This paper describes the conceptions about complex numbers that a group of university students has, these were built from the application of an activity sequence centered on these numbers. This sequence is based on the APOS theory, some aspects of semiotic representation theory, and the use of digital technology. Particularly, both the general…

Introducing new concepts to learners in an order of increasing complexity appears to be beneficial for learning, but typically introduction of concepts does not always adhere to this principle. We examined whether introducing new algebra concepts in a contrasted manner or in an order of increasing complexity instead of a different more typical…

This article examines the process of shifting to a "Physics First" sequence in science course offerings in three school districts in the United States. This curricular sequence reverses the more common U.S. high school sequence of biology/chemistry/physics, and has gained substantial support in the physics education community over the…

Students benefit from learning multiple procedures for solving the same or related problems. However, past research on comparison instruction has focused on comparing multiple formal procedures. This study investigated whether the benefits of comparing procedures extend to comparisons that involve informal and formal procedures. We also examined…

This review investigates effective interventions for teaching algebra to students with learning disabilities and evaluates the complexity and alignment of skills with the Common Core State Standards in math. The review includes the results of 10 experimental and 5 single-subject designs (N = 15) producing a moderate overall effect size (g = 0.48).…

In this paper, we describe our learning progressions approach to early algebra research that involves the coordination of a curricular framework, an instructional sequence, written assessments, and levels of sophistication describing the development of students' thinking. We focus in particular on what we have learning through this approach about…

Competence in algebra is linked to access to higher education, employment in better-paying jobs, and, increasingly, the ability to earn a high school diploma. For many students with learning disabilities, developing proficiency in algebra represents a challenging, but necessary goal. Teachers of students with learning disabilities need access to…