This paper describes the conceptions about complex numbers that a group of university students has, these were built from the application of an activity sequence centered on these numbers. This sequence is based on the APOS theory, some aspects of semiotic representation theory, and the use of digital technology. Particularly, both the general…

What is the foundational knowledge that children rely on to provide meaning as they construct an exact symbolic number system? People and animals can quickly and accurately distinguish small exact quantities (i.e., 1 to 3). One possibility is that children's ability to map small quantities to spoken number words supports their developing exact…

This paper reports on an experiment involving 108 sixth-grade French students in which the history of Chinese numeration was used in mathematics education. The aim of this study is to evaluate the relevance of using ancient number systems in mathematics education, which is common in French textbooks. In the experiment a pre-test with usual…

The paper presents some reflections and activities developed by researchers and teachers involved in teacher education programs on cultural transposition. The construct of cultural transposition is presented as a condition for decentralizing the didactic practice of a specific cultural context through contact with other didactic practices of…

The aim of this study was to examine the number sense performance of 8th-grade Turkish students. In this study, the students' performances on number sense were also examined in terms of gender, school location, parents' education level, maths achievement, perceived student satisfaction with the maths teacher, perceived importance of maths and…

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…

The ability to perceive structures in sets and to use them to determine cardinality is one important basis for arithmetical learning. This study is based on a theoretical model that distinguishes between the two processes of perception and determination. A total of 95 5-year-old children were interviewed individually to find out whether and how…

The cardinal and ordinal aspects of number have been widely written about as key constructs that need to be brought together in children's understanding in order for them to appreciate the idea of numerosity. In this paper, we discuss similarities and differences in the ways in which understandings not only of ordinality, cardinality but also…

Children's knowledge of the ordinal relations among number symbols is related to their mathematical learning. Ordinal knowledge has been measured using judgment (i.e., decide whether a sequence of three digits is in order) and ordering tasks (i.e., order three digits from smallest to largest). However, the question remains whether performance on…

When young children attempt to locate numbers along a number line, they show logarithmic (or other compressive) placement. For example, the distance between "5" and "10" is larger than the distance between "75" and "80." This has often been explained by assuming that children have a logarithmically scaled…

Evaluating the proving process of mathematics teachers is important for the development of their proof skills. Developing the proof skills of teachers can contribute to their students' meaningful learning of mathematics. For example, teachers showing simple proofs about number theory can make it easier for students to understand the concepts of…

There have been many efforts to measure pedagogical content knowledge with multiple-choice survey instruments, but little is known about how different types of items contribute. In this study, we examined interviews with 9 Grade 4 teachers to develop a deeper understanding of how teachers select pedagogical representations in the context of a…

This research aims to determine second-year university students' understanding in interpreting and representing fractions. A set of fraction tests was given to students through two direct learning interventions. An unstructured interview was used as an instrument to obtain explanations and confirmations from the purposive participants. A total of…

In Asia, some children are taught a calculation technique known as the 'mental abacus'. Previous research indicated that mental abacus experts can perform extraordinary feats of mental arithmetic, but it disagrees as to whether the technique improves working memory. The present study extended and clarified these findings by contrasting performance…

This paper focuses on how Inuit students responded to a Southern mathematics teaching strategy, known as number talks, in a Nunavut elementary school. Research on the effectiveness of number talks has been conducted in the elementary context (Boaler, 2015; Murata et al., 2017), yet there is little research that focuses on Inuit students'…