Modelling the Relationships Between Quantities: Meaning in Literal Expressions

Marijana Zeljić

doi:10.12973/eurasia.2015.1362a

Abstract

Background:Algebra is often considered to be difficult and mysterious doctrine due to numerous symbols that represent mathematical notions. Results of the research on students’ interpretation of literal expressions show that only a small number of students are ready to accept that a letter can represent a variable. The aim of this research conducted with students of the fourth grade of elementary school was to examine the impact of the use of various symbols, which represent the relationships between quantities, on students’ understanding of the meanings of literal expressions.Materials and methods:We used an experimental method (with one group) and testing techniques (pre-test and final-test comparisons).Results:The research results show that the iconic representation of the structure of literal expressions, namely, giving meaning to a term through its reliance on certain schemes in the learning process, significantly affects the ability of students in modelling generic quantitative relationships, and in the development of the meaning of letters in the role of the algebraic variable.Conclusions:However, the results of our study show that it is possible to develop procedural as well as structural understanding of literal expressions in younger elementary school students.

Highlights

Devising new approaches to teaching algebra, which would successfully develop the meaning of algebraic symbols and concepts among students, has been the focal point of international mathematical community in the last few decades
By comparing students‟ success rate on tasks which pertain to literal expressions and examine the ability of iconic representation of literal expressions after the application of the Model, we concluded that differences in students‟ achievement on initial and final tests were statistically significant at level .01. (Tables 1 & 2)
Predominant tendency noted in their results is the iconic representation of each unit of counting with images corresponding to real objects

Summary

Introduction

Devising new approaches to teaching algebra, which would successfully develop the meaning of algebraic symbols and concepts among students, has been the focal point of international mathematical community in the last few decades. Algebraic symbols, which function as a highly effective means of thinking for some, are for others a great obstacle in communication. 685) claims: „Algebraic symbolism does not possess a wide variety of means such as adverbs, adjectives and noun complements which have the main role in written and spoken language.

Objectives

Results

Conclusion