Mathematical ideas are developed and spread during argumentative whole class discussions between a teacher and her students. The goal of the current study is to characterize how ideas about quadratic functions emerge and are spread during a whole-class discussion among ninth graders. To this end, we recorded both discussions between pairs of…

In this article, the author shares two investigations that relate the variables of height and volume using different contexts. Each of the investigations surfaced unfinished learning for students, regardless of their starting place, and facilitated growth in understanding of measurement and algebra. The Functions and Volume of Vases task…

Joint activity, or interaction, can be the basis for understanding how language use organizes both social activity as well as individual thought. These interactions can be a useful unit of analysis for studying how students use language to make sense of mathematical concepts and how students learn to appropriate specific mathematical language…

Calculus has long been known as a "gateway course" to STEM fields in postsecondary education. To moderate this gatekeeping effect, Montclair State University researchers developed a peer-led, inquiry-based instructional support (IBIS) to run parallel to Calculus classes. The design of the IBIS model was informed by an instructional…

Social interactions, including collaborative problem-solving situations, can trigger critical thinking skills. Giving questions that are not routine can trigger students' critical thinking skills in solving problems collaboratively. This research aims to develop non-routine mathematics problems that can be used to explore students' critical…

In the age of artificial intelligence where standard problems are increasingly processed by computers, creative problem solving, the ability to think outside the box is in high demand. Collaboration is also increasingly significant, which makes creative collaboration an important twenty-first-century skill. In the research described in this paper,…

The purpose of this study is to examine the performances of university students' using dynamic mathematics software GeoGebra in argumentations and proving processes. A task related to the limit involving "sinx/x" was designed and 18 university students worked on the task during the collaborative learning, scientific debate, and…

Multiple studies have been conducted regarding teachers' error-handling practices, and how errors can be treated as opportunities for learning, albeit in the context of whole-class discussions. The aim of the present research is to continue to investigate teachers' error-handling practices as they occur in different phases of maths lessons:…

The ability of solving problems collaboratively has been increasingly significant. This research takes mathematics open-ended problems as the tasks and carries out collaborative problem solving with multi-machine video recording in the classroom environment aimed at 112 student pairs and 56 four-person student groups stemming from 224 students in…

This study describes prospective teachers' perspectives on collaborative problem-solving (CPS) in mathematics. The study employed a 20-item questionnaire distributed to 47 prospective mathematics teachers in Indonesia. The questionnaire responses were scored, and two participants with the highest and lowest mean score were interviewed. Despite…

Groupwork provides opportunities to learn important communication and collaboration skills, but how can we ensure all students are participating equitably while also engaging with the academic content when working in groups? Group-worthy tasks provide participation structures needed for students to engage with the content as well as develop and…

This article discusses a pedagogical technique for utilizing breakout rooms for small group discussions and synchronous drawing features in Zoom to create crowdsourced solutions to mathematical problems that involve graphing or visualization. Students begin with specific examples and then move quickly to the development of a more general…

This study investigates social, mathematical, and sociomathematical norms perceived by college students in an engineering mathematics course and examines the students' sense of mathematics as signals of individual merit. Data sources include a survey and one-on-one interviews with 38 students. The findings help illustrate student perceptions of…

Fractals describe many natural phenomena; their strong visual-figurative nature found its mathematical conceptualization in the concept of self-similarity. In the current study, we investigate how students construct (fully or partially) the self-similarity concept while recursively constructing the Sierpinski triangle, working in small group and…

The purpose of the study was to explore the effect of the Montessori Method integrated with cooperative learning on mathematical reasoning skills in the preschool period. In this study, an experimental design with a pretest-posttest control group was used. The study group included a total of 30 children, 15 of whom were in the experimental group…