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Early Developmental Trajectories Toward Concepts of Rational Numbers

机译：朝着有理数概念的早期发展轨迹

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摘要

Difficulties with rational numbers have been explained by a natural number bias, where concepts of natural numbers are inappropriately applied to rational numbers. Overcoming this difficulty may require a radical restructuring of previous knowledge. In order to capture this development, we examined third- to fifth-grade students' understanding of the size of rational numbers across a 1-year period. On three occasions, students answered a test about the size of decimals and fractions. Latent transition analysis allowed profiling five different rational number size concepts and mapping students' developmental trajectories during the early learning of this topic. Development from natural number-based reasoning to mathematically correct understanding was almost nonexistent during this time period. Instead, students appear to move through intermediary concepts. Locating these temporary and mediating number concepts supports the idea of a slow and gradually developing conceptual change in rational numbers.
机译：有理数的困难已由自然数偏差解释，其中自然数的概念不适当地应用于有理数。克服这一困难可能需要对先前的知识进行彻底的重组。为了捕捉这种发展，我们研究了三年级至五年级学生对一年内有理数大小的理解。学生有3次回答了有关小数和小数大小的测试。潜在的过渡分析允许概要分析五个不同的有理数大小概念，并在此主题的早期学习期间绘制学生的发展轨迹。在此期间，从基于自然数的推理到数学上正确理解的发展几乎不存在。相反，学生似乎在经历中介概念。找到这些临时的和中介的数字概念将支持有理数在概念上的缓慢而逐步发展的想法。

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  • 来源
    《Cognition and instruction》 |2017年第1期|4-19|共16页
  • 作者

    Kainulainen Mikko; McMullen Jake; Lehtinen Erno;

  • 作者单位

    Univ Turku, Dept Teacher Educ, SF-20500 Turku, Finland|Univ Turku, Ctr Learning Res, SF-20500 Turku, Finland;

    Univ Turku, Dept Teacher Educ, SF-20500 Turku, Finland|Univ Turku, Ctr Learning Res, SF-20500 Turku, Finland;

    Univ Turku, Dept Teacher Educ, SF-20500 Turku, Finland|Univ Turku, Ctr Learning Res, SF-20500 Turku, Finland;

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