Recent research on integration has shown the importance of quantities-based meanings for integrals. However, this research body is still in need of detailed empirical accounts of "how" students develop such understandings across an entire unit on integration. This paper contributes by providing one such account, based on a…

Rational numbers are represented by multiple notations: fractions, decimals, and percentages. Whereas previous studies have investigated affordances of these notations for representing different types of information (DeWolf et al., 2015; Tian et al., 2020), the present study investigated their affordances for solving different types of arithmetic…

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…

This study investigated children's knowledge of the addition of fractions with unlike denominators. It focussed on the strategies used by children to add fractions with unlike denominators. A cross-sectional survey of Grade 8 children in schools in two districts in Ghana was used. A test on the addition of fractions with unlike denominators was…

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…

This study investigated the effects of working memory load (WML) and automaticity on mental addition through an examination of both task and individual characteristics within the framework of cognitive load theory. Results from 73 fourth graders showed that WML, automaticity, and their interaction had significant effects on mental addition.…

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…

This paper presents a replication study investigating the effectiveness of a strategy to assist students with learning difficulties in adding fractions. Drawing on the research conducted by Grünke et al. (2023), this single-case analysis extends the application of the "Look, Ask, Pick" (LAP) mnemonic technique initially introduced by…

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…

This study examined a cohort of middle school pre-service mathematics teachers' understanding of the rate of change as they engaged in a model development sequence. By adopting a design-based research perspective, a model development sequence on the concept of rate of change has been designed and implemented as part of a mathematical modeling…

It is critical that elementary students develop understanding of fractional numbers because understanding concepts such as fraction magnitude predict later mathematics success. Representing fractions in multiple ways assists students in developing a sense of fraction magnitude. A systematic approach to presenting multiple representations is the…

Nowadays, tablets and their applications are part of the children's daily lives. These digital educational activities can become a potent educational tool for efficient and effective in neurotypical as well as children with autism spectrum disorder (ASD). Tablets and their applications allow children to take advantage of new learning platforms and…

Teachers require support in developing the pedagogical skill of interpreting students' mathematical thinking and providing effective feedback that promotes learning. However, there is a lack of research assessing the quality of feedback based on teacher noticing in mathematics classes. This study analysed 20 preservice teachers' (PSTs) feedback…

This study used units coordination as a theoretical lens to investigate how whole number and fraction reasoning may be related for preservice teachers at the conclusion of a math methods class. The study contributes quantitative evidence that units coordination provides a common foundation for both mathematical knowledge for teaching whole number…

Fractions are an integral part of the mathematics curriculum. Most students acquire proficiency with these concepts during the course of their elementary education and are usually able to perform basic fractions operations when reaching middle-school age. However, a considerable number of students require extra help to not fall further and further…