Hähkiöniemi, Markus2024-09-042024-09-042007-06-01Teaching Mathematics and Computer Science, Vol. 5 No. 1 (2007) , 81-971589-7389https://hdl.handle.net/2437/379598This paper reports how an advanced 11th-grade student (Daniel) perceived the derivative from a graph of a function at a task-based interview after a short introduction to the derivative. Daniel made very impressive observations using, for example, the steepness and the increase of a graph as well as the slope of a tangent as representations of the derivative. He followed the graphs sequentially and, for example, perceived where the derivative is increasing/decreasing. Gestures were an essential part of his thinking. Daniel's perceptions were reflected against those of a less successful student reported previously [Hähkiöniemi, NOMAD 11, no. 1 (2006)]. Unlike the student of the previous study, Daniel seemed to use the representations transparently and could see the graph as a representation of the derivative.application/pdfcase studyderivativeembodied worldgesturegraphrepresentationtransparencyfolyóiratcikkOpen AccessMarkus Hähkiöniemihttps://doi.org/10.5485/TMCS.2007.0140Teaching Mathematics and Computer Science15Teach. Math. Comp. Sci.2676-8364