id: 06676040
dt: j
an:
au: Robinson, Katherine M.; Dubé, Adam K.; Beatch, Jacqueline-Ann
ti: Children’s understanding of additive concepts.
so: J. Exp. Child Psychol. 156, 16-28 (2017).
py: 2017
pu: Elsevier, Amsterdam
la: EN
cc: F32 F33 C32 C33
ut: arithmetic; conceptual knowledge; addition; subtraction; identity;
negation; commutativity; inversion; associativity; equivalence
ci:
li: doi:10.1016/j.jecp.2016.11.009
ab: Summary: Most research on children’s arithmetic concepts is based on one
concept at a time, limiting the conclusions that can be made about how
children’s conceptual knowledge of arithmetic develops. This study
examined six arithmetic concepts (identity, negation, commutativity,
equivalence, inversion, and addition and subtraction associativity) in
Grades 3, 4, and 5. Identity ($a-0=a$) and negation ($a-a=0$) were well
understood, followed by moderate understanding of commutativity
($a+b=b+a$) and inversion ($a+b-b=a$), with weak understanding of
equivalence ($a+b+c=a+[b+c]$) and associativity ($a+b-c$=$[b-c]+a$).
Understanding increased across grade only for commutativity and
equivalence. Four clusters were found: The Weak Concept cluster
understood only identity and negation; the Two-Term Concept cluster
also understood commutativity; the Inversion Concept cluster understood
identity, negation, and inversion; and the Strong Concept cluster had
the strongest understanding of all of the concepts. Grade 3 students
tended to be in the Weak and Inversion Concept clusters, Grade 4
students were equally likely to be in any of the clusters, and Grade 5
students were most likely to be in the Two-Term and Strong Concept
clusters. The findings of this study highlight that conclusions about
the development of arithmetic concepts are highly dependent on which
concepts are being assessed and underscore the need for multiple
concepts to be investigated at the same time.
rv: