This paper reports changes of the quality of instruction and students' attitudes towards mathematics at one high school during 3 years while teachers participated in a teacher community. The setting for this research was a small-sized high school in South Korea with 154 students and three mathematics teachers. I analyzed the teachers' mathematics…

Recent evidence demonstrates that mathematics knowledge in the early years is an important contributor to students' learning and later achievement in mathematics. As early mathematics education has assumed heightened importance, the quality of early mathematics teaching and learning experiences has attracted global attention. Several researchers…

Across many international contexts, more recent standards-based and other educational reforms have largely intended to transform teaching. Given the importance of teacher learning to such transformations, we argue that a learning-focused support approach will be essential if such reforms are to be productively taken up by schools and teachers. We…

Although basing instruction on a learning trajectory (LT) is often recommended, there is little direct evidence to support the premise of a "LT approach"--that to be maximally meaningful, engaging, and effective, instruction is best presented one LT level beyond a child's present level of thinking. The present report serves to address…

Counting is fundamental to early mathematics. Most studies of teaching counting focus on teachers observing children count. The present study compares mathematical ideas that 12 PK, transitional kindergarten (TK), and kindergarten teachers noticed from observing their own students count during a classroom session of Counting Collections with ideas…

In this study, the relationship between preschool teachers' perceptions of efficacy in mathematics education they give and their attitudes towards mathematics education was investigated. The research method of the study is the relational screening model, one of the quantitative research methods. The research was carried out on 122 preschool…

Like many others around the world, the authors have moved their busy lives and research-practice partnership to the planet of distal learning and remote working. While the news about the spreading of the pandemic and the dire economic consequences entered their homes, they did not want to lose what had brought them together in partnership this…

This article reports on a combined quantitative and in-depth qualitative study of 315 Danish upper secondary (grades 10-12) mathematics students' answers to six modelling tasks that place emphasis on the early phases of the so-called modelling cycle. In order to focus attention on the extra-mathematical aspects of modelling, the technical…

Many studies on visuospatial reasoning have drawn upon a psychological perspective. Importantly, some research has shown that spatial capabilities are developed through experiences and others emphasize the value of physical involvement. This article reports on investigations of how ecocultural experiences, that is cultural experiences in the…

Four operations algorithm is among the major topics occupying a significant position in primary school schedule. Moreover, utilizing alternative strategies during the education process and improving operation flexibility of students also considered important in teaching of mathematics. Flexibility in computing is the ability of solving any…

With the advancement of digital technology, the roles of teachers and students are slowly changing. The classroom is on the verge of becoming a new, more open place, one with fewer barriers to the rest of society. Our purpose in this paper is to discuss how the creation of videos with mathematical content may contribute to this process of…

Visualising positive and negative numbers on a number line is helpful for exploring problems involving operations with positive and negative numbers. This is because number lines lend themselves to exploring problems involving continuous linear contexts such as travelling distances and temperature. Teachers in a professional development program…

During the sixteenth century, a relevant number of books related to practical arithmetic were published in Spain. This paper presents a comparative study that aims to identify the object and target of five old mathematics books and the main contents of these books. In order to do so, all the contents and all the examples found in five arithmetic…

An important goal in school algebra is to help students notice the covariational nature of functional relationships, how the values of variables change in relation to each other. This study explored 102 Year 7 (12 to 13-year-old) students' covariational reasoning with their constructed graphs for figural growing patterns they had generalised. A…

A key motivational tactic in undergraduate mathematics teaching is to launch topics with fundamental questions that originate from surprising or remarkable phenomena. Nonetheless, constructing a sequence of tasks that promotes students' own routes to resolving such questions is challenging. This note aims to address this challenge in two ways.…