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Solving and sense making of complex arithmetic expressions : the cognitive obstacles faced by primary five pupils
Author
Teng, Swee Hoon
Supervisor
Ng, Swee Fong
Abstract
Research studies have shown that pupils exhibited cognitive obstacles while solving arithmetic expressions of multiple operations. Their difficulties with such expressions invariably affect the way they solve algebraic equations. This study investigated the cognitive obstacles faced by a class of Primary Five pupils when they solved familiar and unfamiliar arithmetic expressions of multiple operations. The study also looked at these pupils' sense-making of the order of operations through the word problems they had created. Forty-one Primary Five EM2 mixed-ability pupils, comprising of 10 girls and 31 boys, participated in the study. They had already been taught the order of operations. Pupils' cognitive obstacles were investigated by getting pupils to solve five multi-operation arithmetic expressions of different degree of familiarity. There were two parts to the test. First, they had to solve the arithmetic expressions. Second, they had to create a word problem to match each expression. Their solutions to the expressions were analysed and categorised according to the 'cognitive obstacles' they faced. Their word problems were also analysed and categorised according to the sense they had made of the order of operations. Thirty-four pupils were selected for interviews and these data were used to supplement the pupils' written responses.
This study found that pupils faced cognitive obstacles, in particular, with unfamiliar expressions. This was because they lacked the concept of arithmetic equivalence and the understanding of the properties of the four operations. These obstacles were further confirmed from the analysis of their word problems. The ability to create word problems required more than just knowing the rules of the order of operations. It required the pupils to know the properties of the operations and their relationships, to have a global view of the expression as well as to be able to think of logical contexts to match the expressions. On the whole, pupils did know the order of operations. What they lacked was the understanding of the properties of the order of operations, and this probably hindered them in applying the rules to unfamiliar expressions.
This study found that pupils faced cognitive obstacles, in particular, with unfamiliar expressions. This was because they lacked the concept of arithmetic equivalence and the understanding of the properties of the four operations. These obstacles were further confirmed from the analysis of their word problems. The ability to create word problems required more than just knowing the rules of the order of operations. It required the pupils to know the properties of the operations and their relationships, to have a global view of the expression as well as to be able to think of logical contexts to match the expressions. On the whole, pupils did know the order of operations. What they lacked was the understanding of the properties of the order of operations, and this probably hindered them in applying the rules to unfamiliar expressions.
Date Issued
2002
Call Number
QA135.6 Ten
Date Submitted
2002