Learning Progression

The general aim of the research was to conduct a rare test of the efficacy of hypothetical learning progressions (HLPs) and a basic assumption of basing instruction on HLPs, namely teaching each successive level is more efficacious than skipping lower levels and teaching the target level directly. The specific aim was evaluating whether counting-based cardinality concepts unfold in a stepwise manner. The research involved a pretest—delayed-posttest design with random assignment of 14 preschoolers to two conditions.

Measuring and Visualizing Space in Elementary Mathematics Learning explores the development of elementary students’ understanding of the mathematics of measure, and demonstrates how measurement can serve as an anchor for supporting a deeper understanding of number operations and rational numbers.

This poster presents findings on middle school students’ understanding of core computer science (CS) concepts, such as variables and control structures, using cognitive think-aloud interviews with eight students. Each student worked on 16-22 formative assessment tasks designed to assess understanding on the ‘Algorithms and Programming’ middle school CS standards. Our study describes students’ interpretations of the CS concepts and discusses potential factors influencing student interpretations. Significance and next steps are described.

‘Algorithms’ is a core CS concept included in the K-12 CS standards, yet student challenges with understanding different aspects of algorithms are still not well documented, especially for younger students. This paper describes an approach to decompose the broad middle-school ‘algorithms’ standard into finer grained learning targets, develop formative assessment tasks aligned with the learning targets, and use the tasks to explore student understanding of, and challenges with, the various aspects of the standard.

'Algorithms’ is a core CS concept included in the K-12 CS learning standards, yet student challenges with understanding and using algorithms are still not well documented. This paper describes an approach to decompose the broad middle-school ‘algorithms’ standard into finer grained learning targets, develop formative assessment tasks aligned with the fine-grained learning targets, and use the tasks to explore student understanding of and challenges with the various concepts underlying the standard.

In this report section, we discuss the importance of aligning classroom assessments with learning goals and instructional practices to both shape and evaluate students’ learning opportunities. We describe a plausible solution for improving alignment by integrating theories of learning in the design of classroom assessments. We discuss ways in which the specification of theories of learning as learning progressions can improve alignment between classroom assessments and instruction by focusing on the content, task design, and data generated from classroom assessments.

Learning progressions represent the relationship between concepts within a domain and how students develop increasingly sophisticated thinking therein. Typical evidence sources used to validate theorized learning progressions are also used to validate the use and interpretation of assessments, such as student cognitive interviews and psychometric analyses of item responses on assessments (Alonzo, 2018; Duschl et al., 2011).

Designed to be integrated with any curriculum, each grade level includes 18-20 one-hour lessons to be conducted throughout the school year. Each LEAP lesson lasts about an hour is designed to fit within a typical daily math instructional period.

LEAP early algebra curriculum for Grades K-5. Grades 3 and 4 currently available, with the remaining books for Grades K-2, 5 in press.

Blanton, M., Gardiner, A., Stephens, A., & Knuth, E. (2020). LEAP: Learning through an early algebra progression. Didax: Rowley, MA.