This work explores the complex cognitive processes students engage in when addressing contextual tasks requiring linear and exponential models. Grounded within Piagetian constructivism and the Knowledge in Pieces (KiP) epistemological perspective (diSessa, 1993, 2018), this empirical study in a clinical setting develops a Microgenetic Learning…

Teachers choose to supplement their curriculum for various reasons (Drake, 2010) and use online resources to search for and choose these supplements for their curriculum (Silver, 2022). TeachersPayTeachers.com (TPT) is a popular choice for online curriculum resources. TPT is a virtual resource pool that allows teachers to create and share…

This study explores the development and implementation of a five-day curriculum designed to enhance students' understanding of algebraic concepts through the integration of educational robotics and growth mindset principles. The study is structured around three research questions that investigate influences on decision-making in curriculum design,…

In K-12 statistics education, there is a call to integrate statistics content standards throughout a mathematics curriculum and to teach these standards from a data analytic perspective. Annotated lesson notes within a lesson plan are a freely available resource to provide teachers support when navigating potentially unfamiliar statistics content…

For Freudenthal, the practice of mathematics in the curriculum is not a set of predetermined theories, goals and means. On the contrary, it is always associated with positively understood phenomenological processes in mathematics, as the curriculum is often used in conjunction with the transformation or development of practice. For Freudenthal…

This study reports on the design and implementation of an equity-focused, project-based algebra curriculum in two advanced eighth-grade classrooms. We document with substantial detail a promising approach to capturing how students demonstrate and build robust mathematical understandings in ways that strongly connect to equity issues. We illuminate…

The aim of this paper is to analyse the reasoning and symbolisations used by sixth grade Moroccan students in solving a task based on figurative patterns. Our analysis aims at identifying the systems of actions elaborated by the students to give the general expression of the sequence, according to their perceptions of the sequence of its patterns.…

The paper describes how designers used the construct of learning trajectories to create a tool, Math-Mapper 6-8, to help scaffold curricula toward increased learner-centered coherence. It defines "learner-centered curricular coherence" as "an organizational means to promote a high likelihood that each learner traverses one of many…

Drawing on evidence from the Longitudinal Investigation of the Effect of Curriculum on Algebra Learning (LieCal) Project, issues related to mathematics curriculum reform and student learning are discussed. The LieCal Project was designed to longitudinally investigate the impact of a reform mathematics curriculum called the Connected Mathematics…

This study investigated how a group of 10 prospective secondary mathematics teachers (PST) read, evaluated, and adapted a textbook lesson involving the symbolic manipulation capabilities of computer algebra systems (CASS). PST read the entire lesson and tended to focus on the organizing question at the beginning of the student lesson and the CAS-S…

This paper addresses the role of learning progressions in informing many international standards documents, discussing the affordances and limitations of building standards and curricula from a learning progression model. An alternate model, the hypothetical learning trajectory, is introduced and contrasted with learning progressions. Using the…

Historically, algebra has served as a gatekeeper that divides students into academic programs with varying opportunities to learn and controls access to higher education and career opportunities. Successful completion of Algebra 1 demonstrates mathematical proficiency and allows access to a sequential and progressive path of advanced study that…

This research examines secondary mathematics teachers' use of textbook curriculum materials within "typical" cycles of planning and teaching in a school year. The curriculum use of four teachers from the western US was examined before and after engagement in a form of professional development focused on more purposeful and flexible…

In this paper, the authors investigate the consequences of curricular intensification by examining changes in the social organization of schooling and student achievement in one California school district. The authors' analyses consider the following three research questions: (1) What effect did 8th grade curricular intensification have on…

This study applies the constructs from effective instruction from the literature on teacher education to understand the impact of school district strategies on algebra outcomes for minority students. The purpose of this study was to examine the strategies utilized by superintendents and district personnel and the impact of these identified…