This study aimed to investigate prospective middle school mathematics teachers' noticing of students' algebraic thinking based on students' correct and incorrect solutions within the context of pattern generalization. Designed as a qualitative case study, three noticing prompts were asked of thirty-two prospective middle school mathematics…

This article presents a set of "work-sharing routines," which teachers can use to broaden their repertoire of using student work, with an eye toward cultivating students' belonging. The authors define work-sharing as using actual mathematical student work, ideally from students in the class, to facilitate learning. Although there are…

Research suggests that collaborative learning may enhance the benefits to learners when solving cognitively demanding tasks. However, there are concerns about how students with different achievement and engagement levels perceive these benefits. This study examines how students with varying achievement and engagement levels respond to…

Background: Metacognitive processes have been linked to the development of conceptual knowledge in STEM courses, but previous work has centered on the regulatory aspects of metacognition. Purpose: We interrogated the relationship between epistemic metacognition and conceptual knowledge in engineering statics courses across six universities by…

This grounded theory study identified and described eight leadership phases of the school consolidation process from the perspective of receiving school principals. The study was conducted during the 2023-2024 academic year in a large suburban district that was undergoing wide-ranging consolidation of elementary schools due to declining…

Word problems are frequently used math problems that aim to bridge the gap between school mathematics and real life. As real-life situations usually involve many factors, word problems should not be oversimplified by focusing only on the numerical information provided by word problem statements. Furthermore, students should be expected to solve…

This research examines the integration of computational thinking in mathematics education, specifically examining its impact on students' algebraic reasoning. By teaching core computational concepts such as pattern recognition, decomposition, and algorithmic thinking, students develop a deeper understanding of algebraic structures and processes.…

Creative idea selection--the selection of the most creative idea(s) from available ideas--is an important yet understudied topic. Creative idea selection can be performed by the idea generator (i.e., "intrapersonal" selection) or by another person (i.e., "interpersonal" selection). In the current research, we examined whether…

Many design frameworks introduced to novices are not compatible with the behaviours and habits of mind of expert designers. This creates a barrier to effective practice, especially when novice designers tackle ill-defined, wicked problems. The W-model is a pedagogical framework that provides a prescriptive design model for novices, enabling them…

Recently, the field of adaptive learning has significantly attracted researchers' interest. Learning path adaptation problem (LPA) is one of the most challenging problems within this field. It is also a well-known combinatorial optimization problem, its main target is the knowledge resources sequencing offered to a specific learner with a specific…

This note deals with some variants of the integral mean value theorem. Mainly a variant of Sahoo's theorem and a variant of Wayment's theorem were proved. Our approach is rather elementary and does not use advanced techniques from analysis. The simple auxiliary functions were used to prove the results.

Conducted based on the idea that there are similarities between "action research" and "curriculum development" processes, in this study, the aim was to develop a model that practitioners can use to understand and improve the practical curriculum. To this end, first, the phenomena of "curriculum", "curriculum…

A 12-episode constructivist teaching experiment with two pairs of elementary preservice teachers was conducted to examine how they reason distributively and proportionally. Specifically, I studied how prospective teachers reason with ratios as multiplicative comparisons. Prospective teachers solved different problems in one specific context (Step…

Decomposition of organic matter controls the flow of carbon and nutrients in terrestrial and aquatic ecosystems. Several kinetic laws have been proposed to describe decomposition rates, but they neglect adaptation of the microbial decomposer to environmental conditions. Here we formalise decomposition as an optimal control problem by assuming that…

Distance education has received a lot of attention in contemporary policy as something that makes it possible for more students to participate, but also involves a certain set of challenges. When it comes to distance education, Swedish municipal adult education (MAE) stands out with its long history of flexible education, often provided on…