Conceptions of function translation: obstacles, intuitions, and rerouting |
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Authors: | Rina Zazkis Peter LiljedahlKaren Gadowsky |
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Institution: | a Faculty of Education, Simon Fraser University, 8888 University Drive, Burnaby V5A 1S6, BC, Canada b Delta Secondary School, BC, Canada |
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Abstract: | A horizontal translation of a function is the focus of this study. We examine the explanations provided by secondary school students and secondary school teachers to a translation of a function, focusing on the example of the parabola y=(x−3)2 and its relationship to y=x2. The participants’ explanations focused on attending to patterns, locating the zero of the function, and the point-wise calculation of function values. The results confirm that the horizontal shift of the parabola is, at least initially, inconsistent with expectations and counterintuitive to most participants. We articulate possible sources of this perceived inconsistency and describe a pedagogical approach aimed at resolving it. |
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Keywords: | Function Transformation Translation Obstacle Transformation of function Horizontal translation |
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