Improving reading outcomes for students with reading disabilities/difficulties (RD) has been commonly studied relative to 'what' a reading intervention entails. Here, we offer a broader perspective on 'when' we implement reading services to improve our interpretation of reading progress. We address several aspects related to timeframes (i.e.,…

Dialogic classroom discussions where students collaboratively share and reason through complex ideas are critical for achieving ambitious reform goals for student learning. However, K-12 classroom talk is predominantly characterized by monologic, "teacher-centered" discourse patterns that have proven exceedingly resilient to change.…

Responsive teaching requires teachers to have knowledge of children's thinking. Prospective teachers need support in developing such knowledge because they often enter teacher preparation programs with fragile mathematical knowledge and anxiety about teaching mathematics to children. We designed a learning trajectory-based intervention to support…

This study is a case study within a three-year-long design research study. The purposes of this study are twofold. The first purpose includes investigating whether there is a significant difference in seventh-grade students' proportional reasoning skills before and after a teaching experiment conducted in line with the perspectives of Hypothetical…

Measurement is a critical component of mathematics education, but research on the learning and teaching of measurement is limited. We previously introduced, refined, and validated a developmental progression -- the cognitive core of a learning trajectory -- for length measurement in the early years. A complete learning trajectory includes…

This study explores a spatial reasoning learning trajectory of a student with difficulty in mathematics. Using a teaching experiment methodology across 15 instructional sessions, we observed how the student responded to instruction based on an established 2D shape composition learning trajectory (Sarama & Clements, 2009). A narrative…

One challenge facing the fields of mathematics education and special education is how to design instruction on fraction concepts that can meet the needs of diverse learners. An innovation that shows promise is to base instructional design upon well-established trajectories of students' fraction learning. However, little research has been done to…

We describe here lessons learned in designing an early algebra curriculum to measure early algebra's impact on children's algebra readiness for middle grades. The curriculum was developed to supplement regular mathematics instruction in Grades K-5. Lessons learned centered around the importance of several key factors, including using conceptual…