In this writing, I report on how two 12-year old children used fraction strips to add 1/2 and 2/5. In their interaction with the tool, I look for the emergence of the tool-mediated Zone of Proximal Development to analyse the knowing that become available to the children. In thinking about this interaction, I ask what is the role of the more…

A key aim of mathematics teaching is for children to develop appropriate and efficient strategies for solving tasks. The analysis presented in this paper moves beyond the exploration of changes in the strategies that children employ to solve tasks and extends to observation and exploration of changes that occur when their overall solving approach…

A central issue in the mathematics curriculum is that we want students to make connections. This issue has been analysed in a series of curricula and instruction design and analysis studies. Moving towards mathematics connections--and away from treating mathematics as a body of isolated concepts and procedures--is an important goal of mathematics…

Whole Number Arithmetic (WNA) appears as the very first topic in school mathematics and establishes the foundation for later mathematical content. Without solid mastery of WNA, students may experience difficulties in learning fractions, ratio and proportion, and algebra. The challenge of students' learning and mastery of fractions, decimals, ratio…

This paper shares how fourth grade students solved a unique type of number line task. Instead of giving students the unit and asking them to locate a fraction on the number line, students were given two points on the number line and asked to either find 1, or another number on the number line. This type of task is called "reconstructing the…

Children's understanding of fractions, including their symbols, concepts, and arithmetic procedures, is an important facet of both developmental research on mathematics cognition and mathematics education. Research on infants', children's, and adults' fraction and ratio reasoning allows us to test a range of proposals about the development of…

In this work we will analyze the relation between registers of representation and the construction of the fraction concept. Ninety-six students from first year of compulsory secondary education participated in the study, and performed equal share tasks in the context of Egyptian fractions (unit fractions with different denominators). The aim was…

In this study, Turkish and Singaporean textbooks were compared in terms of teaching content for multiplying fractions, a subject that most students have difficulty in understanding. The study analyzed the 6th-grade mathematics textbook published by the Turkish Ministry of National Education and its Singaporean counterpart. While the Singaporean…

The aim of this study is to investigate Danish pre-service teachers' (PSTs) mathematical and didactical knowledge of operations with rational numbers. This knowledge is studied through their collaborative activities to certain tasks related to the teaching of operations with rational numbers. An explicit model of the teachers' mathematical and…

Twenty-five first-year preservice teachers attending a university in the Midwest of the United States of America participated in a whole-class-setting study aimed at investigating their knowledge of how they made sense of fraction concepts and operations, and how the development of this knowledge was facilitated during a mathematics education…

Feedback in exploratory learning systems has been depicted as an important contributor to encourage exploration. However, few studies have explored learners' interaction patterns associated with feedback and the use of external representations in exploratory learning environments. This study used Fractions Lab, an exploratory learning environment…

In this set of tips, parents and caregivers will learn how to: (1) support children's understanding of fractions at home with activities on dividing objects (recommended for grades K-5); (2) support children's understanding of fractions at home with measurement activities (recommended for grades K-4); (3) support children's understanding of…

In this paper, we analyse the results of an experience designed and implemented to evaluate the epistemic and cognitive conflicts identified in the study of proportionality, carried out by a group of 21 students in their last year of primary education. Initially the students exhibit difficulties to recognize situations where proportionality can be…

This article discusses the importance of visual models in problem solving, in the scope of rational numbers. We seek to highlight the potential of this approach, as a structuring theme in the mathematical development of students in elementary education and the connections it allows to establish. In order for students to be mathematically competent…

In this article the authors overview how the recently revised (version 9) Australian Curriculum (Australian Curriculum Assessment and Reporting Authority, 2022) and student difficulties with fractions relate to five developmental Fraction Schemes developed from multiple research projects in the literature. The article shares research findings from…