MENTAL PROCESSING STRATEGIES IN PRIMARY SCHOOL STUDENTS: THE EMPTY NUMBER LINE

Oct 15, 2026

Uploaded by Aditya

This research determines mental processing strategies used by 3rd-grade primary school students when solving addition and subtraction tasks with the empty number line. The study adopts a qualitative case-study model with 143 participants (75 girls, 68 boys), aged 8. Data were analyzed through content analysis. Results group strategies into four categories: counting, balancing, first process step, and partitioning. The most frequent strategy is using “multiples of 10,” followed by “counting all” and “partitioning the second number”; the least used is employing “equivalent numbers.”

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages13

Reading Time33 min

AccessFree to download

Abstract

1. Introduction

Models and learning meaning

Number lines and the empty number line

Mental calculation and strategy development

Educational value of the empty number line

MENTAL PROCESSING STRATEGIES IN PRIMARY SCHOOL STUDENTS: THE EMPTY NUMBER LINE Halil ÖNAL Abstract: The aim of this research is to determine the mental processing strategies used by 3rdgrade primary school students in addition and subtraction using the empty number lines. The model of the research is a case study, one of the qualitative research methods. The participants consist of 143 students; 75 girls and 68 boys, attending the third grade (8-years-old) . Content analysis method was used in data analysis. Considering the results of the research, the mental strategies used by primary school 3rd-grade students were gathered in four categories: counting, balancing, first process step and partitioning. It was concluded that the students mostly used the mental processing strategy of using "multiples of 10", which is in the first process category, and this strategy was followed by "counting all" and "partitioning the second number”, the least used mental processing strategy by the students was "using equivalent numbers" . Key words: Empty number line, mental processing strategies, primary mathematics 1. Introduction No physical model can directly demonstrate or explain a concept on its own. The person who will learn the concept should attribute this meaning to the model. Children do this attribution of meaning by making use of the relationships between the objects or the parts of the object presented in the model. In a model, the child may not see a relationship that the teacher sees. This indicates that the child is not yet ready to use the model (Olkun & Toluk-Uçar, 2012) . Many teachers only use the model that their students like or understand better. It's a mistake. Concepts should be created by students and these concepts should be applied to models (Van de Walle, Karp & Bay-Williams, 2014) . Students should experience the models and discuss the similarities and differences in the representation of the different models. At an early age, children develop their counting skills (forward and backward) and the meaning of ordinal numbers, by using the number line where each integer is represented by a separate square, and later on by using the number line model 0, 1, 2, 3, 4, ... etc. with equal intervals. Later, children learn to use the number line model in which only the multiples of 10 (0, 10, 20, 30, etc.) are marked (Haylock & Cockburn, 2014) . Number lines have numbers whose positions are indicated by signs at regular intervals along the line. The number line encourages children to draw and count step by step with numbers forward or backward (Mosley, 2001) . Children sometimes use the number line without starting from 0. In this process, the idea in children develops that the number line is a flexible tool to represent numbers and operate with them. The empty number line actually takes it a step further. An empty number line is a number line that has not been scaled. The numbers in a calculation to be made can be placed at any point as long as their order is preserved. For example, the points representing the number 52, 60, and 100 can be placed at any point on the empty number line, where the number 60 is between 52 and 100 (Haylock & Cockburn, 2014) . Mosley (2001) stated the important skills that children should develop before using the empty number lines as making jumps in different sizes (especially to tens), moving confidently both forward and backward on the number line, spliting and being able to recombine the numbers using the number that completes 10 and then 20. Klein Beishuizen and Treffers (1998) stated that the empty number line provides learning support with a higher level of mental activation, a more natural and transparent model for numerical operations, providing support for children to develop more figured, formal and efficient strategies, and especially a model that increases the flexibility of mental strategies. According to Haylock and Manning (2014), because the empty number is actuall

FAQs

What is the purpose of the study on 3rd-grade students’ mental processing strategies?

To determine which mental processing strategies primary school 3rd graders use for addition and subtraction when working with the empty number line.

How was the research conducted and analyzed?

The study used a case-study model and applied content analysis to the data collected from 143 students.

What strategy was used most and what was used least by the students?

Students most often used the strategy of “multiples of 10,” while the least used strategy was “equivalent numbers.”

Oct 15, 2026

Uploaded by Aditya