The purpose of this study is to investigate how students interpret expressions from calculus statements in the graphical register. To this end, I conducted 150-minute clinical interviews with 13 undergraduate mathematics students who had completed at least one calculus course. In the interviews, students evaluated six calculus statements for…

The authors wondered if there was a way to support their reluctant Grades 4, 5, and 6 students in contributing their starting points and strategies and advancing their collective knowledge. They wanted to ensure that the students had the space to develop and take ownership of the strategies they produced through a visual representation of ideas…

Recent research has highlighted the role of functional relationships in introducing elementary school students to algebraic thinking. This functional approach is here considered to study essential components of algebraic thinking such as generalization and its representation, as well as the strategies used by students and their connection with…

Little research has examined specific instructional variables that influence the development and effectiveness of task-analysis instruction. We conducted two experiments using text-based task analyses to teach college students to create single-subject reversal design graphs. In Experiment 1, we tested the effects of presenting antecedent and…

Self-regulated learning (SRL) is an essential skill to achieve one's learning goals. This is particularly true for online learning environments (OLEs) where the support system is often limited compared to a traditional classroom setting. Likewise, existing research has found that learners often struggle to adapt their behaviour to the…

Educational bodies are weighing up the extent to which generative artificial intelligence (genAI) is embedded within educational settings. Although researchers have examined how (generative) AI can be used for effective teaching and learning, less is known about how genAI was being integrated within teachers' practice shortly after the wide-scale…

Designing and implementing purposefully developed tasks have been linked to students' understanding of mathematical topics. We report on design principles and intentions that guided the development of "inquiry-oriented tasks." Through a qualitative analysis of the tasks, we identified seven themes that encapsulated these design…

The aim of this study was to examine the impact of the Predict-Explain-Observe-Discuss-Explain (PEODE)-based laboratory on enhancing the verbal and figural creativity of gifted students. The quasi-experimental research design utilised a pre- and post-test approach with a non-equivalent control group, consisting of 60 sixth-grade gifted students.…

Mathematical problem solving remains a struggle for many students today (Celebioglu et al., 2010; Englard, 2010; Gavaz et al., 2021; N. H. Lee et al., 2014; Yeo, 2011). Though intervention studies have reported measured impact on improving students' problem-solving abilities (Gavaz et al., 2021; Gidalevich & Kramarski, 2019; N. H. Lee et al.,…

A growing consensus holds that preservice K-8 teachers (PSTs) need to experience the modeling process as learners to understand it and envision teaching modeling in their future classrooms. We examine this recommendation by exploring how PSTs construct models and how collaborative learning practices influence them in revising and refining their…

The authors developed an instructional nudges as part of a larger research project. These instructional nudges are designed to be small but powerful changes to teachers' existing practices. Some instructional nudges focus on modifying tasks used in classrooms. In this article, the authors share Rate and Review. The goal of Rate and Review is to…

Even though there is a great temptation as teachers to share what is known, many are aware of an idea called "rules that expire" (RTE) and have realized the importance of avoiding them. There is evidence that students need to understand mathematical concepts and that merely presenting rules to carry out in a procedural and disconnected…

The variational thinking of high school students based on mathematical connections was analyzed through a laboratory on linear functions. This qualitative research based on design was developed in three phases: diagnostic test, implementation of the mathematics laboratory and final test, with students from a public institution in Barranquilla,…

Climate change is a complex issue that requires collective actions from various disciplines, including educating future generations about sustainability. Some countries such as Indonesia and Australia have included sustainability into their school curricula, which require teachers to design and implement tasks related to a sustainability issue.…

In this article, the authors provide some insight into how teachers can potentially facilitate among students' representations and activities on mathematical tasks: between or among -- (1) student representations and the context; (2) multiple forms of student representations; and (3) processes in student representations. The authors use the…