Page 477 - 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 Equals Sign: The Challenges of Learning Arithmetic
Table 2 Test Tasks by Level of Understanding of the Equals Sign
() First grade Third grade ()
Write the correct number in the blanks: Write the correct number in the blanks: Operational
+ = ___ ___ = + + = ___ ___ = + level
+ = ___ ___ = + + = ___ ___ = +
Write the missing number in the blanks: Write the missing number in the blanks:
___ + = + ___ = ___ + = + ___ =
= ___ + = + ___ = ___ + = + ___
Write the missing number in the blanks: Write the missing number in the blanks: Basic rela-
+ = ___ + – = + ___ + = ___ + tional level
___ + = + + ___ = – – = + ___
+ ___ = + – = ___ – ___ + = +
+ ___ = –
+ ___ = +
– = ___ –
Write the missing number in the blanks: Write the missing number in the blanks: Complex
+ = ___ + = ___ + + = – ___ = ___ + relational
– ___ = ___ + = + ___ = – = ___ + level
+ = – ___ = + ___ – ___ = + = ___
= + ___ = + ___ = ___ – = + ___
Write the missing numbers and help the Write the missing numbers and help the
bear reach the honey jar: ship reach the pier:
Notes Column headings are as follows: (1) task, (2) Level of understanding of the equal sign.
grade students (T2). Each test included five tasks (problems) for testing the
development of the equals sign in their respective grades. The tests were
identical in terms of requirements; only the blocks of numbers that formed
the framework for the tasks were different. Each task consisted of several
examples designed so as to match different levels of understanding of the
equals sign (table 2).
In order to examine the understanding of the equals sign at operational
level, we used the first and the second task, the aim of which was to determine
whether students view the equals sign as a command ‘to calculate,’ or rela-
tionally. The third task aimed to examine the development of understanding
of the equals sign at basic relational level. The fourth and the fifth task re-
477
Table 2 Test Tasks by Level of Understanding of the Equals Sign
() First grade Third grade ()
Write the correct number in the blanks: Write the correct number in the blanks: Operational
+ = ___ ___ = + + = ___ ___ = + level
+ = ___ ___ = + + = ___ ___ = +
Write the missing number in the blanks: Write the missing number in the blanks:
___ + = + ___ = ___ + = + ___ =
= ___ + = + ___ = ___ + = + ___
Write the missing number in the blanks: Write the missing number in the blanks: Basic rela-
+ = ___ + – = + ___ + = ___ + tional level
___ + = + + ___ = – – = + ___
+ ___ = + – = ___ – ___ + = +
+ ___ = –
+ ___ = +
– = ___ –
Write the missing number in the blanks: Write the missing number in the blanks: Complex
+ = ___ + = ___ + + = – ___ = ___ + relational
– ___ = ___ + = + ___ = – = ___ + level
+ = – ___ = + ___ – ___ = + = ___
= + ___ = + ___ = ___ – = + ___
Write the missing numbers and help the Write the missing numbers and help the
bear reach the honey jar: ship reach the pier:
Notes Column headings are as follows: (1) task, (2) Level of understanding of the equal sign.
grade students (T2). Each test included five tasks (problems) for testing the
development of the equals sign in their respective grades. The tests were
identical in terms of requirements; only the blocks of numbers that formed
the framework for the tasks were different. Each task consisted of several
examples designed so as to match different levels of understanding of the
equals sign (table 2).
In order to examine the understanding of the equals sign at operational
level, we used the first and the second task, the aim of which was to determine
whether students view the equals sign as a command ‘to calculate,’ or rela-
tionally. The third task aimed to examine the development of understanding
of the equals sign at basic relational level. The fourth and the fifth task re-
477
