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Secondary four express students’ difficulties in solving linear inequalities
Author
Lee, Chiou Kwei
Supervisor
Ng, Swee Fong
Abstract
The purpose of this study is to find out the difficulties faced by two groups of Secondary Four Express students when solving linear inequalities.
One hundred and thirty-six secondary four express stream students from one neighbourhood school participated in this study. Sixty-nine students took single mathematics (SM) and sixty-seven students took double mathematics (DM). A paper-and-pencil test designed for this study was administered and these students were given an hour to answer the six items. The test consisted of standard items which students were familiar with and non-standard items which were more challenging than standard items. Based on their written responses, fifteen students were then selected to be interviewed. The purpose of the interviews was to provide further insights to their responses to selected items.
The findings showed that students were able to do well for standard items. However, items which involved reverse in inequality symbol when multiplying a negative numbers on both sides of an inequality and involved three-part inequality were not as easy for students. Non-standard items were challenging to both SM and DM students. Although they were taught more mathematics, DM students failed to perform in nonstandard items.
Analysis of students’ written work was interpretive. Based on the students’ responses in the written test, observation from the errors and the interviews, it was found the students had difficulties working with the structure of inequalities and interpreting the graphical solution of inequalities. A noteworthy finding was that these students were weak in providing reasons and justifying the solutions of inequality.
This study provides mathematics teachers knowledge of the type of difficulties faced by secondary school students when inequalities are taught. This knowledge may be useful for teachers when they prepare to teach the topic of inequality such as solving different types of linear inequalities, quadratic inequalities. It is recommended that concepts in linear inequality might be better learnt by students if linear inequalities are taught relationally linking the symbolic form with its graphical representation. Teachers should encourage students to explain the procedures they use, justify their reasoning, judge the reasonableness of their solutions and reflect on their thinking.
One hundred and thirty-six secondary four express stream students from one neighbourhood school participated in this study. Sixty-nine students took single mathematics (SM) and sixty-seven students took double mathematics (DM). A paper-and-pencil test designed for this study was administered and these students were given an hour to answer the six items. The test consisted of standard items which students were familiar with and non-standard items which were more challenging than standard items. Based on their written responses, fifteen students were then selected to be interviewed. The purpose of the interviews was to provide further insights to their responses to selected items.
The findings showed that students were able to do well for standard items. However, items which involved reverse in inequality symbol when multiplying a negative numbers on both sides of an inequality and involved three-part inequality were not as easy for students. Non-standard items were challenging to both SM and DM students. Although they were taught more mathematics, DM students failed to perform in nonstandard items.
Analysis of students’ written work was interpretive. Based on the students’ responses in the written test, observation from the errors and the interviews, it was found the students had difficulties working with the structure of inequalities and interpreting the graphical solution of inequalities. A noteworthy finding was that these students were weak in providing reasons and justifying the solutions of inequality.
This study provides mathematics teachers knowledge of the type of difficulties faced by secondary school students when inequalities are taught. This knowledge may be useful for teachers when they prepare to teach the topic of inequality such as solving different types of linear inequalities, quadratic inequalities. It is recommended that concepts in linear inequality might be better learnt by students if linear inequalities are taught relationally linking the symbolic form with its graphical representation. Teachers should encourage students to explain the procedures they use, justify their reasoning, judge the reasonableness of their solutions and reflect on their thinking.
Date Issued
2009
Call Number
QA295 Lee
Date Submitted
2009