Students’ understanding of the general notion of a function of two variables
Students’ understanding of the general notion of a function of two variables
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学生对二元函数一般概念的理解
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
María Trigueros Gaisman
中科院分区：
文献类型：
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作者：
Rafael Martínez;María Trigueros Gaisman
在这项研究中，我们分析了学生的二元函数的理解，特别是我们考虑他们的域的理解，可能的任意性质的函数分配，唯一性的函数图像，和范围。我们使用APOS理论和符号表征理论作为一个理论框架，分析数据从采访了十三名学生谁采取了多变量微积分课程。结果表明，很少有学生能够构建二元函数的客观概念。大多数学生表现出难以找到域的功能，特别是，当他们被限制在一个特定的区域在xy平面。他们还表明，他们没有完全协调他们的R3，集和功能的一个变量图式。我们的结论是，许多受访的学生的功能的概念可以被认为是前布尔巴基。
In this study we analyze students’ understanding of two-variable function; in particular we consider their understanding of domain, possible arbitrary nature of function assignment, uniqueness of function image, and range. We use APOS theory and semiotic representation theory as a theoretical framework to analyze data obtained from interviews with thirteen students who had taken a multivariable calculus course. Results show that few students were able to construct an object conception of function of two variables. Most students showed difficulties finding domains of functions, in particular, when they were restricted to a specific region in the xy plane. They also showed that they had not fully coordinated their R3, set, and function of one variable schemata. We conclude from the analysis that many of the interviewed students’ notion of function can be considered as pre-Bourbaki.