The early years of education are a crucial time to develop a strong foundation of critical mathematical skills. A growing body of research continues to demonstrate that this foundational knowledge can be successfully built through teacher-facilitated, or guided, approaches to play. Despite its benefits, the implementation of guided play is…

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…

In tracing recent research trends and directions in mathematical problem-solving, it is argued that advances in mathematics practices occur and take place around two intertwined activities, mathematics problem formulation and ways to approach and solve those problems. In this context, a problematizing principle emerges as central activity to…

In this paper, we are interested in a dynamic vision of diagrams, focusing on their evocative power, their force in mathematical activity and their potential for interaction with mathematical objects. We are inspired by the work of C. S. Pierce to see diagrams as "inscriptions that organise space and articulate relations" and that of the…

Mastery of the cardinality principle (CP) is foundational for children's mathematical development. Children's age and subitizing and counting skills contribute to their CP acquisition. This study aimed to investigate the effectiveness of different types of instruction for supporting 3-4-year-olds' CP development and its interplay with child…

Students with autism spectrum disorder (ASD) are included in the general education classroom more often than ever before. Despite mathematical strengths and early success, these students experience poor outcomes (academic and employment) compared to their typically developing peers. The language of mathematics increases in complexity, use, and…

This single-case study assessed the effectiveness of a mnemonic pegword strategy designed to enhance the multiplication fact fluency of three 6th-grade students who demonstrated persistent learning difficulties in mathematics. A nonconcurrent multiple baseline across subjects design was utilized, incorporating 3-5 baseline sessions followed by…

This paper reports on the development of complex unfamiliar mathematics questions using conventional mathematics questions. The autoethnographic research data included retrospective reflections of two educators and review of literature. Data analysis resulted in a three-phase development process: identifying conventional questions and subject…

Several studies indicate that exploring mathematical ideas by using more than one approach to prove the same statement is an important matter in mathematics education. In this work, we have collected a few different methods of proving the multinomial theorem. The goal is to help further the understanding of this theorem for those who may not be…

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…

To understand the ways that manipulatives might support changes in students' reasoning about algebraic generalizations, a constructivist teaching experiment was conducted with two sixth-grade students. The students interpreted numerical situations with units of one and could construct units of units in mental activity. Initially, the students'…

In this case study, two teacher educators at Minority Serving Institutions explore how artifacts can foster deep, original thinking in a classroom. We share how we modeled the use of artifacts to design an interdisciplinary social studies lesson with teacher candidates (TCs). Making connections to "realia," such as maps, brochures, and…

Developing students' mathematical creativity constitutes a key objective in curricula worldwide. Although teachers recognize their key role in fostering mathematical creativity, research indicates a discrepancy between their beliefs and classroom practices--the "creativity gap". Professional development programs have enhanced teachers'…

The aim of this article is to buid a Guide to the Analysis of Probability Textbook Lessons for secondary education (students aged 12-14), using the framework of Didactic Suitability. The facets, components and indicators of the didactic suitability construct are applied to categorize and organize didactic-mathematical knowledge on teaching and…

The aim of this study is to reveal the impact of Inquiry-Based Learning (IBL) on students' ability to come up with the rules of divisibility themselves and on their academic achievement in the 8th grade Mathematics course as well as to obtain students' views on the learning and teaching process, through the use of a mixed-methods sequential…