
06239243
j
2014a.00531
McGowen, Mercedes A.
Tall, David O.
Flexible thinking and metbefores: impact on learning mathematics.
J. Math. Behav. 32, No. 3, 527537 (2013).
2013
Elsevier, New York, NY
EN
E45
C35
D75
flexible thinking
metbefores
mathematical symbols
minus sign
supportive aspects of function
problematic aspects of minus sign
formative assessment
doi:10.1016/j.jmathb.2013.06.004
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 twoyear 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 longterm 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.