Kc. Fuson et al., LEVELS IN CONCEPTUALIZING AND SOLVING ADDITION AND SUBTRACTION COMPARE WORD-PROBLEMS, Cognition and instruction, 14(3), 1996, pp. 345-371
This article presents an analysis of conceptual and linguistic complex
ities of matching situations expressed as word problems and describes
possible ways of conceptualizing and solving such problems. Data from
first and second graders suggest a progression of four levels in conce
ptualizing and solving these problems. In the first-Relational-level,
children can answer ''Who has more/less?'' but not ''How much more/les
s?'' In the second-language Cue-level, children are more likely to sol
ve problems with action, Equalizing language (''If he gets 2 more cats
, he will have as many cats as dogs'') than with static, Compare langu
age (''He has 2 more dogs than cats''). They are especially likely to
solve problems in which finding the unknown compared quantity is direc
ted by keywords in the relational sentence. At the third-Understand Ma
tching Situations-level, children find Inconsistent problems (those in
which the relational sentence is opposite to the needed solution acti
on) considerably more difficult than other types. Children overwhelmin
gly solve problems in which one compared quantity is unknown by using
an Equalizing approach in which the Extra quantity is added to or take
n from the other known quantity. They predominantly solve problems in
which the difference between two known compared quantities is unknown
by using a Matching conception in which the Small quantity is taken fr
om the Big quantity. At the fourth-Solve Inconsistent-level, children
come to be able to solve Inconsistent problems, primarily by using Equ
alizing conceptions in which the relation given in the relational sent
ence is reversed.