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Primary 5 pupils' difficulties in using the model method for solving complex relational word problems
Author
Goh, Siew Ping
Supervisor
Foong, Pui Yee
Abstract
The model method is a key heuristic to solve word problems in our primary mathematics curriculum. The main product, a model, could depict explicitly the known and unknown quantities involved in a problem and aid pupils to determine which mathematical operation to use to solve the problem, if correctly drawn. Despite its effectiveness in solving many challenging arithmetic word problems and its emphasis in classroom teaching and learning, many pupils still experience varying degree of difficulty in using this method to help them solve word problems. At the upper primary level, the difficulties pupils faced are more apparent as increasing number of complex multiple-step arithmetic word problems are given which often require pupils to use the model method or other methods that would require algebraic reasoning.
This study aimed to document the errors and deduce the difficulties pupils at the Primary Five level faced when solving relational before-after word problems. A written test was administered to a class of Standard Stream, mixed-ability pupils. Their workings using the model method (the most prevalent heuristic used) and the direct number sentence method were compared against an analysis framework to facilitate the analysis of their transformation and translation errors.
The study found that drawing “inaccurate” or incorrect models were the transformation errors committed in the simple one-step relational problems. The possible difficulties were pupils’ incomprehension of the “inconsistent” language used in one of the problems or their lack of basic skills in transforming models. For the multiple-step relational problems, transformation errors were mainly partially transformed models and these appeared to be associated with pupils’ inability to combine the complexity of comparative relationships with an added element - the value of change.
Common translation errors committed in the one-step relational problems were either incorrect number sentences formed due to incorrect models, or incorrect direct translations into number sentences based on random numerical cues. The latter errors were indications of pupils’ difficulties in comprehending existing and, or new relationships in the before and after change situations and their subsequent interrelationships. For the multiple-step relational problems, translation errors include pupils’ inability to identify and calculate the value of one basic unit, incorrect translations into number sentences based on incorrect models drawn and incorrect direct translations into number sentences based on random numerical cues. Possible difficulties include (a) pupils’ incomprehension of existing relationships and interrelationships, (b) pupils’ inability to interpret “visual” information and (c) pupils’ lack of skill in drawing appropriate models for meaning deductions.
Based on the errors collated, implications and recommendations for teachers were made to improve the teaching and learning of the model method in classrooms and enhance pupils’ ability to solve complex relational word problems.
This study aimed to document the errors and deduce the difficulties pupils at the Primary Five level faced when solving relational before-after word problems. A written test was administered to a class of Standard Stream, mixed-ability pupils. Their workings using the model method (the most prevalent heuristic used) and the direct number sentence method were compared against an analysis framework to facilitate the analysis of their transformation and translation errors.
The study found that drawing “inaccurate” or incorrect models were the transformation errors committed in the simple one-step relational problems. The possible difficulties were pupils’ incomprehension of the “inconsistent” language used in one of the problems or their lack of basic skills in transforming models. For the multiple-step relational problems, transformation errors were mainly partially transformed models and these appeared to be associated with pupils’ inability to combine the complexity of comparative relationships with an added element - the value of change.
Common translation errors committed in the one-step relational problems were either incorrect number sentences formed due to incorrect models, or incorrect direct translations into number sentences based on random numerical cues. The latter errors were indications of pupils’ difficulties in comprehending existing and, or new relationships in the before and after change situations and their subsequent interrelationships. For the multiple-step relational problems, translation errors include pupils’ inability to identify and calculate the value of one basic unit, incorrect translations into number sentences based on incorrect models drawn and incorrect direct translations into number sentences based on random numerical cues. Possible difficulties include (a) pupils’ incomprehension of existing relationships and interrelationships, (b) pupils’ inability to interpret “visual” information and (c) pupils’ lack of skill in drawing appropriate models for meaning deductions.
Based on the errors collated, implications and recommendations for teachers were made to improve the teaching and learning of the model method in classrooms and enhance pupils’ ability to solve complex relational word problems.
Date Issued
2009
Call Number
QA63 Goh
Date Submitted
2009