Eliciting student thinking during mathematics instruction allows teachers to choose tasks with high cognitive demand while also engaging students to use productive struggle to solve mathematical problems, thus increasing their conceptual understanding. Often, students who require intensive intervention in mathematics, in particular, students who…

A case study of calculus instructional material (comprising of lecture notes and tutorial practice worksheets) designed by teachers from a Singapore pre-university is presented in this paper. As textbooks have not been available for mathematics at the pre-university levels, the instructional material was a product of the teachers' collaborative…

The purpose of this study was to examine prospective teachers ' uses of diagrams and approaches to congruence while solving proof tasks. Eight prospective high school mathematics teachers were given three proof tasks to solve at the beginning and end of a mathematics education course. The course used the history of mathematics as the context for…

In engineering, kinematics is widely regarded as a fundamental topic with the literature agreeing that students possess a wide range in understanding of the topic. This study aims to take a second-order approach by understanding and exploring the qualitatively different ways in which students approach solving kinematics problems. Phenomenography…

This study links the teaching practice of productive struggle, a psychological perspective of classroom activities, and the classroom microculture, an interactionist perspective that combines sociocultural and psychological considerations (Cobb & Yackel, 1996). The research question for this study is: "In what ways does a teacher…

This design case introduces a design and development process of theories from environmental psychology, humanities, and social sciences as heuristic thinking devices to measure human-centered design solutions. The pedagogical review of the traditional studio design process revealed obstacles as students translated their research and program to the…

The aim of the present study was to examine how social evaluation influences creative idea generation, and whether this effect develops with age. To do so, early adolescents, middle adolescents, and late adolescents performed a creative task either alone or under the supervision of an adult examiner. Three major findings emerged: 1) the social…

Many research results show that students often highlight "mixed-type" reasoning when tackling problematic situations and problems. This reasoning is based on the simultaneous use of common-sense and mere descriptions of facts, perceived as sufficient to build an "explanation" of observed or proposed situations and problems.…

We used a sequential synthesis problem to investigate novice teachers' conceptual difficulties in hydrodynamics. Twenty-one new secondary level physics teachers from various regions of China, who had been in service for no more than 2 years, participated in the study. Each participant completed a written hydrodynamics problem consisting of four…

Preparing students for their future is a clear and concise goal of education. STEM education is no different and is often considered a key way to increase students' 21st century skills or prepare students for a future career (Bybee 2010). We also believe that education should engage students as empathetic problem solvers (as described in Bush and…

The development in mathematical flexibility should be included in the mathematics teaching training of students in Primary Education Degree. Teachers in training have to acquire the skill to modify the problem resolution and be able to break with stereotyped methods. This document presents an analysis of spontaneous mathematical flexibility…

Mathematics scores on the 2019 National Assessment of Education Progress increased by only two points for both fourth and eighth grade students since 2007, indicating that students continue to struggle in mathematics (National Center for Educational Statistics, 2007; U.S. Department of Education, 2019). The development of both conceptual and…

Representation is widely viewed as central to mathematical problem solving, while online scaffolding is considered helpful in supporting learners' progress from actual to potential developmental levels of mathematics understanding. Therefore, this study investigated the effectiveness of employing online single vs. multiple representational…

Motivation: This research investigates the transformative impact of integrating AI into mathematics education, aiming to enhance students' conceptual understanding and self-efficacy. It addresses the crucial need for innovative teaching methods in response to contemporary challenges in education and aims to fill gaps in understanding the potential…

In this brief article, Peter, Larissa and Doug present a single-page scaffold that challenges us to think of the mathematical proficiencies in a whole new way. By thinking of the proficiencies as verbs, they can be seen as purposeful learner actions and offer clues as to what it might mean to be a mathematician.