从系统的观点看一元二次方程的解法教学设计
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摘要
从知识的发生和发展的视角,从系统的观点分析一元二次方程不同解法的内在联系,需要突出降次解法中的转化思想,基于学生的认知基础,把配方法作为解一元二次方程解法的重点方法,这是合理的,但这还不够,还需要用解一元多项式方程之因式分解降次的思想来统一认识其他的解法,为学生今后学习奠基,让学生体会与方程研究相关的数学文化.
In order to analyze the internal connection of different solutions to quadratic equations as a whole, and from the perspective of the formation and development of knowledge, we need to highlight the idea of reducing the power of x. Based on students' cognitive ability, we considered the method of completing the square as being the key method to solve quadratics. This was considered proper, but not sufficient. It was necessary to unify the understanding of power reduction by factoring, which was often used in polynomial equations. Through the basic idea of solving single variable polynomial equations, students would acquire the foundations for future study, and experience the mathematical culture regarding equation research.
In order to analyze the internal connection of different solutions to quadratic equations as a whole, and from the perspective of the formation and development of knowledge, we need to highlight the idea of reducing the power of x. Based on students' cognitive ability, we considered the method of completing the square as being the key method to solve quadratics. This was considered proper, but not sufficient. It was necessary to unify the understanding of power reduction by factoring, which was often used in polynomial equations. Through the basic idea of solving single variable polynomial equations, students would acquire the foundations for future study, and experience the mathematical culture regarding equation research.
引文
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[2]王红权,应佳成.二元一次方程教学设计的几点建议[J].中学数学杂志,2016(12):24-27.
[3]孙旭花.中国数学教育优势:隐性的代数教学设计模型[J].数学教育学报,2016,25(5):5-8.
[4]陈蓓,喻平.哲学数域下的数学教育研究——“第二届全国数学教育哲学暨数学教育高层论坛”综述[J].数学教育学报,2016,25(5):99-102.
[5]冯承天.从一元一次方程到伽罗瓦理论[M].上海:华东师范大学出版社,2012:26.
[6]范宏业.一元二次方程的六种几何解法[J].数学教学,2005(10):25-27.
[7]范良火.义务教育教科书·数学(八年级下册)[M].杭州:浙江教育出版社,2013:31-35.
[8]沈志军,洪燕君.“一元二次方程的配方法”:用历史体现联系[J].教育研究与评论,2015(10):38-42.
[9]李迪.中国数学史简编[M].沈阳:辽宁人民出版社,1984:72.
[10]欧几里得.几何原本[M].兰纪正,朱恩宽,译.西安:陕西科学技术出版社,2003:48-49.
[11]王红权,任敏龙.穿越千年寻本源“四探”定理为育人[J].中学数学教学参考,2016(8):18-21.
[12]严家丽.试析影响教师使用教科书水平的因素——基于15位小学数学教师的调查[J].数学教育学报,2016,25(6):51-55.
[13]范良火,熊斌,李秋节.现代数学教育中的教材研究:“概念”“问题”和“方法”[J].数学教育学报,2016,25(5):1-4.
[14]章建跃.从整体性上把握好数学内容[J].中小学数学·高中版,2010(3):封底.
[15]吕世虎,吴振英,杨婷,等.单元教学设计及其对促进数学教师专业发展的作用[J].数学教育学报,2016,25(5):16-21.