Reasoning is the process of thinking used to make claims and reach conclusions. It is among the first skills that should be taught to students in mathematics lessons and contributes to the creation and development of mathematical foundations. This study identifies evolution and trends in research on mathematical reasoning over the last four…

Early math skills predict later achievement for young children; thus, it is important to expand what is known about how to support preschool children's development of these skills. While there has been some research on interventions, including those using systemic instruction, to teach math skills to preschoolers, there is a need for additional…

Background/purpose: The application of learning models is expected to significantly promote the enhancement of students' problem-solving abilities through the development of interactive learning models. This study aims to (1) determine whether the Development of the Component Display Theory (CDT) Model is categorized as valid, practical, and…

This paper reports on our study of the effectiveness of the course instruction in the numeracy course 'Numbers for Life', offered at McMaster University, Canada, and taught by one of the co-authors. In this course students explore the ways to reason with numbers in a variety of contexts important not only for their individual lives and their…

Researchers increasingly identify virtual reality (VR) simulations as a potentially effective professional development tool. However, simulations used in education and behavior analysis typically require active oversight from technicians and instructors. "Smart" VR integrated with artificial intelligence could independently administer…

The reasons for teaching programming in school are indeed manifold. Programming can for example be utilized as a vehicle for understanding and learning particular mathematical subject matter, or as a tool for solving mathematical problems. In this paper, however, we propose to utilize programming as a vehicle for developing mathematical…

Professional noticing has been stressed as one of the key professional competencies that teachers must develop. To date, there is a robust amount of literature on teacher noticing with a focus on students' mathematical thinking. However, we have thus far not found any study that focuses on teacher noticing of classroom situations in which…

Math language plays a crucial role in early math skill development. However, previous studies have measured math language using children's knowledge or the environmental input of mathematical language, often limiting the scope to specific types of mathematical language. This study examined both numerical (e.g., number-related) and non-numerical…

This study examines how Scratch can influence mathematical generalization in secondary school students. Real-life problems were adapted and presented to students as part of a problem-solving process. The study focused on the generalization process in terms of mathematization and verification. Data was collected through screen recordings and…

Early numerical skills are important not only for later mathematical achievement but for overall achievement and are associated with later income, health, and quality of life. Socioeconomic disparities in numerical skills are visible before children begin school, and widen throughout schooling. It is, therefore, important to support the…

The paper presents findings from a study that examined, through the lens of the Image Having layer of the Pirie-Kieren model, the qualitative characteristics of the images that different children formed when engaging with eight, novel partitive quotient tasks. The Image Having layer is the first point of abstraction within the Pirie-Kieren model.…

This study scrutinizes the influence of project-based learning (PBL) and inquiry-based learning (IBL) on fourth graders' teamwork skills and critical thinking in math classes. A historical review reveals that while they have positive effects in multiple fields, their sole use in elementary math teaching is yet to be explored. 55 fourth-grade…

In the present study, we explored whether future teachers considered spatial skills to be built up slowly and incrementally (incremental view) or considered spatial skills to be an innate, static aptitude (entity view). We also examined whether these views were associated with personal spatial skills, confidence in spatial problem-solving, or…

Using Action, Process, Object, and Schema (APOS) theory in learning basic mathematics is an alternative to promote the students' Mathematical Critical Thinking Skills (MCTS). This experimental study aims to compare the improvement of students' MCTS in learning Basic Mathematics using a pretest-posttest control class design. Ninety students…

The study investigated the impact of pedagogies of practice approach on pre-service teachers' professional noticing skills in perimeter and area measurement concepts. Thirty-two pre-service teachers engaged in a video-based module situated in pedagogies of practice framework, and the analysis of three pre-service teachers was provided for in-depth…