数理优秀的学生和大部分学生学习方法上的差异?

Viewed 24

从小学到初中,有几个现象,学生的分化更明显,大部分普通学生怎么努力,也很难突破超越,和头部有明显的差异,尤其反映在数学学习方面:

产生分化的原因是什么?或者说数学很好的学生和普通学生数学思维方法上有何不同?后者进一步提升的困境究竟是什么?

有一个基本判断(待验证):可能的原因是前者更早的觉察和培养了知识框架思维,也就是对知识连接的敏感性,这也是多元思考、知识图谱的价值;而多数学生潜意识里沿用的习惯性方法,比如单一的记忆、套路等;不适合初高中,思维的广度和深度不足等等。而优秀学生具有的知识框架模型思维带来更多兴趣、主动性,从而形成学习的正反馈系统。

1 Answers

近日找到相同的观点,出自《数学的力量》,其中提到:

“数学成绩较差的学生对数学知识的掌握只停留在记忆层面;而那些数学成绩较好的学生则会更进一步,将零碎的数学知识视为一个互相关联的整体。”

引文:
Yet data from the 13 million students who took PISA tests showed that the lowest achieving students worldwide were those who used a memorization strategy – those who thought of math as a set of methods to remember and who approached math by trying to memorize steps. The highest achieving students were those who thought of math as a set of connected, big ideas.

然而,参加国际学生评估项目测试的 1300 万名学生的数据显示,全世界成绩最差的学生是那些使用记忆策略的学生--他们认为数学是一套需要记忆的方法,他们通过努力记忆步骤来学习数学。 而成绩最好的学生则是那些把数学看成是一套相互联系的、大思想的系统。

Mathematics is a broad and multidimensional subject. Real mathematics is about inquiry, communication, connections, and visual ideas. We don’t need students to calculate quickly in math. We need students who can ask good questions, map out pathways, reason about complex solutions, set up models and communicate in different forms. All of these ways of working are encouraged by the Common Core.

数学是一门广泛而多维的学科。 真正的数学是探究、交流、联系和形象思维。 我们不需要学生在数学上快速计算。 我们需要的是能够提出好问题、绘制路径图、推理复杂的解决方案、建立模型并以不同形式进行交流的学生。 所有这些工作方式都是共同核心所鼓励的。

Technology leaders are publically arguing that calculation is not math, and that math is a much broader subject. Conrad Wolfram, one of the leaders of one of the world’s most important mathematics companies, Wolfram-Alpha, urges schools to stop emphasizing calculating and focus instead on problem solving, modeling, thinking, and reasoning as these are the mathematical abilities that students need in the workplace and their high tech lives. This broad, multidimensional mathematics is the math that engages many more learners and puts them on a pathway to life long success.

科技领袖们公开表示,计算不是数学,数学是一门更广泛的学科。 世界上最重要的数学公司之一 Wolfram-Alpha 的领导人之一康拉德-沃尔夫拉姆(Conrad Wolfram)敦促学校不要再强调计算,而应把重点放在解决问题、建模、思考和推理上,因为这些才是学生在工作场所和高科技生活中所需要的数学能力。 这种宽泛、多维的数学才能吸引更多的学习者,让他们走上终身成功之路。

Mathematics is not a subject that requires fast thinking. Award winning mathematicians talk about their slow, deep thinking in math. Fields Medal winning mathematician Laurent Schwartz wrote in his autobiography that he felt stupid in school because he was one of the slowest thinkers in math. Eventually he realized that speed was not important – “What is important is to deeply understand things and their relations to each other. This is where intelligence lies. The fact of being quick or slow isn’t really relevant.”

数学不是一门需要快速思考的学科。 获奖数学家都谈到他们在数学中缓慢而深入的思考。 菲尔兹奖得主劳伦特-施瓦茨(Laurent Schwartz)在自传中写道,他在学校里觉得自己很笨,因为他是数学中思维最慢的人之一。 最终,他意识到速度并不重要--"重要的是深刻理解事物及其相互之间的关系。 这就是智慧所在。 快与慢并不重要"