This action research study examined the effects of professional development on teaching for conceptual understanding in Algebra I. "Conceptual knowledge refers to knowledge of the underlying structure of mathematics-the relationships and interconnections of ideas that explain and give meaning to mathematical procedures" (Eisenhart et…

Proportional reasoning is the cornerstone of many higher-level mathematics topics. We evaluated the sustainability effects of schema-based instruction (SBI) on proportional reasoning and the impact of professional development (PD) on the instructional practices of two cohorts of seventh-grade teachers (i.e., SBI-experienced-teacher implementers,…

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…

Teaching fraction operations for conceptual understanding is a challenging task. For the topic of fraction division especially, teachers need support because teachers find this difficult to teach and elementary and middle school students struggle to learn this concept. Well-structured professional development can assist teachers in exploring their…

A crucial step in improving the use of digital technology (DT) for learning mathematical concepts in the classroom appears to be increasing teacher involvement in task development. Hence, this research considered the effect of a professional development (PD) programme designed to assist teachers with DT task production for implementation in their…

For professional learning to "stick," teachers need to connect what they learn to their practice--and particularly to their work with their current students. The authors describe a PD program they've developed for math teachers with emergent multilingual students (English language learners) in their classes. Teachers choose "focus…

"Math Expressions" is a curriculum for students in prekindergarten through sixth grade that aims to build students' conceptual understanding of mathematics and to develop fluency in mathematical problem solving and computation. The curriculum encourages student learning of mathematics through real-world situations, visual supports such…

"Math Expressions" is a curriculum for students in prekindergarten through sixth grade that aims to build students' conceptual understanding of mathematics and to develop fluency in mathematical problem solving and computation. The curriculum encourages student learning of mathematics through real-world situations, visual supports such…

Decades of research have emphasized the need for engaging, accessible ways to help students learn fundamental mathematical concepts. Research also shows that teacher beliefs about teaching and learning have an outsized influence on the quality and effectiveness of curricular interventions. This article reports results of an independent evaluation…

This paper discusses the implementation and evaluation of an innovative professional development program that supported 8th grade mathematics teachers in designing learning activities that assisted students in developing a conceptual understanding of mathematics. Funded by an Investing in Innovation (i3) grant from the U.S. Department of…

Proportional reasoning, the ability to use ratios in situations involving comparison of quantities, is essential for mathematical competence, especially in the middle school years, and is an important determinant of success beyond school. Research shows students find proportional reasoning and its foundational concepts difficult. Proportional…

Contemporary state math standards emphasize that students must demonstrate an understanding of the mathematical ideas underlying the computations that have typically been the core of the elementary school math curriculum. The standards have put an increased emphasis on the study of fractions in upper elementary grades, which are the years during…

This Record of Study summarizes my journey in the program and my investigation of the problem of improving mathematics instruction. The exploration of the problem space spanned three years before culminating in the problem statement. Using a positive deviance approach and understanding the values of stakeholders narrowed the scope of the problem…

This study examined the efficacy of a kindergarten mathematics intervention program, ROOTS, focused on developing whole-number understanding in the areas of counting and cardinality and operations and algebraic thinking for students at risk in mathematics. The study utilized a randomized block design with students within classrooms randomly…

There are urgent calls for more studies examining the impact of Professional Development (PD) programs on teachers' instructional practices. In this study, we analyzed how grades 5-9 mathematics teachers used graphs to teach mathematics at the start and end of a PD program. This topic is relevant because while many studies have investigated…