How Dragging Changes Students’ Awareness: Developing Meanings for Eigenvector and Eigenvalue

Gol Tabaghi, Shiva1
1Faculty of Education, Simon Fraser University, Burnaby, Canada

Tóm tắt

The complementary use of the theories of instrumental genesis and shifts of attention enabled me to obtain insights into students’ understandings of the concepts of eigenvector and eigenvalue. My analysis suggests that the use of different dragging modalities can provide evidence of shifts in structure of a student’s attention and consequently can reveal processes involved in her understanding of the concepts. Inversely, shifts in structure of her attention can result in her use of different dragging modalities. I also identified a newdragging modality—intentionally dragging—that is, to drag a point with the intention of producing a certain configuration.

Tài liệu tham khảo

citation_journal_title=International Journal of Computers for Mathematics Learning; citation_title=Learning mathematics in a CAS environment: The genesis of a reflection about instrumentation and the dialectics between technical and conceptual work; citation_author=M Artigue; citation_volume=7; citation_publication_date=2002; citation_pages=245-274; citation_doi=10.1023/A:1022103903080; citation_id=CR1 citation_title=Representing mathematics with digital media: Integrative theoretical framework; citation_publication_date=2006; citation_id=CR2; citation_author=M Artigue; citation_author=R M Bottino; citation_author=M Cerulli; citation_author=C Kynigos; citation_author=J B Lagrange; citation_author=M Maracci; citation_author=C Morgan citation_journal_title=Zentralblatt fuer Didaktik der Mathematik; citation_title=A cognitive analysis of dragging practises in Cabri environment; citation_author=F Arzarello, F Olivero, D Paola, O Robutti; citation_volume=34; citation_issue=3; citation_publication_date=2002; citation_pages=66-72; citation_doi=10.1007/BF02655708; citation_id=CR3 citation_journal_title=The College Mathematics Journal; citation_title=The linear Algebra Curriculum Study Group recommendations for the first course in linear algebra; citation_author=D Carlson, C R Johnson, D C Lay, A D Porter; citation_volume=24; citation_issue=1; citation_publication_date=1993; citation_pages=41-46; citation_doi=10.1080/07468342.1993.11973504; citation_id=CR4 citation_title=Mathematizing and symbolising: The emergence of chains of signification in one first-grade classroom; citation_inbook_title=Situated cognition theory: Social, semiotic, and neurological perspectives; citation_publication_date=1997; citation_pages=151-233; citation_id=CR5; citation_author=P Cobb; citation_author=K P E Gravemeijer; citation_author=E Yackel; citation_author=K McClain; citation_author=J Whitenack; citation_publisher=Lawrence Erlbaum Associates citation_title=From artifacts to instruments: A theoretical framework behind the orchestra metaphor; citation_inbook_title=The mathematics teacher in the digital era; citation_publication_date=2013; citation_id=CR6; citation_author=P Drijvers; citation_publisher=Springer citation_journal_title=Mathematics Education and Technology—Rethinking the Terrain; citation_title=Integrating technology into mathematics education: Theoretical perspectives; citation_author=P Drijvers, C Kieran, M A Mariotti, J Ainley, M Andresen, Y C Chan, M Meagher; citation_volume=2; citation_publication_date=2010; citation_pages=89-132; citation_id=CR7 citation_journal_title=Annales de didactique et de sciences cognitives; citation_title=Signe et object [Sign and object], I, II; citation_author=R Duval; citation_volume=6; citation_publication_date=1998; citation_pages=139-163; citation_id=CR8 citation_title=The science of education part 1: Theoretical considerations; citation_publication_date=1987; citation_id=CR9; citation_author=C Gattegno; citation_publisher=Educational Solutions citation_journal_title=International Journal of Computers for Mathematical Learning; citation_title=The complex process of converting tools into mathematical instruments: The case of calculators; citation_author=D Guin, L Trouche; citation_volume=3; citation_publication_date=1999; citation_pages=195-227; citation_doi=10.1023/A:1009892720043; citation_id=CR10 citation_title=Modes of