id: 06361437
dt: j
an: 2014f.00693
au: Aydin, Sinan
ti: Using example generation to explore studentsâ€™ understanding of the
concepts of linear dependence/independence in linear algebra.
so: Int. J. Math. Educ. Sci. Technol. 45, No. 6, 813-826 (2014).
py: 2014
pu: Taylor \& Francis, Abingdon, Oxfordshire
la: EN
cc: H65 D45 C35
ut: APOS; linear algebra education; linear dependence; student-generated
examples; linear independence
ci:
li: doi:10.1080/0020739X.2013.877606
ab: Summary: Linear algebra is a basic mathematical subject taught in
mathematics and science depar-tments of universities. The teaching and
learning of this course has always been difficult. This study aims to
contribute to the research in linear algebra education, focusing on
linear dependence and independence concepts. This was done by
introducing student-generated examples regarding the concepts. With the
help of these examples, we have analysed studentsâ€™ understanding of
linear dependence/independence and determined the effect of the
example-generation process on student understanding of linear algebra.
In addition, we identified some difficulties that were experienced by
students learning the concepts of linear dependence/independence. In
this study, APOS (action-process-object-schema) theory is the main tool
utilized to explain studentsâ€™ written responses. It was also used
with regard to the interview questions that were posed to students with
the purpose of identifying possible difficulties with linear
dependence/independence and observing the adequacy of the relations
that students might form between different elements of the genetic
decomposition of linear dependence/independence concepts. The findings
of this study confirmed that many students do not have appropriate
mental structures at object and schema levels. Moreover, in order to
ensure the success of such exercises, students must be encouraged to
review and validate their responses to the example requests.
rv: