Mounting evidence of the effectiveness of active learning strategies has prompted many mathematics departments to start engaging in transformational change efforts. Change, however, especially change in instructional practice, is a challenging endeavor. Some departments are using coordination of multi-section courses as a vehicle to enact changes…

We investigated the role of working memory in symbolic and spatial algebra and related tasks across five experiments. Each experiment combined a processing task (expression evaluation, arithmetic, coordinate plane, geometry, or mental rotation) with verbal and spatial memory loads in a dual-task design. Spatial memory was compromised in the…

This study presents the preliminary qualitative results of a larger mixed methods study. The qualitative phase utilized task-based clinical interviews to examine the non-symbolic and symbolic linear generalizations of middle-grades students. This investigation identified similarities and differences in the students' generalizations, and…

Disciplinary literacy involves reading, writing, speaking, listening, and thinking in the context of specific disciplines. Word sorts are a way for students to acquire and examine vital features of mathematics vocabulary as they process and organize new content-specific ideas. Addressing disciplinary literacy (i.e., literacy skills specific to…

This article provides conceptual ideas, data, and exercises, for integrating original sources of recent, state of the art, world-class life science research in the undergraduate mathematics curriculum and classroom. To this end, this article shows how one of the main goals of calculus in the life sciences, fitting parameters to data and assessing…

Creativity is crucial for doing mathematics, yet many United States students may not have opportunities to experience it in their courses. Moreover, the literature base on views of mathematical creativity lacks the student perspective. To explore the connections between views of and feeling creative, we examine differences in views of creativity…

Providing mathematics instruction and supporting students with mathematics difficulties, including students with disabilities, at risk for disabilities, or those who struggle with the content, is important and interventions must be designed to occur face-to-face or virtually. Despite limited research on providing mathematical interventions online…

Noticing is a skill that is not overtly observable yet is consequential to effective mathematics instruction. Researchers have found that prospective and practicing teachers can learn to notice, but little focus has been given to those who teach teachers to notice. The purpose of the study was to characterize mathematics teacher educators'…

The connection between spatial reasoning and mathematics learning and pedagogy in primary school children has been the subject of an increasing number of studies in recent years. There has been no comprehensive analysis, however, of how studies based on spatial reasoning interventions may lead to improvements in students' mathematics learning in…

Engaging with learner errors in mathematics classrooms is an important aspect of teacher pedagogy which can support learner identification with mathematics. This study examined the opportunities that teachers provided for the construction of learner identities based on how the teachers spoke about and interacted with learner errors in two…

The enactment of a large-scale, long-term professional development initiative designed to enhance participants' knowledge base by influencing their identity trajectories as mathematics instructors is complex. Effectively influencing participants' trajectories could be enhanced by understanding the nature of participants' goal structures,…

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…

In this report, we present an advance of doctoral research. We explore teaching alternatives that promote proportional reasoning in Mexican students between 14 and 15 years old with the support of digital technology. We designed a sequence of activities that pretends to signify the concepts of ratio and proportion in their diverse representations…

In this research, pre-service mathematics teachers were asked to prepare scenarios about what possible misconceptions might be in the classroom teaching process and how a solution strategy could be used based on the cognitive conflict approach in order to overcome these misconceptions. Based on these scenarios, it is aimed to determine what type…

Drawing upon constructionism and neo-materialist approaches on the role of physical activity and the human body in teaching and learning mathematics, this paper investigates the meanings constructed by students while collaboratively carrying out tasks focusing on the dynamic aspects of the concept of angle in the educational context of a 6th grade…