- Problem solving in adolescence--Singapore

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# Problem solving in adolescence--Singapore

Author

Ng, Soh Hua

Supervisor

Koay, Phong Lee

Abstract

In assessing pupils, teachers are more concerned with whether pupils are successful at performing a certain mathematical task. Errors that pupils make in performing the task are often overlooked. However, pupils' errors can reveal much about pupils' difficulties in performing the mathematical task. This wealth of information is often left untapped as teachers cannot afford the time to analyse and interpret pupils' errors.

This study looked into pupils' difficulties in solving equations with one variable which could be simplified to the form mx + n = 0 (m,n are constants and x is the variable). The study was divided into two phases. In Phase I, 169 Secondary Two pupils from the Express course of a neighbourhood school took a 30-item written test. Pupils' errors were collated and analysed. Based on their test scores, the pupils' were categorised into three groups; the good solvers, the average solvers and the poor solvers. The errors that the different groups of solvers made were compared. In Phase II, 10 pupils were selected to be interviewed. Each of the three groups of solvers was represented. In the interviews, the selected pupils were observed solving some equations.

A list of rules that the pupils were taught in order to solve equations with one variable was drawn up. These rules were drawn from mathematics textbooks commonly used in secondary schools in Singapore and the mathematics syllabus set by the Ministry of Education. The rules are:

R1 Dividing both sides of the equation by the coefficient of x.

R2 Adding or subtracting a term to or from both sides of the equation.

R3 Adding or subtracting like terms.

R4 Applying the distributive rules.

R5 Multiplying both sides of the equation by the same term.

Thirty test items which tested various combinations of these rules were designed. Some of these test items were modified from those used in other studies (Davis and Cooney, 1977; Carry, Lewis and Bernard, 1980). Pupils' errors were analysed with reference to the application and execution of the rules.

This study found that

● Pupils' success at solving equations was affected by the characteristics of the equation.

● Pupils had difficulties executing four of the equation-solving rules, R2, R3, R4 and R5 even in equations which were familiar to them. Pupils had the most difficulties with rule R5.

● Pupils had only instrumental understanding of the equations-solving rules. They could only apply the rules in equations which are familiar to them. Given unfamiliar though similar equations, pupils applied the rules per se. They did not realise that in some cases, the can only be applied with some adjustments for the different conditions while in other cases, the rules are no loner valid and cannot be applied.

● The better solvers made errors in executing the equation-solving rules whereas the poorer solvers made errors in both executing and applying the rules.

● Pupils' lack of understanding of the structure of algebraic fractions and their difficulties in manipulating them contributed to their failure in solving fractional equations.

● The interviews revealed that pupils did not know the equation-solving rules in their entirety; they had reduced the rules to a few buzz words. This oversimplification of the rules led to manipulation of the rules and confusion over the rules.

The study concluded by discussing some implications for teaching and research.

This study looked into pupils' difficulties in solving equations with one variable which could be simplified to the form mx + n = 0 (m,n are constants and x is the variable). The study was divided into two phases. In Phase I, 169 Secondary Two pupils from the Express course of a neighbourhood school took a 30-item written test. Pupils' errors were collated and analysed. Based on their test scores, the pupils' were categorised into three groups; the good solvers, the average solvers and the poor solvers. The errors that the different groups of solvers made were compared. In Phase II, 10 pupils were selected to be interviewed. Each of the three groups of solvers was represented. In the interviews, the selected pupils were observed solving some equations.

A list of rules that the pupils were taught in order to solve equations with one variable was drawn up. These rules were drawn from mathematics textbooks commonly used in secondary schools in Singapore and the mathematics syllabus set by the Ministry of Education. The rules are:

R1 Dividing both sides of the equation by the coefficient of x.

R2 Adding or subtracting a term to or from both sides of the equation.

R3 Adding or subtracting like terms.

R4 Applying the distributive rules.

R5 Multiplying both sides of the equation by the same term.

Thirty test items which tested various combinations of these rules were designed. Some of these test items were modified from those used in other studies (Davis and Cooney, 1977; Carry, Lewis and Bernard, 1980). Pupils' errors were analysed with reference to the application and execution of the rules.

This study found that

● Pupils' success at solving equations was affected by the characteristics of the equation.

● Pupils had difficulties executing four of the equation-solving rules, R2, R3, R4 and R5 even in equations which were familiar to them. Pupils had the most difficulties with rule R5.

● Pupils had only instrumental understanding of the equations-solving rules. They could only apply the rules in equations which are familiar to them. Given unfamiliar though similar equations, pupils applied the rules per se. They did not realise that in some cases, the can only be applied with some adjustments for the different conditions while in other cases, the rules are no loner valid and cannot be applied.

● The better solvers made errors in executing the equation-solving rules whereas the poorer solvers made errors in both executing and applying the rules.

● Pupils' lack of understanding of the structure of algebraic fractions and their difficulties in manipulating them contributed to their failure in solving fractional equations.

● The interviews revealed that pupils did not know the equation-solving rules in their entirety; they had reduced the rules to a few buzz words. This oversimplification of the rules led to manipulation of the rules and confusion over the rules.

The study concluded by discussing some implications for teaching and research.

Date Issued

1996

Call Number

QA211 Ng

Date Submitted

1996