Page 418 - 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
the basis for a successful solution strategy. As such, a large number of studies
in the past decades have emphasized that the use of visual and concrete rep-
resentations, such as diagrams, is an effective method to lessen difficulties in
arithmetic word problem solving (Ayabe et al. 2022; Boonen et al. 2014; Hem-
bree 1992; Jitendra et al. 2007). Diagrams are visual tools that enable learners
to identify the relevant information in the problem text, organize and inte-
grate it into a coherent mental model, comprehend the semantic relation-
ships between numerical variables, and recognize the underlying arithmeti-
cal operation needed for the solution (Jitendra 2002). Moreover, drawing dia-
grams facilitates self-explaining which in turn leads to deeper understanding
of the problem situation (Ainsworth and Th Loizou 2003). Diagrams also pro-
vide children with strategies that reduce the cognitive demands involved in
problem-solving (Fuchs et al. 2021).
Numerous types of diagrams exist and can be used in word problem-
solving. However, it must be noted that not all diagrams are equal in helping
to generate the correct solution (Ayabe et al. 2022). Indeed, each diagram
provides a different ‘representational guidance’ (Suthers 2003). Below, we
will introduce two types of diagrams particularly effective in solving com-
pare problems: the model method and the schema-based instructions.
Model Method
The model method is a graphical approach for supporting word problem-
solving that first originated in Singapore (Kho 1987; Ng and Lee 2009). Now
it is increasingly used in various countries worldwide (Kaur 2019). The main
aspect of the model method is to draw a bar diagram consisting of a series of
rectangles that graphically depict the problem situation (i.e. the semantic or
mathematical structure of the problem) (Kho 1987; Ng 2004). An example of
the model method applied to an inconsistent compare problem is presented
in figure 2.
Solving arithmetic word problems with the model method involves essen-
tially three phases (Koning et al. 2022). The first phase is focused on the prob-
lem text: the solver reads the given word problem with the intention to iden-
tify the known as well as the unknown variables, quantities, and relations. For
instance, if we consider the word problem presented in figure 2, the student
must identify the names of the two girls (variables), the number of crayons
(quantity), and relational term (relation). In the second phase, the learner rep-
resents the identified text information graphically using the bar diagram. Par-
ticularly, the solver draws a set of rectangles where each rectangle represents
the quantity of a variable. The longer the rectangle, the larger the variable
418
the basis for a successful solution strategy. As such, a large number of studies
in the past decades have emphasized that the use of visual and concrete rep-
resentations, such as diagrams, is an effective method to lessen difficulties in
arithmetic word problem solving (Ayabe et al. 2022; Boonen et al. 2014; Hem-
bree 1992; Jitendra et al. 2007). Diagrams are visual tools that enable learners
to identify the relevant information in the problem text, organize and inte-
grate it into a coherent mental model, comprehend the semantic relation-
ships between numerical variables, and recognize the underlying arithmeti-
cal operation needed for the solution (Jitendra 2002). Moreover, drawing dia-
grams facilitates self-explaining which in turn leads to deeper understanding
of the problem situation (Ainsworth and Th Loizou 2003). Diagrams also pro-
vide children with strategies that reduce the cognitive demands involved in
problem-solving (Fuchs et al. 2021).
Numerous types of diagrams exist and can be used in word problem-
solving. However, it must be noted that not all diagrams are equal in helping
to generate the correct solution (Ayabe et al. 2022). Indeed, each diagram
provides a different ‘representational guidance’ (Suthers 2003). Below, we
will introduce two types of diagrams particularly effective in solving com-
pare problems: the model method and the schema-based instructions.
Model Method
The model method is a graphical approach for supporting word problem-
solving that first originated in Singapore (Kho 1987; Ng and Lee 2009). Now
it is increasingly used in various countries worldwide (Kaur 2019). The main
aspect of the model method is to draw a bar diagram consisting of a series of
rectangles that graphically depict the problem situation (i.e. the semantic or
mathematical structure of the problem) (Kho 1987; Ng 2004). An example of
the model method applied to an inconsistent compare problem is presented
in figure 2.
Solving arithmetic word problems with the model method involves essen-
tially three phases (Koning et al. 2022). The first phase is focused on the prob-
lem text: the solver reads the given word problem with the intention to iden-
tify the known as well as the unknown variables, quantities, and relations. For
instance, if we consider the word problem presented in figure 2, the student
must identify the names of the two girls (variables), the number of crayons
(quantity), and relational term (relation). In the second phase, the learner rep-
resents the identified text information graphically using the bar diagram. Par-
ticularly, the solver draws a set of rectangles where each rectangle represents
the quantity of a variable. The longer the rectangle, the larger the variable
418
