The evolution of mathematics coincided with advancements in its teaching. The 19th and 20th centuries marked a pedagogical revolution in mathematics education. This paper argues that Bruner's (1966) model, Gagné's (1985) taxonomy, innovative teaching methods emphasizing research and problem-solving, and the inclusion of data analysis topics have…

Circle and disc are fundamental concepts introduced in middle school, forming the basis for many other mathematical ideas. Students often face challenges in comprehending circles, discs, and their basic elements. This research examines the processes of sixth-grade students in constructing circles, discs, and their essential components within a…

The relation between mathematical achievement in early childhood and future academic success is well established. However, our knowledge about the effect of instruction on mathematical performance is often reliant upon self-report or videotaped instruction measures and standardized achievement assessments. The current study uses teacher audio…

Parents play a vital role in shaping the ways young children understand the world around them. This paper reports on how the Community Mathematics Project (CMP)--a mathematics tutoring program for parents of diverse young children--affected the ways parents engaged in mathematical sensemaking while using virtual manipulatives and questioning to…

Every educator knows the sinking feeling of a lesson gone wrong. As teachers look around the room and realize that many of their students are just not getting it, they often feel like failures. However, the struggle students experience as they persevere through high-quality challenging tasks is not a sign of failure, but rather a key aspect of…

The ability to relate mathematics teaching to real life is the common goal of many countries' mathematics curriculum National Society for Experiential Education's (NSEE) [2011] "Eight Principles of Good Practice for All Experiential Learning Activities." (intention, originality, planning, clarity, monitoring and evaluation, reflection,…

Mathematical skills significantly predict students' educational paths. Mathematical achievement varies depending on the student's socioeconomic status (SES). However, the extent of the SES gap for specific mathematical skills remains unclear. In this cross-sectional study, we examined age variations by SES in three mathematical skills, applied…

Being able to understand, interpret, and critically evaluate data is necessary for all individuals in our society. Using the PreK-12 Guidelines for Assessment and Instruction in Statistics Education-II (GAISE-II; Bargagliotti et al., 2020) curriculum framework, the current paper outlines five evidence-based recommendations that teachers can use to…

Children's approaches to learning (AtL) are widely recognized as a critical predictor of educational outcomes, especially in early childhood. Nevertheless, there remains a dearth of understanding regarding the dimensionality of AtL, the reciprocal dynamics between AtL and learning outcomes, and how AtL operates in non-Western contexts. This paper…

This research aims to describe the mathematical problems posed by prospective elementary school pre-service teachers in differentiated learning. This research uses a qualitative approach and uses problem-posing tasks and interviews as tools for collecting data. In the problem-posing task, information on learning conditions is provided, which…

Learning fractions is essential for academic and daily life success. A critical first step in acquiring fractions is learning to transcode them (e.g., writing ½ when hearing "one half"). However, little is known about how students master fraction transcoding. We addressed this gap by assessing fraction writing in two groups of Brazilian…

The home numeracy environment (HNE) is an essential factor to explain family engagement in relation to numeracy. Research in this field has mostly focused on English-speaking families and has not taken into consideration cultural differences that contextualize the home environment. Measuring HNE in more ethnically diverse samples might counter…

Teaching requires attention to individual student needs by providing both adequate challenge and sufficient support to help students successfully gain academic skills (Shurr et al., 2019). The learning stages framework divides typical learning into four distinct stages: acquisition, fluency, maintenance, and generalization (Collins, 2012; Haring…

Mathematical reasoning, a fundamental aspect of human cognition, poses significant challenges for artificial intelligence (AI) systems. Despite recent advancements in natural language processing (NLP) and large language models (LLMs), AI's ability to replicate human-like reasoning, generalization, and efficiency remains an ongoing research…

This article is about problems that children may have when learning mathematics, problems that are also typified in publications as 'dyscalculia'. We consider two questions. The first: Is a child a dyscalculic if it runs into trouble learning mathematics? The second: Does a child have problems when learning mathematics because it experiences…