The purpose of the study is to examine how pre-service and in-service mathematics teachers locate repeating decimals and irrational numbers on the number line. The participants of the study included 274 pre-service and 106 in-service mathematics teachers. Data were collected through a written questionnaire including four open-ended questions. In…

Equal representation as a social issue is about the participation of one social group, in a particular context, in proportion to the numbers in the group within the total population. The proportion of women in parliament, and of the participation rate of students of lower socioeconomic status in higher education, are examples. The aims of this…

Whole-number arithmetic is a core content area of primary mathematics, which lays the foundation for children's later conceptual development. This paper focuses on teaching whole-number multiplication (WNM) to build a stepping stone for children's proportional reasoning. Our intention in writing this paper is to obtain a practice-based perspective…

Students require knowledge of fraction, arithmetic and integer to tell the time. The purpose of the current study is to discover the conceptual knowledge related to hours, how the students read the clock and use half and quarter concepts to read the time in Turkey. A qualitative research method with a case study approach was used for this…

In this article, we explore Whitehead's claim that experience is fundamentally affective. We do so in the context of an Italian primary school classroom featuring the use of the multitouch application "TouchCounts." We study the way in which the children and the iPad take each other up and the meanings of number and arithmetic that…

The understandings prospective mathematics teachers develop by focusing on quantities and quantitative relationships within real numbers have the potential for enhancing their future students' understanding of real numbers. In this article, we propose an instructional sequence that addresses quantitative relationships for the construction of real…

Representing repeating nonterminating decimals as rational numbers is a topic introduced in the seventh-grade Common Core State Standards for Mathematics. According to Content Standard 7.NS.2.D., students should be able to represent a rational number as a decimal and understand that the decimal will either end in zeros or eventually repeat (NGO…

This study aims to introduce a method that is based on the relationship between numbers and geometry, which can be used to show the exact location of rational numbers on the number line, compare rational numbers, make calculations, and examine rational numbers conceptually through parallel lines. It is believed that this method will to contribute…

Number line models provide a visual aid for students to examine the relationship of integers with each other and facilitate learning of integers and integer operations. Such models are typically used when students are asked real-life problems. This study employs a qualitative case study design to perform an in-depth analysis of how middle grade…

Algebraic thinking in children can bridge the cognitive gap between arithmetic and algebra. This quantitative study aimed to develop and test a cognitive model that examines the cognitive factors influencing algebraic thinking among Year Five pupils. A total of 720 Year Five pupils from randomly selected national schools in Malaysia participated…

This document includes instructional tips on: (1) Building on students' informal understanding of sharing and proportionality to develop initial fraction concepts; (2) Helping students recognize that fractions are numbers that expand the number system beyond whole numbers, and using number lines to teach this and other fraction concepts; (3)…

The integer is a basic concept in studying arithmetic and algebra. However, students still frequently experience misconceptions, especially in negative integer, count operations. Traditional games are activities that are often carried out by students in coastal areas so that they are relevant to be used as a tool to construct learning trajectories…

This paper makes a proposal, from the perspective of a research mathematician interested in mathematics education, for broadening and deepening whole number arithmetic instruction, to make it more relevant for the twenty-first century, in particular, to enable students to deal with large numbers, arguably an essential skill for modern citizenship.…

Skills and understanding of operations with negative numbers, which are typically taught in middle school, are crucial aspects of numerical competence necessary for all subsequent mathematics. To more swiftly and coherently develop the field's understanding of how to foster this critical competence, we need shared measures that allow us to compare…

Improving the strength of alignment between educational components is essential for quality assurance and to achieve learning goals. The purpose of the study was to investigate the strength of alignment between Senior Phase mathematics content standards and workbook activities on numeric and geometric patterns. The study contributes to…