Open tasks are mathematical problems "that promote mathematical reasoning and problem solving and allow multiple entry points and varied solution strategies" (National Council of Teachers of Mathematics [NCTM], 2014, p. 17). Open tasks can have more than one right answer, solution, or outcome. Facilitation of open tasks offers learning…

The authors share an online collaborative problem-solving activity that integrates support for students' developing conceptual understanding, focused engagement, and positive feelings of agency and identity.

Even before the release of the National Council of Teachers of Mathematics (NCTM)'s Principles to Actions (2014), teachers paid significant attention to mathematics tasks based on their positive influence on student learning (Doyle, 1988; Kazemi, 1998; NCTM, 1989, 2000). Over the last almost quarter century, we have learned a lot about high-level…

Engagement in complex, challenging and multifaceted model-eliciting activities is considered helpful for preparing learners for everyday life. The current study seeks to trace the evolution of modelling routines during two model-eliciting activities. To identify how these routines emerged and evolved, we video-recorded a group of five prospective…

This article uses a cultural-developmental framework to illuminate the interplay between collective and individual activity in the mathematical reasoning displayed in a university Masters level lesson on fractals. During whole class and small group discussions, eleven students, guided by an instructor, engage in inductive reasoning about the area…

The purpose of this article is to demonstrate how exponential functions and patterns can be taught by well-structured lessons composed of classroom activities, mathematical questions, discussions, and solving problems. Sawyer (1943) used a rope-and-post system to introduce the concept of logarithms and to calculate a product by adding the…

This paper analyses information and university students's opinions, from the Faculty of Geography of Babes-Bolyai University, Cluj-Napoca, Romania, regarding the field trips organised during their studies. Information and opinions were collected by means of a questionnaire administered in 2017. There were analysed: the number of field trips…

The implementation of history education at universities has not yet seen able to give optimal results. This study aims to propose a model for improving the quality of history education in higher education. It poses the primary research question: what is the quality improvement model of history education like according to the needs analysis? The…

This qualitative study aimed at describing student verbal interaction verbally through cognitive activities consisting of procedural, disputational, and exploration in solving geometry problems. This research was in the form of students' verbal interaction activities in group discussion which decribe students' thinking process in detail, both the…

This paper analyses meaning-making processes in a blended setting--face-to-face interaction and web forum--purposely created for collaborative learning activity. The analysis focuses on one pair out of 14 dyads. The dyad comprises two female students aged 17 and 18 who attended a Brazilian third-year state secondary school. We envisioned…

This research brief discusses the benefits of teachers using mathematical discourse--allowing students to explain, justify, and debate their individual techniques for solving math problems--to enhance learning. Using this strategy requires educators to discard traditional teacher-centered modes of instruction and adopt new student-centered modes…

Background: This article reports on an analysis of errors that were displayed by students who studied mathematics in Chemical Engineering in derivatives of mostly trigonometric functions. The poor performance of these students triggered this study. The researcher (lecturer) works in a mathematics support programme to enhance students'…

This study investigated communication patterns and behavior in problem-solving groups in a graduate online course. An inductive qualitative analysis method was employed to analyze 732 messages that were retrieved from small group forums. The current study identified a temporal pattern of group development was in comparison with existing…

Researchers have suggested that teachers use a specialized type of knowledge specifically attributed to the work of teaching. One aspect of this specific type of knowledge is the ability to analyze children's work. With continued emphasis on a teacher's ability to analyze their students' thought processes, teacher candidates will need to develop…

This document presents a review of evidence commissioned by the Education Endowment Foundation to inform the guidance document "Improving Mathematics in Key Stages Two and Three" (Education Endowment Foundation, 2017). The review draws on a substantial parallel study by the same research team, funded by the Nuffield Foundation, which…