<![CDATA[Prospective mathematics teachers should have met the Pirie-Kieren model of understanding indicators, to become professional teachers. The purpose of this research is to describe the layers of understanding structure that is filled by students of mathematics teacher prospectives. The description is based on a model hypothesized by Pirie-Kieren. Research subjects selected from female and male mathematics teacher prospective students have been given the task of understanding the concept of derivative functions and interviewed. Data collected from students’ answers from worksheets before the interview, students’ answers from worksheets during interviews, and interview transcripts. After the data were analyzed qualitatively, the description of the understanding layer structure of two subjects grouped by the original Pirie-Kieren Model was obtained. The subjects of female had met the indicators of primitive knowing, then there are the processes of image doing and image reviewing on the layer structure of image making towards image having, then image seeing and image saying on the layer of image having to property noticing, then there are the processes of property predicting and property recording on the layer of property noticing towards formalizing, then there are the processes of method applying and method justifying on the layer of formalizing towards observing, then there are the processes of future identifying and feature prescribing on the layer of observing towards structuring, and there are the prosesses of theorem conjecturing and theorem proving on the layer of structuring towards inventising. She almost fulfilled the inventising layer. Male subjects also meet the same understanding indicators as women. Both subjects have almost fulfilled a layer of creation, we called inventisingoid]]>
