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解题是学好数学基础知识、培养和提高思维能力的重要手段.中学生思维的片面性与表面性影响他们对数学对象理解的真度和深度,通过解题错误可略见一斑.研究表明,错误是把新方法与已有知识统一起来的尝试的必然结果.因此,辨认出学生知识联系上的特殊缺陷从而进行针对性讲授是我们研究解题错误的根本目的,也是本文写作的努力方向.高考有限的考试时间使学生的思维高度紧张,虽然会造成较多失误,但从认知心理学的角度考虑,这种低反应时状态更利于反映考生知识技能的掌握情况和思维倾向.因此,我们以2005年湖南高考文科试卷第16题所出现的典型错误为例说明问题.
Solving problems is an important means to learn basic knowledge of mathematics and cultivate and improve thinking ability.Though the one-sidedness and superficiality of middle school students’ thinking affect their truth degree and depth of comprehension of mathematical objects, it can be seen through the problem-solving errors.The research shows that mistakes are The inevitable result of the attempt to unify the new method with the existing knowledge.Therefore, to identify the specific defects in the students’ knowledge connection and then to carry out the targeted teaching is the fundamental purpose of our study on the problem of error-solving and also the direction of the writing of this article. Of the examination time to make students think highly nervous, although it will cause more mistakes, but from the cognitive psychology point of view, this low-response state is more conducive to reflect the candidates knowledge and skills to grasp the situation and thinking tendency.Therefore, we The typical mistakes in Question 16 of the 2005 Hunan College Entrance Examination Paper as examples illustrate the problem.