This unlikely cast of characters, by working collaboratively in a trusting learning community, was able to identify an approach to teaching rational numbers through measuring from the everyday practices of Yup'ik Eskimo and other elders. "The beginning of everything," as named by a Yup'ik elder, provided deep insights into how practical…

Reasoning about fraction magnitude is an important topic in elementary mathematics because it lays the foundations for meaningful reasoning about fraction operations. Much of the research literature has reported deficits in preservice elementary teachers' (PSTs) knowledge of fractions and has given little attention to the productive resources that…

Examining the Trajectories of Black Mathematics Teachers: Learning From the Past, Drawing on the Present, and Defining Goals for the Future is a three year-long research study funded by the National Science Foundation. Our study was designed to reflect on the dearth of Black mathematics teachers, including problems with recruiting and retaining…

Mathematics teachers are vital components in determining what mathematics students have the opportunity to learn. There are a vast number of factors and reasons that influence a teacher's instructional decisions. As such, teachers rely heavily on their curricular reasoning (CR) to make decisions about what content to teach, how that content is…

One promising approach for connecting undergraduate content coursework to secondary teaching is using teacher-created representations of practice. Using these representations effectively requires seeing teachers' use of mathematical knowledge in and for teaching (MKT). We argue that Rowland's (2013) Knowledge Quartet for MKT, in particular, the…

This paper reports on a theme, the intrusion of the Traditional Western worldview, emerging from an ongoing study of the impact of teachers' engagement in the Transreform approach to the teaching and learning of mathematics on students' affective and cognitive responses to and achievement in mathematics. Newly theorized (Russell & Chernoff,…

In this paper, we present an analytical framework for attending to reflexivity in the context of conducting teaching experiments and rationalize its components by appealing to the constructivist foundations on which the methodology is based. To illustrate the importance and utility of this framework, we discuss our analysis of recent mathematics…

This paper describes the learning trajectory for Early Equations and Expressions (EELT), one of the 18 learning trajectories presented at www.TurnOnCCMath.net, developed to interpret the Common Core Standards for Mathematics based on research on student learning. The EELT is foundational for introducing concepts of early algebra and setting the…

Approaches to standards, curriculum development, and pedagogy are remarkably diverse; however, recent years have seen a growing movement to base each of these on learning trajectories. In this paper, I discuss and compare the various terms and conceptions of this construct, present our definition, differentiate between our conception and that of…

The paper describes the history of how learning trajectories (LTs) were associated with the Common Core State Standards for Mathematics (CCSS-M) and discusses the degree to which the two correspond faithfully. It reports on a website, www.turnonccmath.com, which organizes the K-8 standards into 18 LTs describing the development of big ideas over…

In this paper we discuss how a general theory of instruction called Concept-Focused Instruction (CFI) can assist in the professional development of prospective teachers. CFI provides prospective teachers with a foundation and logical decision-making process for selecting, designing, and teaching mathematics. First, we provide a theoretical and…

Adoption of the Common Core State Standards present challenges to school districts, school administrators, and teachers. To assist in this endeavor, we present our work on unpacking the CCSS-M for the length, area, and volume Learning Trajectory (LT). The overarching theme of "genetic epistemology" and a five-characteristic framework…

The U.S. storyline of emergent bilinguals has historically failed to highlight the mathematical and linguistic assets of this group; instead, it has primarily focused on providing support. To disrupt this narrative, a case study of one elementary teacher, Ms. Bristow, is presented. Ms. Bristow's discursive practices and pedagogy illustrate how she…

This paper presents our initial work to develop trajectories of preservice teachers' knowledge of teaching algebra for equity. We have developed two overlapping hypothetical learning trajectories (HLTs) for teachers' learning to engage and motivate diverse students to solve algebra problems. These HLTs are being used to guide the development of…

This research report presents the final year results of a three-year research project on computational thinking (CT). The project, funded by the National Science Foundation, involved training teachers in grades four through six to implement Scalable Game Design and LEGO® EV3 robotics during afterschool clubs. Thirty teachers and 531 students took…