Students' Use of Prior Conceptions of Symbols in Finding an Equation for a Horizontal Translation of the Graph of a Function.

Research has identified some sources of student difficulty in understanding the horizontal translation of a function. The present study presents and focuses on another source for the difficulties: student conceptions of symbols involved in the horizontal translation of the graph of a function. We explored which student conceptions of the symbols f, x, and y are problematic or supportive in finding the equation of the translated graph when a given graph of y = f(x) is translated −2 units horizontally. For example, student conceptions of x as a general label for any point on the x-axis or as an independent variable of only a given original function emerged as problematic, while a conception of x as an independent variable of a function to describe was supportive. It seemed crucial for students to recruit some background ideas about horizontal translation in order to activate the supportive conceptions of f, x, and y and make them powerful. Our study suggests that horizontal translation of the graph of a function provides an opportunity for students to reflect on their prior conceptions of f, x, and y and restructure the conceptions to be comprehensive. [ABSTRACT FROM AUTHOR]