This study explores gender-based differences in sixth-grade students' potential for mathematical creativity through the interrelated processes of problem solving (PS) and problem posing (PP), grounded in a multidimensional framework of creativity--encompassing fluency, flexibility, and originality. A total of 346 sixth graders from public schools…

This article features a fifth grade mathematics exploration planned to facilitate students' productive struggle. The exploration was a catalyst for a team of educators to unpack the teacher's experience when facilitating students' productive struggle. The team called this "teacher productive struggle" and shares about the construct…

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…

What comes to mind when one thinks about building? One may envision constructions with blocks or engineering activities. Yet, constructing and building a number system requires the same sort of imagination, creativity, and perseverance as building a block city or engaging in engineering design. We know that children invent their own notation for…

The Great Mini-Golf Project requires students to use a ruler to identify measurements to the quarter-inch, with careful precision and accuracy, which supported the Standards for Mathematical Practice 5 and 6: using appropriate tools to solve mathematical problems with precision (NGA Center & CCSSO, 2010). This project also supported Standard…

This study concerns the cognitive process of mathematical problem posing, conceptualized in three stages: understanding the task, constructing the problem, and expressing the problem. We used the eye tracker and think-aloud methods to deeply explore students' behavior in these three stages of problem posing, especially focusing on investigating…

This article reports on an empirical study that investigates the way students' performance in solving arithmetical tasks may be related to their performance in solving algebraic tasks. The sample consisted of 203 Grade 6 students. The arithmetical tasks involved arithmetical expressions with known quantities, whereas the algebraic tasks involved…

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…

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…

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…

Barlow et al. (2018) discussed three types of mistakes worthy of inspection: procedural errors, inappropriate solution processes, and misconceptions. Here, the authors focus on procedural errors, as these often led the teachers in their professional development project to limit their inspection of mistakes to correcting. Despite this narrow focus,…

This essay extends beyond the characteristics and discourse of word problems to, more generally, school mathematical problem-solving and the implications entailed by a predominant paper-and-pencil mode of learning and instruction since the modern era of education. Contrasting what I call "one-handed" (with paper-and-pencil) with…

Previous research has highlighted the importance of social relationships in mathematical group work while working on modelling activities. This study analyses the interaction of sixth-grade students in Primary Education (11 to 12 years old) carrying out a modelling task in groups with a Fermi problem used as the modelling activity. The focus of…

Gifted students' often go unchallenged in the classroom, and this lack of tailored instruction can lead to decreased motivation, which, in turn, influences underachievement, which is a significant concern since these children, theoretically, should be our highest achievers. This 4-week (i.e., eight instructional days) semi-randomized,…