当学生茫无头绪时,你能否给以启迪?当学生没有信心时,你能否唤起他的力量?你能否从学生的眼睛里读出愿望?你能否听出学生回答中的创造?你能否觉察出学生细微的进步和变化?你能否让学生自己明白错误?你能否用不同的语言方式让学生感到关注?你能否使学生觉得你的精神脉搏与他们一起欢跳?你能否让学生的争论擦出思维的火花?你能否使学生在课堂上学会合作,感受和谐的欢愉、发现的惊喜?这些看上去与教学预设无关的教学细节,如果靠着老师的智慧处理有效那就会最大限度点燃学生的学习热情,激发学生的探究精神和创造力,能让课堂生成更活跃,更充分,生命意识更强。
教学预设是课堂生成的主线,课堂生成是教学预设的补充和再生。在课堂教学中更注重课堂生成,这是生命的关怀,改革的需要。对教师而言,课堂不只是为学生成长所做的付出,不只是别人交付任务的完成,它同时也是自己生命价值的体现和自身发展的组成。每一个热爱学生和自己生命、生活的教师,都不应谈轻视作为生命实践组成的课堂教学,由此而激发起自发地上好每一节误,使每一节课都能得到生命满足的愿望,大家要积极地投入教学改革中。