description and the problem of representation in linear algebra; citation_inbook_title=On the teaching of linear algebra; citation_publication_date=2000; citation_pages=191-207; citation_id=CR11; citation_author=J Hillel; citation_publisher=Kluwer Academic citation_title=The geometer’s sketchpad; citation_publication_date=1991; citation_id=CR12; citation_author=N Jackiw; citation_publisher=Key Curriculum Press citation_journal_title=International Journal of Computers for Mathematical Learning; citation_title=Complex calculators in the classroom: Theoretical and practical reflections on teaching precalculus; citation_author=JB Lagrange; citation_volume=4; citation_issue=1; citation_publication_date=1999; citation_pages=51-81; citation_doi=10.1023/A:1009858714113; citation_id=CR13 citation_title=Linear algebra and its applications; citation_publication_date=2006; citation_id=CR14; citation_author=D C Lay; citation_publisher=Addison-Wesley Publisher citation_title=Influence of technologies advances in students’ math learning; citation_inbook_title=Handbook of international research in mathematics education; citation_publication_date=2002; citation_pages=695-723; citation_id=CR15; citation_author=M A Mariotti; citation_publisher=LEA Publishers citation_journal_title=Research in Mathematics Education; citation_title=Proof and proving in the classroom: Dynamic geometry systems as tools of semiotic mediation; citation_author=M A Mariotti; citation_volume=14; citation_issue=2; citation_publication_date=2012; citation_pages=163-185; citation_doi=10.1080/14794802.2012.694282; citation_id=CR16 citation_journal_title=International handbook of mathematics teacher education; citation_title=Being mathematical with and in front of learners: Attention, awareness, and attitude as sources of differences between teacher educators, teachers and learners; citation_author=J Mason; citation_volume=4; citation_publication_date=2008; citation_pages=31-56; citation_id=CR17 citation_title=Tool building: Web-based linear algebra modules; citation_inbook_title=Journal of Online Mathematics and Its Applications; citation_publication_date=2005; citation_id=CR18; citation_author=D E Meel; citation_author=T A Hern citation_journal_title=Canadian Journal of Science, Mathematics and Technology Education; citation_title=Justifications-on-demand as a device to promote shifts of attention associated with relational thinking in elementary arithmetic; citation_author=M Molina, J Mason; citation_volume=9; citation_issue=4; citation_publication_date=2009; citation_pages=224-242; citation_doi=10.1080/14926150903191885; citation_id=CR19 citation_journal_title=Journal of Mathematical Behavior; citation_title=On ways of symbolizing: The case of Laura and the velocity sign; citation_author=R C Nemirovsky; citation_volume=13; citation_publication_date=1994; citation_pages=389-422; citation_doi=10.1016/0732-3123(94)90002-7; citation_id=CR20 citation_title=A study of students’ theoretical thinking in a technology-assisted environment; citation_publication_date=2008; citation_id=CR21; citation_author=A Pruncut citation_title=On some aspects of students’ thinking in linear algebra; citation_inbook_title=On the teaching of linear algebra; citation_publication_date=2000; citation_pages=209-246; citation_id=CR22; citation_author=A Sierpinska; citation_publisher=Kluwer Academic citation_journal_title=Recherches en Didactique des Mathematique; citation_title=Evaluation of a teaching design in linear algebra: The case of linear transformations; citation_author=A Sierpinska, T Deyfus, J Hillel; citation_volume=19; citation_issue=1; citation_publication_date=1999; citation_pages=7-41; citation_id=CR23 citation_journal_title=European Journal of Psychology of Education; citation_title=Cognition and artifacts: Acontribution to the study of thought in relation to instrumented activity; citation_author=P Verillon, P Rabardel; citation_volume=9; citation_issue=3; citation_publication_date=1995; citation_pages=77-101; citation_doi=10.1007/BF03172796; citation_id=CR24 citation_title=Mind in society: The development of higher psychological processes; citation_publication_date=1978; citation_id=CR25; citation_author=L S Vygotsky; citation_publisher=Harvard University Press