id: 05807703
dt: j
an: 2010f.00340
au: Thomas, Michael O.J.; Wilson, Anna J.; Corballis, Michael C.; Lim, Vanessa
K.; Yoon, Caroline
ti: Evidence from cognitive neuroscience for the role of graphical and
algebraic representations in understanding function.
so: ZDM, Int. J. Math. Educ. 42, No. 6, 607-619 (2010).
py: 2010
pu: Springer, Berlin/Heidelberg
la: EN
cc: C35 M65 C85 I25
ut: representation; conversion; functional magnetic resonance imaging (fMRI);
versatility; mathematical cognition; functions; graph of a function;
cognitive neuroscience; university students; empirical investigations
ci:
li: doi:10.1007/s11858-010-0272-7
ab: Summary: Using traditional educational research methods, it is difficult to
assess studentsâ€™ understanding of mathematical concepts, even though
qualitative methods such as task observation and interviews provide
some useful information. It has now become possible to use functional
magnetic resonance imaging (fMRI) to observe brain activity whilst
students think about mathematics, although much of this work has
concentrated on number. In this study, we used fMRI to examine brain
activity whilst ten university students translated between graphical
and algebraic formats of both linear and quadratic mathematical
functions. Consistent with previous studies on the representation of
number, this task elicited activity in the intra-parietal sulcus, as
well as in the inferior frontal gyrus. We also analysed qualitative
data on participantsâ€™ introspection of strategies employed when
reasoning about function. Expert participants focused more on key
properties of functions when translating between formats than did
novices. Implications for the teaching and learning of functions are
discussed, including the relationship of function properties to
difficulties in conversion from algebraic to graphical representation
systems and vice versa, the desirability of teachers focusing attention
on function properties, and the importance of integrating graphical and
algebraic function instruction.
rv: