Page 414 - 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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onora Doz, Mara Cotič, and Maria Chiara Passolunghi
Compare word problems contain a relational statement (e.g. more than,
less than) that compares in a static manner the numerical values of two vari-
ables (Jitendra et al. 2007). Based on the semantic of the relational term, we
can distinguish two subtypes of compare problems (Hegarty, Mayer, and
Green 1992): consistent and inconsistent problems. In consistent problems,
the relational term semantically aligns with the required mathematical op-
eration. An example of a consistent problem is presented in table 1. We can
notice that the relational term ‘more than’ present in the problem text is con-
sistent with the arithmetic operation needed to solve the problem (e.g. addi-
tion). In contrast, in inconsistent problems the relational statement is incon-
sistent or incoherent with the required mathematical operation. To give an
example of an inconsistent problem, consider the following problem: ‘Jenny
has 14 crayons. She has 5 crayons more than Evelyn. How many crayons does
Evelyn have?’ The featured adverb ‘more’ semantically evokes the concept of
addition; however, the correct solution necessitates a subtraction (e.g., 14 –
5).
Several studies have documented that students make a higher number of
errors and take a longer time to solve inconsistent problems compared to
consistent ones (see Daroczy et al. 2015). We refer to this phenomenon as the
lexical consistency effect (Hegarty, Mayer, and Monk 1995). Interestingly, the
most frequent error in inconsistent problems is a reversal error in which the
solver incorrectly applies the operation that is primed by the relational term
(e.g. addition when the relational term is ‘more than’ and subtraction when
the relational term is ‘less than’), although the opposite operation is required.
The Role of the Mental Model
The lexical inconsistency effect could be related to the use of suboptimal
solving strategies. According to Hegarty, Mayer, and Monk (1995), there
are two solving procedures for arithmetic word problems: (1) the direct-
translation strategy, a shortcut approach focused on ‘grabbing numbers and
keywords’ and then applying the corresponding arithmetic operation(s), and
(2) the problem model strategy, a meaningful approach in which the prob-
lem text is translated into a mental model of the problem situation in order
to derive the mathematical event. The authors postulated that when con-
fronted with an arithmetic word problem, unsuccessful problem-solvers rely
on the direct-translation strategy, meaning that they search for numbers
and keywords from the problem text and use that keyword to determine
the operation needed to find the solution. In this respect they bypass the
phase of creating a mental representation of the problem situation. In con-
414
Compare word problems contain a relational statement (e.g. more than,
less than) that compares in a static manner the numerical values of two vari-
ables (Jitendra et al. 2007). Based on the semantic of the relational term, we
can distinguish two subtypes of compare problems (Hegarty, Mayer, and
Green 1992): consistent and inconsistent problems. In consistent problems,
the relational term semantically aligns with the required mathematical op-
eration. An example of a consistent problem is presented in table 1. We can
notice that the relational term ‘more than’ present in the problem text is con-
sistent with the arithmetic operation needed to solve the problem (e.g. addi-
tion). In contrast, in inconsistent problems the relational statement is incon-
sistent or incoherent with the required mathematical operation. To give an
example of an inconsistent problem, consider the following problem: ‘Jenny
has 14 crayons. She has 5 crayons more than Evelyn. How many crayons does
Evelyn have?’ The featured adverb ‘more’ semantically evokes the concept of
addition; however, the correct solution necessitates a subtraction (e.g., 14 –
5).
Several studies have documented that students make a higher number of
errors and take a longer time to solve inconsistent problems compared to
consistent ones (see Daroczy et al. 2015). We refer to this phenomenon as the
lexical consistency effect (Hegarty, Mayer, and Monk 1995). Interestingly, the
most frequent error in inconsistent problems is a reversal error in which the
solver incorrectly applies the operation that is primed by the relational term
(e.g. addition when the relational term is ‘more than’ and subtraction when
the relational term is ‘less than’), although the opposite operation is required.
The Role of the Mental Model
The lexical inconsistency effect could be related to the use of suboptimal
solving strategies. According to Hegarty, Mayer, and Monk (1995), there
are two solving procedures for arithmetic word problems: (1) the direct-
translation strategy, a shortcut approach focused on ‘grabbing numbers and
keywords’ and then applying the corresponding arithmetic operation(s), and
(2) the problem model strategy, a meaningful approach in which the prob-
lem text is translated into a mental model of the problem situation in order
to derive the mathematical event. The authors postulated that when con-
fronted with an arithmetic word problem, unsuccessful problem-solvers rely
on the direct-translation strategy, meaning that they search for numbers
and keywords from the problem text and use that keyword to determine
the operation needed to find the solution. In this respect they bypass the
phase of creating a mental representation of the problem situation. In con-
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