Through a constructivist teaching experiment, we studied how a 6th-grade student (Adam, pseudonym) struggling in mathematics may reorganize his available additive scheme (count-up-to) into a more advanced scheme involving the decomposition of composite units (break-apart-make-ten, or BAMT). First, we posed a task that led us to infer Adam was yet…

Students with mature number sense make sense of numbers and operations, use reasoning to notice patterns, and flexibly select the most effective and efficient problem-solving strategies (McIntosh et al., 1997; Yang, 2005). Despite being highlighted in national standards and policy documents (CCSS, 2010; NCTM, 2000), the association between…

In a research study designed to investigate the emergence of collective creativity in elementary classroom settings, and in which teachers' decision-making practices were analyzed alongside both the teachers' observed teaching practices in their classrooms and their students' problem solving actions, the first author developed four metaphors for…

This study investigated the relationship between non-cognitive factors (mathematics anxiety, Emotional Intelligence, and mathematics self-concept) and mathematics performance in students with and without Mathematics Learning Disability (MLD). Participants were 340 3rd, 4th, and 5th grade students from a public elementary school. Results showed…

A problem influencing mathematics performance and student's perceptions of their ability to learn mathematics is mathematics anxiety. This mixed method study examined the perceptions, correlations, and mathematical conversations of Hispanic fourth and fifth grade low-performing students and their parents. A psychological approach provided the…

During the past two years, the COVID-19 pandemic has forced teachers to shift their instruction online, further exacerbating the challenges for teachers in orchestrating rich mathematics discussions. To tackle this issue, this study explored an approach that integrates online video-sharing culture (e.g., YouTube) into mathematical practices.…

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…

Eye-tracking studies need adequate theoretical frameworks for producing insights about mathematics learning. The current study uses eye-tracking to investigate the effectiveness of tables and diagrams for supporting covariational reasoning amongst elementary students (n = 60). The theoretical framework emphasizes the cognitive functions of…

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…

Fractions are one of the most difficult areas of mathematics for all students and especially for students with learning disabilities (LD). An incomplete understanding of fractions during the elementary and middle school may be why some students view fractions as "really small" or "less than 1" compared to others who view them…

Over the past two decades, the landscape of research on mathematics teacher educators (MTE) has grown considerably. One particular area of interest has focused on the knowledge needed by MTEs for their work with preservice K-8 teachers (PTs). In an effort to understand this varied landscape, we conducted an extensive review of research on…

We analyzed 5th grade students' interactions with one computer-based modeling simulation to examine how they defined and prioritized variables in a dynamically simulated environment. Results revealed that exposure to the simulation environment helped students visualize continuous motions, interpret the different quantities present in the model,…

People often view mathematics as abstract, cold, and irrelevant to real-life, and their school experiences influence such views. In this case study, we investigated the mathematics learning experiences of two women who participated in an afterschool girls STEM club 26 years ago. We explored their experiences in and out of school and how such…

This study investigates the use of manipulatives by elementary students working on a fraction task. Extending previous work on the role played by the manipulatives in students' activity, we aim at describing how the choices made for the task design disrupt students' activity, creating opportunities to learn. The theoretical underpinnings allow…

In this article we show how students' productive struggle on a mathematical task can lead to collective mathematical creativity. We use observable (co)actions and interactions from a video record that features three Grade 6 students in a problem-solving session to document the emergence of collective creativity leading to a solution. We discuss…