# Mathematics

Use of Manipulatives to Develop Second Year High School Students’ Understanding of Equality and Linear Equations

by Melanie Rivera

Mary Grace Sinfuego

Adrian Paul Tudayan

This thesis aimed to study and analyze the students’ understanding of equality and their skills in solving Algebraic Equations specifically Linear Equations. The researchers wanted to find out the misconceptions of selected 2nd Year students regarding the said topic. Moreover, they also wished to find out if using manipulatives such as counters and rectangles could help in correcting these misconceptions and provide a better understanding on the concept of equality and their skills in solving.

It was clearly stated in the first part of the paper the concern researchers would like to address. Moreover, the objectives of the study were also given in order to provide a clear idea of what the paper is all about. The idea was further supported by background concepts regarding the definition of equality and equivalence and how is it important in solving Algebraic Equations.

The understanding or perception of students regarding equality was limited into 4 different categories: operational, relational, other alternative or no knowledge at all. These understandings are known to interfere with the ability of the student to solve and analyze linear equations. We classify someone’s understanding as operational if he thinks that the equal sign serves as a signal for the answer. It is classified as relational if the student perceives equal sign as equivalence or the two quantities are equal. As for the remaining two, we distinguish it as alternative if the student just translates directly the equal sign and no knowledge if he/she doesn't have any idea.

On the other hand, the students’ skills are classified into two categories namely Procedural Knowledge and Conceptual Knowledge. Procedural pertains to the automatic response which is brought by the student’s...

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