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    赵思林. 论数学全息定义与教学[J]. 内江师范学院学报, 2018, (12): 19-23. DOI:10.13603/j.cnki.51-1621/z.2018.12.004
    引用本文: 赵思林. 论数学全息定义与教学[J]. 内江师范学院学报, 2018, (12): 19-23.DOI:10.13603/j.cnki.51-1621/z.2018.12.004
    shu
    ZHAO Silin. On Definition of Holographic and Teaching in Mathematics[J]. Journal of Neijiang Normal University, 2018, (12): 19-23. DOI:10.13603/j.cnki.51-1621/z.2018.12.004
    Citation: ZHAO Silin. On Definition of Holographic and Teaching in Mathematics[J].Journal of Neijiang Normal University, 2018, (12): 19-23.DOI:10.13603/j.cnki.51-1621/z.2018.12.004
    shu

    论数学全息定义与教学

    On Definition of Holographic and Teaching in Mathematics

      摘要
    • 摘要:如果一个数学定义包含该定义的被定义项的全部信息 (包括性质等) , 那么这个定义是全息定义.从全息的角度来看, 数学定义可以分为全息定义和非全息定义两类.比如, 对数定义是全息定义, 人教A版新教材三角函数定义是全息定义, 而方程的定义、一元二次方程的定义、不等式的定义等是非全息定义.对于全息定义, 从建构数学科学体系的角度来看它是好的定义, 但从教学的角度来看它是既难教更难学的定义.全息定义和非全息定义的教学有较大区别, 全息定义一般应强化, 而非全息定义一般宜淡化.

      Abstract:
      If a mathematical definition contains all the information of the defined item including properties etc, then such a definition is a holographic definition.From the holographic point of view, mathematical definition can be divided into two categories:holographic and non-holographic definition.For example, the definition of logarithm is holographic, so is the definition of trigonometric functions in the new teaching material by People’s Education Press.But none of the definitions of equation, quadratic equation and inequality is holographic.The holographic definition is good from the perspective of constructing the system of the mathematics science.Yet from the perspective of pedagogy, one will find it difficult to teach and learn a holographic definition.The teaching of holographic and non-holographic definitions differs significantly with emphasis placed on the former and deemphasis on the latter.

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