Teacher responses to student mathematical thinking (SMT) matter because the way in which teachers respond affects student learning. Although studies have provided important insights into the nature of teacher responses, little is known about the extent to which these responses take into account the potential of the instance of SMT to support…

Elementary teachers in California were tasked to use cognitively guided instruction (CGI) strategies in mathematics classrooms, but it was uncertain if they had the self-efficacy, confidence, resources, and support to do so consistently. The purpose of this basic qualitative study was to investigate K-5 teachers' perceptions about their…

Mathematicians teaching at the university level have a deep understanding and appreciation for the mathematics that they teach. However, they rarely receive much formal training in teaching. Thus, university mathematicians must rely on their mathematical understandings and personally developed ideas of teaching to guide their decision-making.…

This study aims to understand a middle school mathematics teacher's instruction and reflections on her experiences with supplementary curricular materials enriched with interactive simulations--PhET interactive simulations (sims) and sim-based materials--over two years. We conceptualize Linda's (pseudonym) teaching in terms of both thinking and…

We examine in-service high school teachers' journals to explore the emerging themes in a mathematics content course for their professional development. We use a sociocultural perspective and characterize journals as signifying teachers' communication and written discourses about their thinking and experiences in the course. We use applied thematic…

In this paper, we offer a novel framework for analyzing the Opportunities for Reasoning-and-Proving (ORP) in mathematical tasks. By drawing upon some tenets of the commognitive framework, we conceptualize learning and teaching mathematics via reasoning and proving both as enacting reasoning processes (e.g., conjecturing, justifying) in the…

Many studies use instructional designs that include two or more artifacts (digital manipulatives, tables, graphs) to support students' development of reasoning about covarying quantities. While students' forms of covariational reasoning and the designs are often the focus of these studies, the way students' interactions and transitions between…

The purpose of this research was to develop and evaluate a number sense-based curriculum aiming to eliminate student errors due to mathematical misconceptions. A mixed method research model as one of the qualitative research approaches was adopted in this study aiming to develop a number sense-based instructional design to eliminate student errors…

The aim of the research was to examine and evaluate how preservice mathematics teachers' use of manipulatives to teach mathematics. In the current research, one of the qualitative research methods, case study was used. The research was conducted with 21 preservice mathematics teachers. Ten instructional sessions with manipulatives were carried out…

The purpose of the study was to investigate the experiences and perceptions of middle school students about the flipped classroom applications used in geometry lessons. The research was designed as a case study. Data were collected through field notes, focus group interviews, and semi-structured interviews. The sample consisted of 26 eighth-grade…

The aim of this study is to determine the level of compliance of the educational digital game designs developed by the form teachers for teaching mathematics with the determined criteria and to analyze the opinions of the classroom teachers on the educational digital game design process. Case study, one of the qualitative research designs, was…

The purpose of this study was to analyze the need to develop a teaching material needed in mathematics statistics lectures I. This study used a qualitative descriptive method oriented to the development of a product. The subjects of this study were fourth semester mathematics education students who were taking mathematics statistics course I and…

Information and communication technology (ICT) competences are among the most important requirements to effectively teach mathematics and science in today's classrooms. Teacher educators in the Southern African Development Community (SADC) region have prioritised ICT competences for pre-service teachers (PSTs) to effectively select suitable…

Shulman (1986) conceptualized pedagogical content knowledge (PCK) at the intersection of content knowledge and pedagogical knowledge. In this paper, I re-explore the intersection of content--in our case, mathematics--and pedagogy, not in terms of domains of knowledge, but in terms of domains of practice. I conceptualize, describe, and exemplify…

In this article special sequences involving the Butterfly theorem are defined. The Butterfly theorem states that if M is the midpoint of a chord PQ of a circle, then following some definite instructions, it is possible to get two other points X and Y on PQ, such that M is also the midpoint of the segment XY. The convergence investigation of those…