id: 06304595
dt: j
an: 2014d.00525
au: Baker, William J.; Czarnocha, Bronislaw; Dias, Olen; Doyle, Kathleen;
Kennis, James R.; Prabhu, Vrunda
ti: Procedural and conceptual knowledge: adults reviewing fractions.
so: Adults Learn. Math. 7, No. 2, 39-65 (2012).
py: 2012
pu: Adults Learning Mathematics (ALM)
la: EN
cc: F48 C38
ut: adult education; research; teaching; learning; fractions; sub-constructs;
operator; measure; part-whole concept; concept formation; conceptual
knowledge; procedural knowledge; Piagetian theory; Kieren-Behr model;
APOS; concept development; measurement; multiplicative reasoning
ci: ME 2013d.00404
li: http://www.alm-online.net/images/ALM/journals/almij-volume7-2-dec-2012.pdf
ab: Summary: In the United States a majority of the students who enroll in
community colleges require a review of secondary math before they are
eligible for college level mathematics. In the pre-algebra course, that
has a high drop-out rate, the most difficult topic for students is
fractions. In order to better understand the fraction concept Kieren
separated it into five related sub-constructs. In Kieren’s model the
foundational sub-construct of part-whole provides a path to the
sub-constructs of ratio, operator, quotient and measure. This model was
previously investigated and found effective by Charalambous and Pitta
Pantazi with children and Baker, Dias, Doyle, Czarnocha and Prabhu with
adults. This article extends the earlier study of {\it W. Baker} et al.
[Didactica Mathematicae 32, 5‒41 (2009; ME 2013d.00404)] with adults
by considering an alternate pathway to competency with operator and
measure through multiplication and addition of fractions. This path is
based upon Piaget’s theories in which concepts develop through
reflection upon corresponding procedures. The goal is to show that the
path through direct extension of part-whole knowledge and the path
through procedural knowledge work together and complement one another
in explaining students’ competency with operator and measure. An open
question of whether measure is part of the multiplicative structure of
fractions is also addressed using a mixed methodology of quantitative
and qualitative analysis.
rv: