PROFIL LAPISAN PEMAHAMAN MAHASISWA CALON GURU (Universitas Dr. Soetomo, 2015)
At the end of the decade was diverse any researches has been done regarding understanding. Pegg and Tall (2005) identified two types of theories of cognitive growth of global and local. Dubinsky with APOS theory (action, process, object, scheme), Pirie & Kieren with the model of understanding.layer (level). Pirie &Kieren (1994) has provided a theoretical framework of eight levels (layers) of understanding, namely; i) primitive knowing, ii) image making, iii) image having, iv) property noticing, v) formalizing, vi) observing, vii) structuring and viii) inventising. Martin (2008) describes a framework in folding back the three elements, namely i) the source of folding back, ii) the form of folding back and iii) the results of folding back. Guided by the model Pirie & Kieren and indicator of the form of folding back of Martin, research was conducted on student teachers. Devices in the interview given problem based task is to find the derivative of function f(x) = (2x + 4)4(1-3x)5. After the interview was analyzed, be concluded that: 1. The subject with high-math capable outermost achieving layer of understanding that inventising. This subject meets the indicators understanding of image making, image having, property noticing, observing, formlising, structuring. Even up to the last layer of the subjects had a complete understanding of the derivative function structured form of the product of two polynomial functions, answering questions, write and explain the application of the concept of the derivative function in Physics. 2. The subject of being reached lining mathematical capable outermost achieving layer of understanding primitive knowing, not reaching the formalizing because he only uses derivative chain rule function composition, but are not able to mention the name of the rule. This subject did folding back form