The aim of this study is to reveal and evaluate the attending and interpreting skills of student thinking of prospective teachers, as well as their instructional suggestions as responding skills. The current study was conducted with 29 prospective mathematics teachers (PMTs) within a qualitative design in the context of probability. First, three…

This article reports on a national survey of post-secondary mathematics instructors (n = 458) of mathematics courses designed for elementary teachers. The article links the use of various instructional practices to instructor characteristics. Specifically, there were statistically significant differences in reported use of class time depending on…

In this article, the authors share their favorite "Construct It!" activity, which focuses on rate of change and functions. The initial approach to instruction was procedural in nature and focused on making use of formulas. Specifically, after modeling how to find the slope of the line given two points and use it to solve for the…

Purpose: Research shows that postsecondary students are largely unaware of the impact of algorithms on their everyday lives. Also, most noncomputer science students are not being taught about algorithms as part of the regular curriculum. This exploratory, qualitative study aims to explore subject-matter experts' insights and perceptions of the…

Teacher education programs are pivotal in the professional preparation and formation of pre-service secondary mathematics teachers (PSMTs), but there appears to be a lack of understanding of how best to prepare PSMTs for the profession. The purpose of this study was to examine and monitor changes over time in PSMTs' views about approaches to…

This study addressed the challenge of connecting elementary teacher candidates' course work and fieldwork in order to foster a cohesive experience in learning to teach mathematics. In this study, a Mediated Field Experience was designed for five elementary teacher candidates in their internship setting. The study utilized qualitative methods to…

Construct maps and related item type frameworks, which respectively describe and identify common patterns in student reasoning, provide teachers with tools to support instruction built upon students' intuitive thinking. We present a methodological approach--embedded within common assessment development processes--for developing such construct maps…

This paper explores student emotion and learning experiences fostered by lecturing-style instruction in Real-Analysis problem-centered lessons. We focus on two lessons that were taught by two reputable instructors and involved challenging, mathematically-related problems the students did not understand. Nonetheless, one lesson evoked negative…

Although research highlights the importance of analyzing the geometric work of teachers, there are few validated instruments in this line. This study presents the processes of design and validation of a forced-choice questionnaire that allows the characterization, from a theoretical basis, of how geometry teachers organize their teaching practice.…

The presented article is dedicated to a new way of teaching substitution in algebra. In order to effectively master the subject matter, it is necessary for students to perceive the equal sign equivalently, to learn to manipulate expressions as objects, and to perceive and use transformations based on defining their own equivalences. According to…

For educators, identifying and characterising problems in their teaching practice is essential for triggering inquiries into their practice. Knowing what educators consider problematic is essential for generating strategies for situated approaches to help teacher educators manage their problems and promote professional learning. In this study, we…

Preservice elementary teachers' attitudes towards mathematics are often negatively influenced by their K-12 education. Accordingly, teacher educators must allow preservice elementary teachers to experience mathematical instruction differently to change their attitudes toward mathematics and their conceptions about what it means to teach and learn…

ABN (Abierto Basado en Números--Open Calculation Based on Numbers) is a method for teaching basic arithmetic operations in primary education that has become popular in recent years and that is based on the decomposition of numbers through manipulative materials that encourage mental calculation. Currently there is limited number of tools that can…

Acknowledging that our professional development (or methods course) was not going as well as we had hoped was difficult. However, knowing what to do and correcting the problem was even more challenging. This article explains how we engaged teachers in helping us rethink our video club by listening to and acting on their ideas. Through "coffee…

Recent research syntheses have identified several potentially high-leverage teaching strategies for improving low-attaining secondary school students' learning of mathematics. These strategies include the structured use of representations and manipulatives and an emphasis on derived facts and estimation. This paper reports on 70 semi-structured…