A student's conceiving a pattern of change between two varying quantities in a quadratic functional situation and its representations: The case of Min-Seon

• Journal title : The Mathematical Education
• Volume 54, Issue 4,  2015, pp.299-315
• Publisher : Korea Society of Mathematical Education
• DOI : 10.7468/mathedu.2015.54.4.299
Title & Authors
A student's conceiving a pattern of change between two varying quantities in a quadratic functional situation and its representations: The case of Min-Seon
Lee, Dong Gun; Moon, Min Joung; Shin, Jaehong;

Abstract
The aim of this qualitative case study is twofold: 1) to analyze how an eleventh-grader, Min-Seon, conceive and represent a pattern of change between two varying quantities in a quadratic functional situation, and 2) further to help her form a concept of 'derivative' as a tool to express the relationship with employing a concept of 'rate of change.' The result indicates that Min-Seon was able to construct graphs of piecewise functions that take average rates of change as range of the functions, and managed to conjecture the derivative of a quadratic function, $\small{y=x^2}$. In conclusion, we argue that covariational approach could not only facilitate students' construction of an initial function concept, but also support their understanding of the concept of 'derivative.'
Keywords
covariational reasoning;rate of change;quadratic function;exponential function;derivative;
Language
Korean
Cited by
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