Analyzing the Meanings Fourth Grade Elementary School Students Assign to the Four Operation Symbols and Their Forms of Representation

Oct 15, 2026

Uploaded by Aditya

This qualitative case study examines how fourth grade elementary students interpret the four operation symbols (+, -, x, :) when presented in different representations. Students’ responses were collected through a researcher-developed evaluation tool, addressing writing mathematical sentences and term expressions, forming problems, and representing problem situations with figures/diagrams. Findings show students associate both concept and operation meanings with the symbols, generate more routine word problems, and perform better in writing suitable mathematical sentences than in drawing diagrams. Errors also emerged in punctuation, spelling letters/numbers, naming terms, and maintaining legible writing.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages20

Reading Time50 min

AccessFree to download

Introduction

Mathematical concepts and symbols

The relationship between symbols, problems, models, and operations

ANALYZING THE MEANINGS THAT FOURTH GRADE ELEMENTARY SCHOOL STUDENTS ASSIGN TO THE FOUR OPERATION SYMBOLS AND THEIR FORMS OF REPRESENTATION Berat DEMİRTAŞ, Neşe IŞIK TERTEMİZ Abstract: The aim of this study is to reveal the meanings that fourth grade students in elementary school attach to the four operation symbols (+, -, x, :) that are abstract, in different representations. The pattern of the study is a case study of qualitative research methods. In the study, the evaluation tool developed by the researchers was applied to elementary school fourth grade students. It was tried to present the situations of writing a mathematical sentence and expressing terms, formulating a problem, displaying the problem with a figure/diagram from students related to the symbols (+, -, x, :) for four processing skills. Based on the findings obtained in the study, it is seen that students attach concept and operation meanings to four operation symbols (+, -, x, :), create more routine word story problems related to symbols, and are more successful in writing a mathematical sentence appropriate for the problem they are writing than drawing a figure/diagram. In addition, it can be said that students made mistakes throughout the process from a linguistic point of view in terms of; using punctuations correctly, writing letters, numbers, units and expressions correctly, naming terms, and legible and understandable writing. Key words: Multiple presentations, four operations, symbols, primary school mathematics courses 1. Introduction We can look at the cognitive, affective, and motor skills that people are able to learn as learning products. Different from attitude, positive or negative experiences and motor skills; mental skills are skills that enable people to use symbols and communicate with their nature of forming an answer to the "...how?" question. We utilise mental conversions and calculations by using symbols to solve problems, and in this way, we indirectly interact with our environment (Busbridge & Özçelik, 1997) . According to the Turkish Language Association (TLA) (2021), the word "symbol" was passed on to our language from the word (symbole), whivironment (ch has French roots, and it means "sign". Symbols constitute the basis of mathematical language. The meanings of mathematical symbols must be learned in order to understand and apply mathematics correctly. 1.1. Mathematical concepts and symbols It is stated that one of the constant difficulties in learning mathematics is due to the consusion between mathematical concepts and symbols (Pimm, 2003) . For this reason, the necessary importance and attention should be given to the teaching of concepts and symbols from the first years of mathematics teaching. Symbols can be used as a substitute for mathematical terms that can be expressed both as processes and as concepts. For example, the symbol for the addition operation, which we can express as an adding (action) or a sum (concept), is “+”. when we see the “+” symbol, it is known to symbolize words like " addition, adding, etc." . According to Gray and Tall (1994), while stating that the symbols meet both process and concept expressions, they indicate that it can be called a “procept”. A single symbol represents many words at once, so the brain does not waste time reading and understanding words and concepts. This, in turn, empowers the individual substantially. While Haylock ve Cockburn (2014:13) answer to question"Are mathematical symbols just abbreviations?" as "In fact, they may be an abbreviation of mathematical ideas in a way”, they emphasize that this does not mean that a particular word or expression is just an abbreviation. When children begin to understand numbers and operations, considering their connections between concrete experiences, symbols, words and models/images, they start to understand that symbols are not just abbreviations of a word or a model/image. The children need to see this association. Consid

FAQs

What question does the study investigate about fourth grade students and the four operation symbols?

The study investigates the meanings fourth grade students attach to the four operation symbols (+, -, x, :) under different forms of representation.

How were students’ understanding assessed in the study?

A researcher-developed evaluation tool was used, focusing on tasks such as writing mathematical sentences, expressing terms, formulating problems, and representing problems with figures/diagrams.

What major results were found regarding students’ performance?

Students tended to connect both concept and operation meanings to the symbols and produced more routine word problems. They were also more successful at writing mathematical sentences appropriate to the problem than at drawing figures/diagrams.

Oct 15, 2026

Uploaded by Aditya