Tenth grade pupils engagement with the use of brackets in algebra : a case study in a school in Albania
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Since algebra is considered as a language, it has its syntax, semantics, and pragmatics. In the third linguistic level (pragmatics) stand the relations between the elements of language and the users. Since brackets are elements of algebra language they have their syntax, which involves some rules that lead transformations of algebraic expressions even with brackets; and brackets have their semantic aspect, which is related to tackling of algebraic expressions into brackets such as mathematical objects. On the other side, the consideration of the syntactic aspect of algebraic expressions leads to instrumental understanding of the use of brackets; and the consideration of semantic aspect of algebraic expressions leads towards relational understanding of the use of brackets. Based on relational understanding of the use of brackets, it is possible to identify cases of using brackets, to discriminate them, to generalize each of them, and finally to achieve the synthesis concerning the use of brackets in algebraic expressions. In terms of this theoretical framework I have designed my study and I tried to give answer to my two research questions: 1. What kind of mistakes pupils in grade 10, involved in my study, do? In order to achieve an overview of mistakes concerning the use of brackets that Albanian pupils in tenth grade, involved in my study, do I conducted test for thirty pupils. After I checked all the tests, I selected four pupils to be interviewed about their test‟s answers and to present in depth analysis of the answers of two of them. I conducted interviews about the test (both, test and the interview are called pre-test) and some teaching lessons in order to affect pupils‟ performances during the task-based-interview (post-test). Form data analysis, it seems that some pupils show evidence of improvement in their performance during the post-test comparing to the pre-test. Thereby I want to address the following research question, which is composed by two parts: 2. a) What kind of improvement is showed in performance during the post-test? 2. b) What kind of causes can be identified concerning the improvement? In general, the pupils showed that they know how to operate with brackets in algebraic expressions. However, mostly of them had an instrumental learning concerning the use of brackets, and other pupils had done mistakes in their answers concerning the use of brackets and tackling of algebraic expressions. In terms of the two selected pupils‟ performance during all my data collection, it is noticed an improvement of their mathematical thinking concerning the use of brackets in algebraic expressions.
Masteroppgave i matematikkdidaktikk- Universitetet i Agder, 2012