This study was designed to examine the use of mistakes to promote students' performance in undergraduate Algebra classes by developing a growth mindset. Participants were seventy-four students from three Algebra classes and received one of the three interventions along with regular instruction: (a) growth mindset feedback on mistakes…

This paper provides a case study account of a preservice secondary mathematics teacher's thinking while engaging in slope tasks using dynagraphs. The data included audio recordings and screen captures of a small group of preservice teachers engaging with these tasks, with our analysis focusing on the case of Robin. Despite familiarity using slope…

The gold-standard for evaluating the effect of an educational intervention on student outcomes is running a randomized controlled trial (RCT). However, RCTs may often be small due to logistical considerations, and resulting treatment effect estimates may lack precision. Recent methods improve experimental precision by incorporating information…

Here we investigate how college students may conceptualize symbolic algebraic properties. This work uses the theory of Grundvorstellungen (GVs) to analyze how learners' conceptions may or may not align with some desired goals of instruction. Through the analysis of interviews with students across a variety of courses, we describe several…

Whilst educational goals in recent years for mathematics education are foregrounded the development of mathematical competencies, little is known about mathematics teachers' competencies. In this study, a group of practising teachers were asked to solve an algebra problem, and their solutions were analysed to determine the competencies apparent…

The purpose of this study was to examine teachers' perceptions of the Illustrative Mathematics (IM) using data from teacher interviews from year 1 and year 3 of their implementation of IM. In year 1, 22 Algebra 1 teachers were interviewed; in year 3, 13 teachers participated. Interviews were conducted using a semi-structured protocol that included…

Algebra holds an important role in school mathematics, and teachers must recognize the broad range of algebraic ideas and develop a deep understanding of these concepts to teach algebra conceptually. This study aims to investigate two pre-service middle school mathematics teachers' (PSTs) conceptualization of algebraic thinking before and after…

This research reports on the teacher language and gesture that contributed to shifts in thinking about the equal sign and equations observed in twenty kindergarteners who took part in an early algebra intervention. Our analysis revealed ways in which the teacher used language and gesture to support students in moving from describing and working…

Units coordination, defined by Steffe (1992) as the mental distribution of one composite unit (i.e., a unit of units) "over the elements of another composite unit" (p. 264) is a powerful tool for modeling students' mathematical thinking in the context of whole number and fractional reasoning. This paper proposes extending the idea of a…

This study aims to describe how preservice secondary mathematics teachers (PSMTs) reason about different function representations. The study focuses on two PSMTs' reasonings across static and dynamic representations of functions. Sfard's (2008) Theory of Commognition guided our analysis. Findings indicate that while static representations restrict…

In this paper, we explore student solutions to a free response mathematical assessment task which had opportunities for students to notice structural properties in the context of number systems. In total, 308 students aged between 10 years to 13 years participated in the study. Their responses were analysed to determine whether they noticed…

An understanding of the equal sign is a fundamental concept for early algebra. While literature claimed that Chinese students commonly master the relational understanding of the equal sign in the elementary school, these claims are under-researched. This study used the Mathematics Equivalence Assessment with 237 Chinese Grade 5 students. The…

We investigate the beliefs that influence middle and high school algebra teachers' appraisals of contextual problems having diverse mathematical and pedagogical features. We asked six teachers to analyze six contextual algebra tasks and indicate how they would apportion instructional time among the six tasks based on their structure, pedagogical…

Student focusing and noticing, which drive reasoning, are important but under researched aspects of student learning. Quadratic functions representations are perceptually and conceptually complex and thus, offer much for students to focus on and notice. Our study compared a teacher's goals for student focusing and noticing during quadratic…

Emergent graphical shape thinking (EGST) entails conceiving a graph as being dynamically generated via the trace of a moving point constrained by two changing quantities. As such, Paoletti et al. (2023) argue that meanings for quantities within a situation and meanings for graphical representations must be connected, or bridged, to engage in EGST.…