Abstract
Research in undergraduate mathematics education has been active very recently. The purpose of the paper is to investigate how college students make ion from some known informations about integer and rational numbers in algebra. Three college students were involved in the study. We analyze student`s personal answers in order to find where their misunderstandings and difficulties come from based on the theoretical frameworks on mathematical understanding such as APOS-model and P-K-model. Finally we discuss about constructivist teaching ways for algebra and propose new paradigm for teaching undergraduate mathematics.
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