![]() Since difficulties with learning linear algebra by average students are universally acknowledged, it is anticipated that this study may provide suggestions with the potential for widespread positive consequences for learning.īu çalışmanın amacı, ilköğretim matematik öğretmeni adaylarının görsel ve cebirsel temsillerle verilen doğrunun ve çemberin analitiği ile ilgili problemleri çözerken benimsedikleri yaklaşımları incelemektir. In particular the embodied introduction of the concept proved a valuable adjunct to their thinking. However, they also revealed that those with more representational diversity had more overall understanding of the concepts. The results suggest that the students had limited understanding of the concepts, they struggled to recognise the concepts in different registers, and their lack of ability in linking the major concepts became apparent. As part of this research project several case studies were conducted where groups of first and second year students were exposed to teaching and learning some introductory linear algebra concepts based on the framework and expressed their thinking through their involvements in tests, interviews and concept maps. The aim is to investigate the difficulties in understanding some linear algebra concepts and to propose potential paths for preventing them. This research proposes applying APOS theory, in conjunction with Tall’s three worlds of embodied, symbolic and formal mathematics, to create a framework in order to examine the learning of a variety of linear algebra concepts by groups of first and second year university students. The transfer from a primarily procedural or algorithmic school approach to an abstract and formal presentation of concepts through concrete definitions, seems to be creating difficulty for many students who are barely coping with procedural aspects of the subject. Linear algebra is one of the first advanced mathematics courses that students encounter at university level. The conclusion of this study was that the mathematical process of students using realistic selfie culture can achieve the multiplication of two vectors which form right angles. This was one of the multiplication properties of two perpendicular vectors. The results of this study were the mathematical process of students in understanding the concept of vector by using selfie culture. Data was collected during the realistic mathematics learning process using the ethnomathematics approach. Observation sheets, anecdotes and interview guides were the instruments of this research. The subjects of this study were 38 high school students in Bengkulu. This research was the prototype stage of development research. The purpose of this study was to describe the mathematical process of students in understanding vector concepts through learning realistic mathematics and ethnomathematics. Realistic mathematics learning with ethnomathematics approach makes it easy for students to learn mathematics. The concept of vector was one of concepts that was difficult for students to understand. We infer that it is not enough for lecturers to simply be using the technology but that its use needs explicit and sustained attention. Our research supports the view that instrumentation of CAS calculators does not occur naturally or spontaneously, even when students desire to integrate the technology. Generally they only used the CAS procedurally, usually employing it to check answers or to perform single step direct calculations to calculate, for example a determinant, or an inverse, of a matrix. We found that the cost of the technology is an issue preventing many from obtaining it, and that those few students who did choose to purchase and use the CAS did not often use it to improve understanding of conceptual ideas. This was the first time that most of these students had used the CAS, and so we considered issues associated with their initial instrumentation of the CAS and their attitudes to using it in their learning. This research considered the reactions of a group of these first year university students to the use of the CAS calculator in their learning of linear algebra. At Auckland University computer algebra system (CAS) calculators have, in recent years, been made available to beginning students of linear algebra. Many of them find a number of aspects of linear algebra difficult to learn and often seem to prefer to engage in procedural manipulations rather than a study of the underlying concepts and ideas. While a relatively small group of researchers internationally has addressed some of the problems in the learning of linear algebra, including the use of technology, there are still many problems for students.
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