In the current realm of education 4.0, teachers play a pivotal role as facilitators of holistic skill development. The shift in focus towards accentuating creativity, communication, critical thinking and collaboration (4C) skills signifies an acknowledgment of the changing demands brought about by the industrial revolution 4.0. This transformation…

Transform mathematics instruction with the comprehensive mathematical competencies (CMC) framework--a research-based model that integrates seven essential competencies: conceptual and procedural integration, problem solving, logical reasoning, communication, tool use, pattern recognition, and student engagement. Through practical classroom…

We aim to open up discussion about the intertwined roles of teachers and tasks that involve students communicating about mathematics when working in groups. Over many years we have observed, researched and ourselves have taught students working on mathematics in groups and find that it is often easier to pay attention to the forms of communication…

Moving from arithmetic to algebraic thinking at early grades is foundational in the study of number patterns and number relationships. This qualitative study investigates mental computational activity in a third grade classroom's and its relationship to algebraic thinking and reasoning. The data sources include classroom observations, field notes,…

Background: With the recent pivot to online instruction and/or to mixed online/face-to-face (i.e., hybrid) models of teaching necessitated by the novel coronavirus pandemic, the uses of technology to support instruction would seem to have great importance. Whereas effective integration of technology in mathematics classrooms requires recognition…

Many classroom-observation instruments have been developed (e.g., Gleason et al., 2017; Nava et al., 2019; Sawada et al., 2002), but a very small number of studies published in refereed journals have rigorously examined the quality of the ratings and the instrument using measurement models. For example, Gleason et al. developed a mathematics…

Many teachers' experiences in problem-based classrooms are limited, therefore, mathematics teacher educators face a significant challenge when trying to inspire in-service teachers (ISTs) to teach through problem solving. To address this challenge, the professor in a mathematics education course designed and implemented an instructional model…

Speakers in conversation typically repeat and modify earlier comments. In mathematics conversations, these repetitions, or poetic structures, can facilitate the collaborative discovery of mathematical relationships. A close analysis of 90 turns of an algebraic problem-solving conversation reveals eight types of poetic structures. This report…

In this paper I focus on observations made regarding students mimicking of each other's gestures in face-to-face conversation while problem solving. The data supports the idea that the students may use such gestures to subconsciously signal acceptance. Through talk, gesture, prosody, and intonation, combined with context, the interlocutors may…

Recently, over 40 states in the United States adopted the Common Core State Standards for Mathematics (CCSSM) which include standards for content and eight standards for mathematical practices. The purpose of this study was to better understand the nature of young children's mathematical practices through an exploratory examination of the…

Reform efforts in mathematics education arose, in part, in response to constructivist works on conceptual learning. However, little research has examined how students with learning disabilities (LD) respond to constructivist-oriented instruction in mathematics, particularly in moment-to-moment interactions. To understand the nature of…

The U.S. storyline of emergent bilinguals has historically failed to highlight the mathematical and linguistic assets of this group; instead, it has primarily focused on providing support. To disrupt this narrative, a case study of one elementary teacher, Ms. Bristow, is presented. Ms. Bristow's discursive practices and pedagogy illustrate how she…

In this article the authors explain that when engaging in a problem-solving conversation with a child, their goal goes beyond helping the child reach a correct answer. They want to learn about the child's mathematical thinking, support that thinking, and extend it as far as possible. This exploration of children's thinking is central to…

CLIL (Content and Language Integrated Learning) is a teaching method in which learners develop linguistic competence and problem-solving abilities by learning content subjects in another language. However, learners' cognitive gains may depend on their affectivity. Negative affect hampers complex cognitive processing essential for problem-solving,…

Conversational repair often occurs in conversations when people attempt to address communicative breakdowns or inaccuracy by way of repeating what have been said or putting them in another way. The review of literature on conversational repair revealed that as an important concept in pragmatic aspect of language, it is an effective strategy to…