Yliopisto-opiskelijoiden väärinymmärrykset integraalilaskennassa insinöörimatematiikan opintojaksoilla

This thesis studies the errors made by first-year engineering mathematics students in integral calculus and the misconceptions that lie behind those errors. The errors are examined to study the differences between the conceptual and procedural proficiency of the students between the two methods of teaching. The methods are called flipped and traditional models. The flipped model follows the flipped learning ideology, which highlights student-centered learning as well as supports the intrinsic motivation of the students. Instead of traditional lectures the students in the flipped model familiarized themselves with the subject independently using i.e. videos. In the traditional model, the students were offered two lectures each week to familiarize themselves with the subject. The participants of the study consisted of 35 students with the lowest scores in the entry-level test. 11 of them studied in the flipped model and 24 studied in the traditional model. The research material was collected from examination problems concerning integral calculus in engineering mathematics courses 1 and 3 during the academic year 2019-2020. The material was analyzed following a theory-driven content analysis. The errors made by the students were divided into classes, which were categorized either as procedural or conceptual errors. The material was also analyzed using quantitative methods. The qualitative results of the analysis state that the procedural errors made by the students belong to four classes. These classes were integrating factors separate, errors in integrating composite functions, errors in limits of definite integrals, and confusing derivation with integration. The conceptual errors were mostly identified through notes made by the students. Conceptual errors were divided into three classes based on the concept that the misconception was related to. The concepts were definite integral, antiderivative, and integration. The results also showed that students in the flipped model made fewer conceptual errors than the ...