what problems do students demonstrate in solving linear equation with one variable?
What strategies do students adopt to solve linear equation with one variable?
What is the students level of understanding of linear equation with one variable and its related concepts?
How does the use of computers support students in overcoming the difficulties in understanding linear equation?
To study the students level of understandingof linear equations.
To explore the strategies used by the studentsin solving linear equations.
To identify the difficulties faced by students in understanding of linear equations.
After teaching learning with computers, to study the changes in
students understanding level of linear equations
Adopting strategies to solve linear equations.
Difficulties faced by students.
66 students from two schools of delhi were selected for the study.
Worksheet of linear equation
The present study used one group pre-test post test design of experiment.
All the students(100%) recognized the symbols ‘+’, ‘-’ and ‘÷’ in pretest and post test both. The percentage of students who could do arithmetic operations on the number with unknown increased after the intervention. The results showed that the majority of students improved their understanding level from recognition level to operational level.
All the students recognized the equal symbol. After the exposure of computer based visual representation (NLVM Software), majority of them improved their understanding of equal sign from result finder (before teaching) to representing equal values on both sides ie. ‘balance’ (after teaching).
In the pretest, the majority of the students responded that only positive integer values could be assigned to x and only negative integer values could be assigned to -x and rational numbers or fraction could be assigned to 1/x. But after intervention, their understanding of unknown/ variable was changed. Majority of them admitted that unknown/variable may represent any numerical value and they responded as any number can be assigned to x.
After the exposure of computer based visual representation, the majority of them improved their understanding of linear equation and its related concepts from recognition level to operational level.
After the use of computers in the teaching learning, the majority of students showed improvement in the procedural understanding as they could solve the most of the equations and they used balance strategy to solve the linear equations.
The results showed a significant difference between the number of students who solved the equation completely before teaching and students who solved the equation completely after teaching. It is evident the percentage of students who solved the equation completely before teaching is increased after teaching with computer which indicates that students understanding of linear equation is improved after getting exposure of computer based teaching learning.
The results showed a significant difference between the number of students who did not attempt to solve the equations completely before teaching and students who solved the equation completely after teaching. It is evident that the percentage of students, who did not attempt to solve the equation, is decreased after teaching with computer which indicates that students are empowered with better understanding of linear equation so that the percentageof students who attempted equation is increased.
The majority of students used transpose strategy to solve the equations in the pre-test. After teaching with computer, the majority of students used balance strategy to solve the equations. This shows that students moved from transpose strategy to balancing strategy which indicates that students understanding of linear equation is improved after getting exposure of computer based teaching learning.
Before the exposure of computer based visual representations, majority of students faced difficulties related to:
sign of unknown while shifting from one side to other
minus sign detachment
misconception with position of unknown/fixing the position of unknown
inverse operation error
incapability to operate on unknown
misconception with division
the addition error
the exhaustion error
the other inverse error
switching addends error
students inconsistency in committing mistakes
After teaching with computer based visual representation (NLVM software), majority of students overcame the difficulties:- sign of unknown while shifting from one side to other,
minus sign detachment,
misconception with position of unknown/fixing the position of unknown,
inverse operation error
The results show that the majority of students overcame most of the difficulties after the teaching with computer based visual representation which indicates that students understanding of linear equation is improved after getting exposure of computer based teaching learning.
This study has thrown light about the different aspects and levels of students understanding of linear equations with one variable and its related concepts. Thus it may be suggested to teachers to consider these aspects and levels of understanding while they are planning for the teaching.
Dialogue/ interview with the students should be done with great interest and in details so that the students difficulties in understanding and solving linear equations and its related concepts may be understood and can be handled effectively.
This study suggests that deep understanding of the concepts must be an integral part of our syllabus as well as pedagogy. Teaching learning of algebraic concepts like algebraic expression and equation which are symbolically presented most of the time, need to be made more interesting and must be presented through virtual presentations. Teachers and other stakeholders can utilize the strength of virtual manipulative in order to facilitate the learning and overcoming the difficulties in learning linear equations with one variable.
Teachers may plan to use computer based visual representation in teaching learning of other algebraic concepts. Teacher and other stakeholders may lead to doing further investigation to devise such computer based visual representation and find out the benefits of utilizing it in their pedagogical practices.
Keyword(s): Mathematics Education, algebra, linear equation