Investigating Students' Modes of Thinking in Linear Algebra: The Case of Linear Independence

Autor/in	Çelik, Derya
Titel	Investigating Students' Modes of Thinking in Linear Algebra: The Case of Linear Independence
Quelle	In: International Journal for Mathematics Teaching and Learning, (2015), (22 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1473-0111
Schlagwörter	Algebra; Mathematics Instruction; Mathematical Concepts; Concept Formation; Problem Solving; Preservice Teachers; Mathematics Teachers; Interviews; Cognitive Processes; Qualitative Research; Content Analysis; Arithmetic; Geometry; Secondary School Mathematics; Undergraduate Study; Grade 6; Grade 5; Grade 8; Grade 7; Comparative Analysis; Classification + Suchen Sie Ihr Suchwort? Mathematics lessons; Mathematikunterricht; Concept learning; Begriffsbildung; Problemlösen; Mathematics; Teacher; Teachers; Mathematik; Lehrer; Lehrerin; Lehrende; Interviewing; Interviewtechnik; Cognitive process; Kognitiver Prozess; Qualitative Forschung; Inhaltsanalyse; Addition; Arithmetik; Arithmetikunterricht; Rechnen; Geometrie; Grundstudium; School year 06; 6. Schuljahr; Schuljahr 06; School year 05; 5. Schuljahr; Schuljahr 05; School year 08; 8. Schuljahr; Schuljahr 08; School year 07; 7. Schuljahr; Schuljahr 07; Classification system; Klassifikation; Klassifikationssystem
Abstract	Linear algebra is one of the most challenging topics to learn and teach in many countries. To facilitate the teaching and learning of linear algebra, priority should be given to epistemologically analyze the concepts that the undergraduate students have difficulty in conceptualizing and to define their ways of reasoning in linear algebra. After the initial conditions are granted, pedagogical arrangements should be made. From this point of view, this study aims to explore undergraduate students' ways of thinking while solving problems in the abstract mode about linearly independent/dependent vectors. It also focuses on what students understood about linear independence/dependence concepts. The study was conducted with 186 mathematics teacher-candidates. The responses of these students to four problems and interview data conducted with eight students were used to identify a student's way of thinking. During qualitative analysis of the responses, Sierpinska's (2000) framework for thinking modes was adopted by the researcher. The content analysis revealed 15 categories of thought modes: 12 arithmetic, 2 geometric, and 1 structural. In arithmetic thinking mode (approximately 68% of the participants), the majority of students presented inappropriate solutions, including mistakes related to operational procedures for the problems in the abstract mode. The responses in geometric thinking mode (10%) were indicators of obstacles related to mathematical generalization. Furthermore, the response ratio in structural mode of thinking was very low (5%). In conclusion, the findings support the view of the inconsistency between the thinking modes of students and the abstract nature of linear algebra problems. (As Provided).
Anmerkungen	Centre for Innovation in Mathematics Teaching. 5th Floor Rolle Building, Faculty of Education University of Plymouth, Drake Circus, Plymouth, PL4 8AA, UK. Tel: +44-1752-585346; Fax: +44-1752-585344; e-mail: feedback@cimt.org.uk; Web site: http://www.cimt.plymouth.ac.uk/journal/
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01