This paper reports on the development of complex unfamiliar mathematics questions using conventional mathematics questions. The autoethnographic research data included retrospective reflections of two educators and review of literature. Data analysis resulted in a three-phase development process: identifying conventional questions and subject…

'Success' is a frequently cited yet ambiguously defined term in mathematics education, often carrying contradictory meanings and messages. We surveyed 139 Australian teachers of mathematics to determine their conceptions of 'success'. This paper documents teachers' responses to an alternate word or phrase for 'success'. Thematic analysis…

The development of the mathematical concept of the infinite, through the reflections that arise from personal notions and perceptions and the analysis of some ideas of Galileo and Cantor, invites us to investigate the relationship between intuition and formalization for the understanding of the said concept. This paper aims to observe and describe…

Considerable amount of research in educational data mining has focused on developing efficient algorithms for Knowledge Tracing (KT). However, in practice, many real-world learning systems used at scale struggle to implement KT capabilities, especially if they weren't originally designed for it. One key challenge is to accurately label existing…

In this report, we present cases where students constructed new quantities through operating on quantities that does not fit the definitions of existing theories on quantitative operations. As a result, we identified five quantitative operators--operators that can be used on single qualities in order to transform the quantity to a new…

The construct of static and emergent shape thinking (Moore & Thompson, 2015) characterizes differences in students' reasoning about graphs. In our previous work with middle school students, we found that this construct may also be useful in characterizing students' reasoning about other representations such as simulations and tables. In this…

Angularity is a persistent quantity throughout K-12+ school mathematics, and many studies have shown that individuals often conflate angularity with linear attributes (e.g., the length of an angle model's sides). However, few studies have examined the productive ways in which students might reason about angularity while attending to linear…

The present study aimed to determine the estimation skills of elementary education pre-service mathematics teachers and the strategies they adopt in estimation. The case study methodology was employed in the study, and the participants included 37 volunteering students attending the fourth grade in the Primary Education Mathematics Instruction…

Subtizing emerges at an early age, but it further develops when supported. In parallel, research has shown that it supports other cognitive skills along with early math skills. For this reason, it is important to identify studies in the literature to determine the subitizing levels of preschool children and provide example practices to help…

Family characteristics such as socioeconomic status (SES) and migration background (MiBa) predict children's early mathematical skills. This study investigated the associations between SES and MiBa and children's mathematical precursor skills, mediated by different facets of the home numeracy environment (HNE) in a German sample (N = 500). In…

In this paper, we raise questions about the role of student empathy and compassion when engaging with social and environmental justice issues -- significant in a world where challenges associated with such disruptions are faced daily. We draw on data from a larger, nationally funded study on enabling students' critical mathematical thinking. These…

Mathematical representation includes the process of transforming problems or ideas into new forms, including changing pictures or physical models into symbols, words, or sentences that can facilitate students in solving mathematical problems. Pythagorean Theorem material is widely used in analytic geometry, so this material becomes important for…

There is emerging evidence that professional noticing is embodied. Yet, there is still a need to better under embodied noticing at a fundamental level, especially from the preservice teachers. This study used traditional and holographic video, along with eye-tracking technology, to examine how preservice teachers' physical act of looking interacts…

Mastery learning -- requiring students to achieve proficiency in a topic before advancing -- is a well-established and effective teaching method. Digital learning systems support this approach by personalizing content sequences, enabling students to focus on practicing topics they have not yet mastered. To achieve this, digital learning systems…

Researchers have recommended using tasks that support students in reasoning covariationally to build productive meanings for graphs, rates of change, exponential growth, and more. However, not many recent studies have been done to identify how students reason when engaging in covariational reasoning tasks in undergraduate precalculus courses. In…