As national and international assessments continue to show students struggle with rational concepts, which are seen as a major stumbling block for future career in STEM fields, we used the certainty of response index (CRI) as a method of analysis to investigate a group of 40 United Arab Emirates (UAE) seventh grade students' understanding of basic…

Background/purpose: Investigation into the misconceptions of preschool students in mathematics and their differences between the ages of 4-5 and 5-6 years old helps form appropriate developmental mathematics teaching programs. However, although several studies have been conducted examining preschoolers' previous knowledge and misconceptions about…

The relation to operands (RO) principles describe the relation between operands and answers in arithmetic problems (e.g., the sum is always larger than its positive addends). Despite being a fundamental property of arithmetic, its empirical relation with arithmetic/algebraic problem solving has seldom been investigated. The current longitudinal…

Learning to calculate with natural numbers by structuring seems promising but how this can be taught in a sustainable manner remains an open question. An eight-month-long intervention based on the idea of using a structural approach to addition and subtraction, and particularly bridging through ten, was implemented in four Swedish first-grade…

Urban and rural children have different levels of performance in arithmetic processing. This study investigated whether such a residence difference can be explained by phonological processing. A total of 1,501 Chinese primary school students from urban and rural areas were recruited to complete nine cognitive tasks: two in arithmetic performance…

The aim of the study was to determine the concepts that primary school fourth-grade students reveal with their mind maps related to four operations (addition, subtraction, multiplication, division) and to compare the mind map and achievement test scores. In the study, a mixed method was used in which quantitative and qualitative data were…

The number line and the neutralization model have been used very extensively in teaching integer additions and subtractions for decades. Despite their advantages, issues concerning subtractions on these models are still debatable. Therefore, the neutralization on an empty number line (NNL) model is proposed in this research to help students better…

This paper presents an analysis of fractions errors displayed by learners due to deficient mastery of prerequisite concepts. Fractions continue to pose a critical challenge for learners. Fractions can be a tricky concept for learners although they often use the concept of sharing in their daily lives. 30 purposefully sampled learners participated…

This study aimed to reveal the conceptual and operational conceptions of sixth-grade students in the process of division. The focus of the study included the strategies used in the division process, the students' understanding of the division algorithm, and their ability to interpret the remainder in a real-life context. Being qualitative in…

Background: The concept of rational numbers is one of the learner's first experiences with a Mathematics concept beyond the basic skills operations on whole numbers. The personal knowledge of fractions that teachers bring to the teaching context is important because teachers mediate the conceptions that their learners construct. Aim: This study…

The integration of virtual manipulatives in classroom practices facilitates student learning processes. For this, the teacher must understand how to support students in establishing mathematical connections between the manipulation and their interpretations of the representations. We present a learning scenario that integrates the use of virtual…

This research investigated students' sources and causes of errors and misconception in solving routine problems involving addition, subtraction, multiplication, and division of integers. This qualitative study involved observation of eight Year 7 classes and interviews with the respective classroom teachers. Sixteen Year 7 students who exhibit…

This study aims to produce a learning trajectory using the mathematical modeling in helping students to understand the concept of algebraic operations. Therefore, the design research was chosen to meet the research aims and to give in formulating and developing local instructional theory in learning algebraic operations. Learning trajectory…

This study aims to develop a learning trajectory to help students understand concept of subtraction of integers using multimedia in the fourth grade. This study is thematic integrative learning in Curriculum 2013 PMRI based. The method used is design research consists of three stages; preparing for the experiment, design experiment, retrospective…

Fraction arithmetic is among the most important and difficult topics children encounter in elementary and middle school mathematics. Braithwaite, Pyke, and Siegler (2017) hypothesized that difficulties learning fraction arithmetic often reflect reliance on associative knowledge--rather than understanding of mathematical concepts and procedures--to…