Background/purpose: Learning mathematics often presents challenges for students, particularly in problem-solving and establishing mathematical connections. Self-regulated learning allows students to direct, adjust, and control their learning processes. This approach is essential in encouraging students to manage their learning strategies…

The main purpose of this research is to examine the informal strategies of fifth and sixth grade students while solving inverse proportional word problems. Multiple case study was used in this study. The research was carried out in a public middle school from a southern city of Türkiye. The participants of the research consist of three fifth and…

Problem solving is widely regarded as a fundamental feature within the school mathematics curriculum. However, there is considerable disagreement over what exactly problem solving is, and if and how it can be taught. In this article, I define problems as non-routine tasks and propose the explicit teaching of domain-specific problem-solving tactics…

The application of decomposition strategies (i.e., associative or distributive strategies) in two-digit multiplication problem solving supports algebraic thinking skills essential for later complex mathematical skills like solving algebra problems. Use of such strategies is also associated with improved accuracy and speed in mathematical problem…

In this paper we present a novel adaptation of a tri-phase assessment tool, originally devised to investigate students' linear equations-related strategy flexibility, to evaluate Danish grade-six students' multidigit arithmetic-related strategy adaptivity and flexibility. Participants, 731 students, median age 12 years and drawn from 20…

In this paper, the multidigit arithmetic-related strategy adaptivity, strategy flexibility and solution accuracy of Danish compulsory school students is examined. Participants, 749 grade three, 731 grade six and 818 grade eight, were drawn from twenty demographically different schools. Drawing on a tri-phase assessment tool, each student completed…

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…

Research has shown there are algebra concepts elementary teachers can introduce that help prepare elementary students for the eventual transition to algebra (e.g., the relational interpretation of the equal sign). "Early algebra" refers to the use of informal approaches to introduce such concepts to elementary students. "Strip…

In recent years, an increasing number of studies have examined the association between mathematical abilities and executive functions (EFs). However, it remains unknown via which mechanisms' mathematical performance is associated with EFs. The current study examined the associations of overall task proficiency, strategy selection, and strategy…

Students with mathematics difficulty, especially students with disabilities and emergent bilinguals, require careful consideration during word-problem instruction. Word problems that include relational terms such as more but are not easily solved using the implied operation (i.e., addition) can be particularly challenging. First, we summarize a…

This research aims to explore both the individual and combined relationships between the use of GeoGebra and productive disposition with students' strategic competence. The use of GeoGebra involves teacher-led activities designed to assist students in managing and engaging with learning, serving as a tool to enhance mathematics learning outcomes.…

To solve an unfamiliar mathematics problem, students of the subject must know more than the appropriate prerequisite content knowledge. They must also know how best to strategically apply their knowledge, how to monitor and gauge the effectiveness of their work, and how to respond (both cognitively and emotionally) to unanticipated results.…

Instructional routines, like "Number Talks" and "Notice and Wonder," engage students in doing and then talking about their mathematical thinking. Number Talk routines are short mathematical discussions where students mentally solve and share the strategies they used to make sense of the problem. In comparison, the Notice and…

Elementary (5 [approximately] 11 years old) students with mathematics difficulties often struggle with word-problem solving. This systematic review and network meta-analysis aimed to examine the comparative effectiveness of various instructional strategies and their combinations for improving word-problem solving skills in this population. We…

Mathematical modeling and applications are an important part of curriculum and considered to be important for students' current and future lives. In this contribution, we focus on mathematical modeling from a cognitive prospective. Following embedding the cognitive perspective within the discourse of mathematical modeling, we describe some of the…