Cara, a seventh-grade student with learning disabilities (LD) in mathematics, believes that the ratio 2:3 is equivalent to 4:5 because there is a difference of one between the two numbers in each ratio and there is a difference of two between corresponding numbers in the two ratios (2 + 2 = 4 and 3 + 2 = 5). This misconception affects her ability…

Ratios and proportions are foundational to student understanding across multiple topics in mathematics and science. In mathematics, they are central to developing concepts and skills related to slope, constant rate of change, and similar figures, which are all fundamental to algebraic concepts and skills. This article examines the importance of…

This field report is the third in a series produced by the Center on Innovations in Learning's League of Innovators. The series describes, discusses, and analyzes policies and practices that enable personalization in education. Issues of the series will present either issue briefs or, like this one, field reports on lessons learned by…

When students struggle in the elementary and middle grades, the likelihood that they will drop out of high school increases dramatically. Although most dropout prevention resources have focused on high schools in a last-ditch effort to keep students in school, earlier interventions in elementary and middle grades provide a better opportunity to…

Developing proficiency in algebra is the focus of instruction in high school mathematics courses and is a minimum expectation for high school completion for all students including those with learning difficulties. However, the foundation for success is laid in grades 4-8 (aged 9-14). In this paper, we assert that students' development of algebraic…

In Canadian Rockies Public Schools (CRPS), educators are committed to meeting the needs of all students. While much of the attention and resources go to the students with special needs who have difficulty learning, the group of students identified as talented and gifted is largely left to the classroom teacher to accommodate. Lawrence Grassi…