This paper is a practical how-to guide to help you start using active learning or to have greater success and more fun with it. We categorize active learning techniques as Think, Pair, Share, Composite, Group, Move, or Lead and discuss how to implement activities in each category, along with advice on creating engaging, effective, and equitable…

Physical experiments in classrooms have many benefits for student learning, including increased student interest, participation and knowledge retention. While experiments are common in engineering and physics classes, they are seldom used in first-year calculus, where the focus is on solving problems analytically and, occasionally, numerically. In…

Coming from a social perspective, we introduce a classroom organizational frame, where students' proofs progress from collaborative construction in small groups, through whole-class presentation at the board by one of the constructors, to a posteriori reflection. This design is informed by a view on proofs as successive social processes in the…

The Euclidean Discus Toss is an active and tactile learning activity that models the extended Euclidean algorithm with a frisbee relay. The extended Euclidean algorithm involves both iterative and recursive programming and is regularly taught throughout the mathematics and computer science curricula. The Euclidean Discus Toss invites students to…

This study examines how collaborative activity among students and the teacher to investigate disciplinary questions, which we term 'joint exploration', is established and maintained in a secondary mathematics classroom. Although collaborative and active learning is increasingly sought after in mathematics classrooms, studies of instances of joint…

This study combines collaborative learning and inquiry-based learning, analyzes the characteristics of fourth-grade mathematics textbook, and designs an instructional model based on collaborative learning and inquiry-based learning. Based on this instructional model, this study adopts a quasi-experimental design, involving 142 fourth-grade…

The Community of Inquiry (CoI) framework has gained widespread recognition as a theoretical model for understanding student learning in online environments. Despite its prevalence, CoI has been critiqued for its limited emphasis on learners' proactive roles in self-regulating their own learning. To address this, researchers have suggested…

Purpose: Creating suitable learning conditions in university classrooms continues to be a topical issue in higher education. The above means that a continued search for innovative teaching and learning strategies in universities remains a priority issue. The study therefore investigated conditions that facilitate the effective implementation of…

In modern times, the importance of education cannot be overstated. Beyond the acquisition of knowledge, perhaps the most important aim of education may be the development of character in individuals, including vitality, courage, sensitiveness, and intelligence, from which our society may experience increased prosperity, peace, and freedom. In this…

In contemporary society, students' analytical thinking and reasoning skills are crucial for their future development. The fourth grade (ages 9-10) is a critical stage for cultivating higher-level cognitive skills in students. Mathematics plays a significant role during this period, serving as a fundamental tool for fostering students' analytical…

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…

One goal of inquiry-oriented instruction is student engagement with others' mathematical ideas. This paper analyzes a relatively short episode in which students engaged with others' ideas; the instructor facilitated engagement in order to support students in making mathematical progress. Students expressed some bafflement pertaining to the…

Team-Based Learning (TBL) is a cooperative learning strategy blending elements of flipped learning, inquiry-based learning, and problem-based learning. Although used quite frequently in other disciplines, use of this strategy in mathematics has been limited. In this article, we describe how TBL can be implemented in math courses with adherence to…

A study conducted by the Mathematical Association of America showed that calculus not only has significant effects on students' decision to pursue STEM fields, but also on their attitudes towards mathematics. Inspired by this large-scale study, the present study sought to deepen the current understanding of the impact of calculus on student…

Analysis of the experimental results presented in the following chapter reveals experiences with introduction of active learning methods in basic mathematics courses at the Faculty of Mechanical Engineering, Slovak University of Technology in Bratislava. Experiment was implemented in the academic year 2018/19, in basic courses Mathematics I and…