The study of how children learn numbers has yielded one of the most productive research programs in cognitive development, spanning empirical and computational methods, as well as nativist and empiricist philosophies. This paper provides a tutorial on how to think computationally about learning models in a domain like number, where learners take…

With democracy in mind, promoting students' cognitive, personal, and social development can inform and shape the mathematics curriculum and classroom practice with the goal of their becoming more capable, self-reflective, and socially aware human beings. Toward that realization, their mathematics experience could include: heuristics, as it…

There is a growing interest in STEM (science, technology, engineering, and mathematics) units and projects in the early childhood and elementary years. There are many advantages of embedding math in STEM contexts and activities; it can be excellent for reinforcing math (as well as science, technology, and engineering) concepts and skills. However,…

Studies have found that some teacher professional development programs that are based on Cognitively Guided Instruction (CGI) can increase student mathematics achievement. The mechanism through which those effects are realized has been theorized, but more empirical study is needed. In service of this need, we designed a novel measure of…

Mathematical thinking is a complex, multi-faceted process that has been described as messy and difficult but can also show growth and insights into conceptual understanding and knowing. This paper explores the application of Edward de Bono's practical thinking, in particular, the occurrence of porridge words to examine the mathematical thinking of…

The Century of Turkey Education Model, introduced in 2024, emphasizes developing critical thinking and analytical skills, with the Mathematics Curriculum. This curriculum integrates literacy skills in learning objectives, particularly financial literacy, to empower students in making informed economic decisions and managing resources effectively.…

This theoretical article examines the crucial role of play-based learning (PBL) in enhancing the mathematical skills of children in the Early Childhood Phase, referred to as Foundation Phase (Grade R-3) learners, within a South African context. The article argues that the traditional approach to teaching early childhood mathematics, where teachers…

When considering the characteristics that teachers should have, concepts such as critical thinking, active learning, taking responsibility, evaluation, analysis, self-evaluation and reflective thinking are important. In this context, microteaching and peer assessment methods come to the fore. Microteaching is defined as sharing a part of the…

This qualitative case study aims to address the ways that pre-service mathematics teachers (PSTs) used a rope in a daylong research meeting for cognitive development of children's understanding of counting numbers in Tanzanian elementary schools. Three university mathematics pre-service teachers volunteered participating in this study. Collective…

Algebra is critical in shaping future mathematics success and is integral to the K-12 curriculum. Despite its inclusion, a common challenge arises as students' progress to higher grades without a solid foundation, resulting in challenging learning experiences. This action research study focuses on the algebraic learning experience of a Grade 7…

In this article we report on a study focused on revealing and categorizing the arguments that preservice mathematics teachers put forward when they are asked about why mathematics is taught, which is a question closely related to the justification problem in mathematics education. Another focus of the study is the identification of myths within…

This study aimed to evaluate the effects of intervention using graphic organizers on the cognitive and affective improvement of students with intellectual disability (ID), with learning disability (LD), without disability, and at-risk learners in Korea. A total of 49 peer-reviewed journals and dissertations for the last 20 years were included for…

This book is an exploration of story and its importance in early childhood. It provides a thorough theoretical foundation, and considers how to practically implement the use of stories to aid children's wellbeing and holistic development. The chapters cover topics including cognitive and emotional development, creativity, play, mathematics,…

Cognitive development of eighth-grade students, as identified by Jean Piaget, occurs during a time when many of them are transitioning between concrete operations and formal operations where the ability to think in abstract concepts becomes possible. Because of this period of transition, many eighth-grade students find difficulty in demonstrating…

A case study of calculus instructional material (comprising of lecture notes and tutorial practice worksheets) designed by teachers from a Singapore pre-university is presented in this paper. As textbooks have not been available for mathematics at the pre-university levels, the instructional material was a product of the teachers' collaborative…