Signifying the accumulation graph in a dynamic and multi-representation environment
Signifying the accumulation graph in a dynamic and multi-representation environment
复制标题
在动态和多表示环境中表示累积图
DOI：
10.1007/s10649-011-9356-8
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发表时间：
2012
影响因子：
3.2
通讯作者：
Osama Swidan
中科院分区：
文献类型：
--
作者：
Michal Yerushalmy;Osama Swidan
本研究的重点是在一个单一的变量函数的集成涉及的积累过程。观察两个高中微积分学生谁还没有学到任何其他积分相关的想法的工作，我们分析了出现的符号之间的关系，个人和数学意义，通过理解数学符号的整合任务。采用拉德福的教育观点，即学习被定义为一个客观化的过程，我们确定了一个三阶段的演变的双重符号意义的下边界和它的作用，在定义的积累图：（1）将与下限相关的零累积客观化，（2）将零客观化为标记累积面积的零和，以及（3）将累积图对象化为依赖于下限值。这种演变的标志是符号的变化有关的关键作用的“零”的积累图。
The present study focuses on the accumulation process involved in the integration of a single-variable function. Observing the work of two high-school calculus students who had not yet learned any other integral-related ideas, we analyze the emergence of the semiotic relationship between personal and mathematical meanings, as expressed through the understanding of mathematical signs in integration tasks. Adopting Radford's educational perspective whereby learning is defined as a process of objectification, we identify a three-stage evolution of the double semiotic meaning of the lower boundary and of its role in the definition of the accumulation graph: (1) objectifying a zero accumulation in relation to the lower limit, (2) objectifying zero as marking the zero sum of accumulated areas, and (3) objectifying the accumulation graph as dependent on the lower-limit value. This evolution is marked by semiotic changes related to the pivotal role of the “zeros” in the accumulation graph.