#### Title

### Students’ perceptions about the symbols, letters and signs in algebra and how do these affect their learning of algebra: A case study in a government girls secondary school, Karachi, Pakistan

#### Date of Award

8-1-2008

#### Document Type

Dissertation

#### Degree Name

Master of Education (M. Ed.)

#### Department

Institute for Educational Development, Karachi

#### Abstract

Algebra uses symbols for generalizing Arithmetic. These symbols have different meanings and interpretations in different situations. Students have different perceptions about these symbols, letters and signs. Despite the vast research by researchers, namely Kuchemann (1981&1998,), Collis (1975), and Booth (1988 & 1984) on the students' difficulties in understanding letters in Algebra, the overall image that emerges from the literature is that students have misconceptions about the use of letters and signs in Algebra. Through my study, I have explored the perceptions of students about the use of symbols and signs in Algebra. Here, I have used the case study method within a qualitative research design. In order to get insights of students' perceptions of Algebra, I have interviewed students in groups and invited them to work on different tasks related to uncovering their perceptions of Algebra. My empirical done through this study has revealed that the students have many misconceptions in the use of symbols in Algebra, which have bearings on their learning of algebra. It appears that the problems encountered by the students appeared to have a connection with their lack of conceptual knowledge and might have been a result of teaching they experience in learning Algebra at the secondary schooling level. Some of the findings also suggest that teachers appeared to have difficulties with their own content knowledge. Here, one can also see that textbooks are also not presenting content in such an elaborate way that these could have provided sufficient room to students for developing their relational knowledge and conceptual understanding of Algebra. Furthermore, the interviews and observation of the classrooms highlighted that the students usually perceive letter and variables as a fixed numbers or value. Some of the students perceive letters as short forms and abbreviations of some objects. Students also have difficulties in interpreting and developing algebraic equations and expressions. Moreover, this study investigates students' difficulty in translating word problems in algebraic and symbolic form. They usually follow phrase-to-phrase strategy in translating word problem from English into Urdu. This process of translating the word problem from English in to their own language appears to have hindered the correct use of symbols in Algebra. Textbooks, mathematical pedagogy, students' prior experience of arithmetic and the students' and teachers' inadequency in algebraic thinking emerged from my study as some of the reasons of students' misconceptions and why they experienced difficulties in learning of Algebra. The findings have some important implications for the teaching of algebra that might help them in developing symbol sense in both students and teachers. By the use of symbol sense, they can use symbols properly, understand the nature of symbols in different situations, like in functions, in variables, and in re4lationships between algebraic representations. This study will contribute to future research on similar topics.

#### Recommended Citation

Samo, M.
(2008).
*Students’ perceptions about the symbols, letters and signs in algebra and how do these affect their learning of algebra: A case study in a government girls secondary school, Karachi, Pakistan*
(Unpublished master's dissertation).
Aga Khan University, Karachi, Pakistan.