id: 06239243
dt: j
an: 2014a.00531
au: McGowen, Mercedes A.; Tall, David O.
ti: Flexible thinking and met-befores: impact on learning mathematics.
so: J. Math. Behav. 32, No. 3, 527-537 (2013).
py: 2013
pu: Elsevier, New York, NY
la: EN
cc: E45 C35 D75
ut: flexible thinking; met-befores; mathematical symbols; minus sign;
supportive aspects of function; problematic aspects of minus sign;
formative assessment
ci:
li: doi:10.1016/j.jmathb.2013.06.004
ab: Summary: In this paper we study the difficulties resulting from changes in
meaning of the minus sign, from an operation on numbers, to a sign
designating a negative number, to the additive inverse of an algebraic
symbol on students in two-year colleges and universities. Analysis of
the development of algebra reveals that these successive meanings that
the student has met before often become problematic, leading to a
fragile knowledge structure that lacks flexibility and leads to
confusion and long-term disaffection. The problematic aspects that
arise from changes in meaning of the minus sign are identified and the
iconic function machine is utilized as a supportive strategy, along
with formative assessment to encourage teachers and learners to seek
more flexible and effective ways of making sense of increasingly
sophisticated mathematics.
rv: