Examining the Conceptual and Procedural Knowledge of Decimal Numbers in Sixth-Grade Elementary School Students

Amalija Žakelj, Andreja Klančar
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Abstract

In this article, we present the results of empirical research using a combination of quantitative and qualitative methodology, in which we examined the achievements and difficulties of sixth-grade Slovenian primary school students in decimal numbers at the conceptual and procedural knowledge level. The achievements of the students (N = 100) showed that they statistically significantly (z = -7,53, p < .001) better mastered procedural knowledge (M = 0.60, SD = 0.22) than conceptual knowledge (M = 0.37, SD = 0.17) of decimal numbers. Difficulties are related to both procedural and conceptual knowledge, but significantly more students have difficulties at the level of conceptual knowledge. At the level of procedural knowledge, or in the execution of arithmetic operations with decimal numbers, we observed difficulties in transforming text notation into numerical expressions, difficulties in placing the decimal point in multiplication and division, and insufficient automation of mathematical operations with decimal numbers. At the level of conceptual knowledge of decimal numbers, the results indicate difficulties for students in understanding the place values of decimal numbers, in estimating the sum, product and quotient of decimals with reflection and in mathematical justification. In relation to difficulties in justification, we observed an insufficient understanding of the size relationship between decimal numbers and difficulties in expressing them in mathematical language. The results indicate that to overcome such difficulties in the learning and teaching of mathematics, more balance between procedural and conceptual knowledge is needed.
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考察六年级小学生的小数概念和程序知识
在本文中,我们采用定量和定性相结合的方法,对斯洛文尼亚小学六年级学生在十进制数的概念和程序知识层面的成绩和困难进行了研究,并介绍了实证研究的结果。学生(N = 100)的成绩显示,他们对十进制数的程序性知识(M = 0.60,SD = 0.22)的掌握程度(z = -7,53,P < .001)明显优于对概念性知识(M = 0.37,SD = 0.17)的掌握程度(z = -7,53,P < .001)。困难既与程序性知识有关,也与概念性知识有关,但在概念性知识层面上遇到困难的学生明显更多。在程序性知识层面,或者说在用小数进行运算时,我们发现学生在将文字符号转化为数字表达式时遇到困难,在乘除法中小数点的位置难以确定,以及用小数进行数学运算的自动化程度不够。在小數的概念知識方面,結果顯示學生在理解小數的位值、估算小數的和、積 和商的反映及數學理據方面有困難。在说明理由方面,我们发现学生对小数之间的大小关系理解不够,而且难以用数学语言表达。结果表明,要克服数学学习和教学中的这些困难,需要在程序性知识和概念性知识之间取得更多的平衡。
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来源期刊
European Journal of Educational Research
European Journal of Educational Research Social Sciences-Education
CiteScore
3.60
自引率
0.00%
发文量
184
审稿时长
4 weeks
期刊最新文献
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