Page 415 - Istenič Andreja, Gačnik Mateja, Horvat Barbara, Kukanja Gabrijelčič Mojca, Kiswarday Vanja Riccarda, Lebeničnik Maja, Mezgec Maja, Volk Marina. Ur. 2023. Vzgoja in izobraževanje med preteklostjo in prihodnostjo. Koper: Založba Univerze na Primorskem
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The Development of Strategies for Solving Arithmetic Word Problems
trast, good problem-solvers are more likely to employ the problem model
strategy: they begin by trying to construct a mental model of the situa-
tion described in the problem and plan their solution on the basis of this
model (Pape 2003). This theory received support from several empirical stud-
ies. Hegarty and colleagues (1995) compared eye fixations of successful and
unsuccessful problem-solvers when attempting to solve consistent and in-
consistent problems and found that unsuccessful problem-solvers focused
significantly more on relational terms and numbers compared to their suc-
cessful peers. This finding from this eye-tracking study confirmed the idea
that unsuccessful problem-solvers use the direct-translation strategy.
As far as consistent problems are concerned, the superficial direct-transla-
tion approach can still result in accurate solutions. Indeed, in consistent word
problems the required mathematical operation can be derived straightfor-
wardly from the keyword. There is no need to internally or externally rep-
resent the described problem situation to reach the solution (Koning et al.
2022).
On the other hand, in inconsistent word problems the required mathemat-
ical operation cannot be directly derived from the relational term because
the language employed in the word problem evokes an inappropriate math-
ematical operation. Thus, the superficial direct-translation strategy is inad-
equate to accurately solve the exercise. Rather, solvers need to engage with
the problem model strategy and construct a coherent mental representation
of the problem situation. In doing so, the solver needs to engage in additional
cognitive processing: integrating text information, selecting relevant infor-
mation and excluding the irrelevant, inferring missing elements, and, most
importantly, dealing with inconsistent language (Kintsch and Greeno 1985).
From a psychological point of view, the construction of the mental repre-
sentation of the problem requires several cognitive abilities. Besides good
reading comprehension skills necessary to properly understand the prob-
lem text (Fuchs et al. 2015), working memory seems to play a pivotal role
(Andersson 2007). Working memory is defined as a limited capacity cogni-
tive system that allows individuals to hold and simultaneously manipulate
information over brief periods of time (Baddeley and Hitch 1974). Thus, it
allows the solver to maintain, integrate and organize verbal and numerical
information retrieved from the text into a mental representation. Addition-
ally, several studies highlighted the importance of inhibition and updating
in problem-solving and, specifically, in the construction of the mental model
(Passolunghi et al. 2022). Inhibition is defined as the ability to suppress irrel-
evant information and to inhibit dominant or prepotent responses, whereas
415
trast, good problem-solvers are more likely to employ the problem model
strategy: they begin by trying to construct a mental model of the situa-
tion described in the problem and plan their solution on the basis of this
model (Pape 2003). This theory received support from several empirical stud-
ies. Hegarty and colleagues (1995) compared eye fixations of successful and
unsuccessful problem-solvers when attempting to solve consistent and in-
consistent problems and found that unsuccessful problem-solvers focused
significantly more on relational terms and numbers compared to their suc-
cessful peers. This finding from this eye-tracking study confirmed the idea
that unsuccessful problem-solvers use the direct-translation strategy.
As far as consistent problems are concerned, the superficial direct-transla-
tion approach can still result in accurate solutions. Indeed, in consistent word
problems the required mathematical operation can be derived straightfor-
wardly from the keyword. There is no need to internally or externally rep-
resent the described problem situation to reach the solution (Koning et al.
2022).
On the other hand, in inconsistent word problems the required mathemat-
ical operation cannot be directly derived from the relational term because
the language employed in the word problem evokes an inappropriate math-
ematical operation. Thus, the superficial direct-translation strategy is inad-
equate to accurately solve the exercise. Rather, solvers need to engage with
the problem model strategy and construct a coherent mental representation
of the problem situation. In doing so, the solver needs to engage in additional
cognitive processing: integrating text information, selecting relevant infor-
mation and excluding the irrelevant, inferring missing elements, and, most
importantly, dealing with inconsistent language (Kintsch and Greeno 1985).
From a psychological point of view, the construction of the mental repre-
sentation of the problem requires several cognitive abilities. Besides good
reading comprehension skills necessary to properly understand the prob-
lem text (Fuchs et al. 2015), working memory seems to play a pivotal role
(Andersson 2007). Working memory is defined as a limited capacity cogni-
tive system that allows individuals to hold and simultaneously manipulate
information over brief periods of time (Baddeley and Hitch 1974). Thus, it
allows the solver to maintain, integrate and organize verbal and numerical
information retrieved from the text into a mental representation. Addition-
ally, several studies highlighted the importance of inhibition and updating
in problem-solving and, specifically, in the construction of the mental model
(Passolunghi et al. 2022). Inhibition is defined as the ability to suppress irrel-
evant information and to inhibit dominant or prepotent responses, whereas
415
