Background/Context: Children enter kindergarten with widely varying backgrounds and academic skill levels (Little et al., 2024). Kindergarten teachers face the challenge of meeting children where they are at the start of the year and helping them master critical skills by the end of the year, regardless of where each child starts. Differentiated…

Inconsistent reporting of critical facets of classroom interventions and their related impact evaluations hinders the field's ability to describe and synthesize the existing evidence base. In this essay, we present a set of reporting guidelines intended to steer authors of classroom intervention studies toward providing more systematic reporting…

Empirical studies of angle, angle measure, and radian angle measure have primarily focused on documenting students' and teachers' conceptions. Representations of angle measure have the potential to inform and build on these conceptions. To gain insight into the concept of radian angle measure from a curricular perspective, I investigated the…

The formal acceptance of a mathematical proof is based on its logical correctness but, from a cognitive point of view, this form of acceptance is not always naturally associated with the feeling that the proof has necessarily proved the statement. This is the case, in particular, for proof by contradiction in geometry, which can be linked to a…

The traditional view of evidence in mathematics is that evidence is just proof and proof is just derivation. There are good reasons for thinking that this view should be rejected: it misrepresents both historical and current mathematical practice. Nonetheless, evidence, proof, and derivation are closely intertwined. This paper seeks to tease these…

The cognitive relationship between intuition and proof is complex and often students struggle when they need to find mathematical justifications to explain what appears as self-evident. In this paper, we address this complexity in the specific case of open geometrical problems that ask for a conjecture and its proof. We analyze four meaningful…

This paper shares findings from the study of a learning sequence designed to support prospective elementary teachers (PTs) in identifying evidence of conceptual understanding and procedural fluency. Conceptual understanding and procedural fluency are widely recognized as important to teaching and learning mathematics, and identifying evidence of…

Many public and private initiatives have focused on improving prekindergarten (PK) through Grade 12 mathematics education, given that the mathematics content learned before college is foundational for later learning and college success across STEM subjects. Although decades of educational research have studied PK-12 mathematics interventions, the…

Guided Mathematical Inquiry (GMI) supports the development of deep understandings about mathematics concepts as students learn to address inquiry questions with evidence-based claims. Developing an evidence-based focus has been shown to be problematic with children. This paper presents how a framework for evidence was developed through the expert…

The objective of this paper is to contribute to the discussion and reflection of a classroom training activity as a method to improve the quality of competency-based assessment in the courses of Mathematics and "Bahasa Indonesia." The Introduction describes the theoretical perspectives and the concept of competency-based curriculum as…

In this paper, using written responses of 37 PSTs preparing to teach grades 1-8 mathematics, we examined explanations they constructed to support their problem solutions and explanations they provided in support of their critiques of student-generated explanations. We also examined features of explanations on which PSTs drew in their critiques of…

This paper brings together general principles for teaching inquiry across disciplines with those generally employed in mathematics classrooms. It describes some broad principles of teaching inquiry to first-year writing students and shows how these can be employed in the context of a course on game theory in popular culture. Although undergraduate…

The idea of data use as an educational reform strategy has gained significant traction in recent years, but there is limited research that illuminates what actually happens when teachers use data in practice. This study investigates the ways a group of middle school mathematics teachers used data in their classrooms and as part of an action…

Increased attention has been given to learning trajectories (LT) as structural frameworks for educational instruction. The purpose of this study was to explore preschool teachers' descriptions of self-change, seven years after the start of their participation in LT-based professional development and instruction. This study was part of a larger…

This three-year study focused on first-year Calculus I students and their abilities to incorporate figures in technical reports. In each year, these calculus students wrote a technical report as part of the Polar Bear Module, an educational unit developed for use in partner courses in biology, computer science, mathematics, and physics as part of…