## Theses & Dissertations

#### Title

Transition of students from arithmetic to algebra

2012

Dissertation

#### Degree Name

Master of Education (M. Ed.)

#### Department

Institute for Educational Development, Karachi

#### Abstract

Primary mathematics curriculum starts with the manipulation of real numbers which is known as arithmetic. Algebra is an extended and generalized form of arithmetic that emerges from basic operations on numbers. However, this connection has not been established in the school mathematics curriculum. This is why students generally consider that arithmetic and algebra are two disjointed subjects. This misconception can be addressed if the teachers engage students in the meaning-making process instead of making them passive listeners in the classrooms. If the teachers engage the students in seeking connections among different mathematical ideas, it is likely that students can perceive algebra as generalized arithmetic, which can enhance their conceptual understanding in this area. Thus, introducing pre-algebraic activities, involving the equal sign and some unknown in the later stage of primary education (class 4 and 5), can be useful for the students to make the transition from Arithmetic to Algebra. These activities not only help the students identify the unknown numbers but also help them understand the concept of the sign of equality. Data reveals that most of the students focus on operational signs (+, −, ×, ÷) only while solving the questions involving unknown and sign of equality. They think that the sign of equality (=) is nothing but a separator of the answer and the basic question. On the other hand, some students call this equal sign (=) as a ‘signal to do something’. The findings of the study indicate that these pre-algebraic activities in the arithmetic classes provide students with opportunities to build a bridge for a smooth transition from arithmetic environment into the algebraic environment. Data also indicates that the introduction of patterns and word problems related to daily life situations are helpful to make the students understand the concept of variables in algebra. Otherwise, they face lots of difficulties in the formation of algebraic expressions and equations. Findings of this study also showed a reasonable progression in the students’ understanding of algebra. This study has also highlighted group and pair work, planning, use of materials as promoting factors in the enhancement of the thinking and reasoning skills of students. The study has implications for mathematics teachers as well as teacher educators in their teaching of Algebra and professional training programmers, respectively. It also generated many possibilities for further studies in the future.

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