- Newman diagnosis of primary 5 pupils’ errors in fraction word problems and remediation through structured conferencing

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# Newman diagnosis of primary 5 pupils’ errors in fraction word problems and remediation through structured conferencing

Author

Cai, Elaine Yu Ling

Supervisor

Foong, Pui Yee

Abstract

The topic of fractions is taught from primary two. As pupils progress through the school years, there is less emphasis on the concrete and pictorial approach of understanding which forms the basis of the abstract approach to solving word problems on fractions. This may result in pupils possessing insufficient conceptual understanding of the mathematics required to solve fraction word problems successfully.

To help pupils break down a word problem so as to enhance their understanding of it, the model method is a strategy often used in Singapore classrooms. The model drawn helps to represent information and illustrate relationships in various contexts, of which, one of them is the concept of part-whole structures.

This study aimed to explore the types of errors primary five low mathematics attaining pupils made when solving fraction word problems using the model method. Pupils underwent an interview and from their written or verbal responses, the errors they made were classified according to the Newman Error Analysis Guideline (NEAG) stages: Reading, Comprehension, Transformation, Process Skills and Encoding. The extent of the errors they committed were quantified using the modified Newman Error Analysis Guideline Rubric. This study also sought to determine the effectiveness of the Structured Conferencing method in helping primary five low Mathematics attainers in solving fraction word problems.

The study found that most pupils committed errors in the comprehension, transformation and process skills stage. Comprehension errors included the misinterpretation of the meanings of the numerator or denominator of a given simple fraction in the context of the questions, misinterpretation of the denominator of a fraction as representing the actual number of a whole in context to the question and misinterpretation of ‘x/y of a remainder’ and relate it to a given known quantity in the context of the question. The transformation errors made by pupils also included mistranslation of a given fraction of a whole into a comparison model of two wholes, mistranslation of two given like fractions of a whole as two fractions of two wholes instead, mistranslation of two given unlike fractions of two different wholes and being unable to change to their equivalent fractions for repartitioning and mistranslation of ‘a/b of the remainder’ as ‘a/b of the whole’ instead in the model. Formulating incorrect number statement to represent relationships among parts in the model drawing is the error committed under the process skill stage.

The improvement in the pupils’ marks in post-test 1 and post-test 2 as compared to the pre-test also proved that the Newman Error Analysis Guideline was useful in diagnosing pupils’ errors. Together with the Structured Conferencing interview sessions, it was a programme which benefited both the teacher and the pupils. Such one-to-one interactions enabled the teacher to identify exactly the type of mistakes the pupils made and immediate remediation was rendered through scaffolding in the structured conferencing technique.

To help pupils break down a word problem so as to enhance their understanding of it, the model method is a strategy often used in Singapore classrooms. The model drawn helps to represent information and illustrate relationships in various contexts, of which, one of them is the concept of part-whole structures.

This study aimed to explore the types of errors primary five low mathematics attaining pupils made when solving fraction word problems using the model method. Pupils underwent an interview and from their written or verbal responses, the errors they made were classified according to the Newman Error Analysis Guideline (NEAG) stages: Reading, Comprehension, Transformation, Process Skills and Encoding. The extent of the errors they committed were quantified using the modified Newman Error Analysis Guideline Rubric. This study also sought to determine the effectiveness of the Structured Conferencing method in helping primary five low Mathematics attainers in solving fraction word problems.

The study found that most pupils committed errors in the comprehension, transformation and process skills stage. Comprehension errors included the misinterpretation of the meanings of the numerator or denominator of a given simple fraction in the context of the questions, misinterpretation of the denominator of a fraction as representing the actual number of a whole in context to the question and misinterpretation of ‘x/y of a remainder’ and relate it to a given known quantity in the context of the question. The transformation errors made by pupils also included mistranslation of a given fraction of a whole into a comparison model of two wholes, mistranslation of two given like fractions of a whole as two fractions of two wholes instead, mistranslation of two given unlike fractions of two different wholes and being unable to change to their equivalent fractions for repartitioning and mistranslation of ‘a/b of the remainder’ as ‘a/b of the whole’ instead in the model. Formulating incorrect number statement to represent relationships among parts in the model drawing is the error committed under the process skill stage.

The improvement in the pupils’ marks in post-test 1 and post-test 2 as compared to the pre-test also proved that the Newman Error Analysis Guideline was useful in diagnosing pupils’ errors. Together with the Structured Conferencing interview sessions, it was a programme which benefited both the teacher and the pupils. Such one-to-one interactions enabled the teacher to identify exactly the type of mistakes the pupils made and immediate remediation was rendered through scaffolding in the structured conferencing technique.

Date Issued

2011

Call Number

QA137 Cai

Date Submitted

2011