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…

In this study, we examined one experienced mathematician's class practices, with particular attention to cognitive model described in genetic decomposition. Our findings indicate that students only had limited opportunities to be familiar with the first three steps in genetic decomposition, which may potentially lead students to answer limit tasks…

We conducted a collective case study investigating two college algebra students' graph reasoning and selection on an online assessment. Students completed the assessment during individual, semi-structured interviews, as part of a broader validation study. The assessment contained six items; students selected Cartesian graphs to represent…

Textbooks play an important role in teachers' instructional decisions (Jones & Tarr, 2007), which consequently affects students' learning. This paper reports on a comparison of the elementary mathematics textbooks used in Iran and the United States, the Go-Math textbook. I analyzed topic sequences, frequency of the tasks, and cognitive demands…

This paper introduces two theoretical constructs, open-loop covariation and closed-loop covariation, that combine covariational reasoning and causality to characterize the way that three preservice mathematics teachers conceptualize a feedback loop relationship in a mathematical task related to climate change. The study's results suggest that the…

We examine in-service high school teachers' journals to explore the emerging themes in a mathematics content course for their professional development. We use a sociocultural perspective and characterize journals as signifying teachers' communication and written discourses about their thinking and experiences in the course. We use applied thematic…

The more researchers understand the subtleties of teaching practices that productively use student thinking, the better we can support teachers to develop these teaching practices. In this paper, we report the results of an exploration into how secondary mathematics teachers' use of public records appeared to support or inhibit their efforts to…

Mathematics education scholars have generally classified students' conception of the equal sign as either operational or relational. Adding to these conceptions, Jones (2008) introduced the idea of substitutional conception. Building off these scholars, I introduce a form of understanding the equal sign that includes a transformative equivalence…

Cognitive Load Theory's Four Component Instructional Design (4C/ID) Model has been used in mathematics education but not confirmed as an instructional theory. Using the Factors Influencing College Success in Mathematics (FICSMath) project and confirmatory factor equation modeling, we empirically validated the model and created the 4C/IDMath Model.…

This lecture reports on aspects of a larger research programme focused on studying mental mathematics in elementary and secondary mathematics classrooms. It specifically addresses an unplanned aspect that became salient through the work conducted in these classrooms. In this research programme, mental mathematics sessions are designed on a variety…

Embodied cognition is growing in theoretical importance and as driving a set of design principles for curriculum activities and technology innovations for mathematics education. The central aim of the EMIC (Embodied Mathematical Imagination and Cognition) Working Group is to connect with inspired colleagues in this growing community of discourse…

This study examined how two small-group discourse types (Reflective and Exploratory) supported the inclusion and enacted levels of cognitive demand of students who typically struggle with mathematics in real-world, task-based assessment activities. The study focused on 11 fifth-grade students within a larger study involving 97 fifth-grade students…

The purpose of this research study is to characterize secondary teachers' orientations toward mathematics engagement. Results indicated that these 16 high school mathematics teachers tended to emphasize a cognitive dimension for engagement in their orientations, usually intertwined with an additional dimension (affective, social, or behavioral).…

Formulating a mathematical model is a dynamic process, and attending to changes in students' models as they engage in modeling tasks is critical for informing pedagogical interventions. In this report, we coordinate constructs from literature on mathematical modeling, quantitative and covariational reasoning, and semiotics to characterize changes…

This paper frames children's mathematics as mathematics. Specifically, it draws upon our knowledge of children's mathematics and applies it to understanding the prime number theorem. Elementary school arithmetic emphasizes two principal operations: addition and multiplication. Through their units coordination activity, children construct two…