Learning Progression

Learning trajectories in early mathematics instruction have received increasing attention from policymakers, educators, curriculum developers, and researchers. They are generally deemed useful for guiding curriculum standards, instructional planning, and assessment. However, the specific contributions of learning trajectories to education and children’s learning are unclear. We review research over the last five years to describe what is known and what still needs to be learned about methods of development, refinement, and validation of the goals, developmental progressions, and instruction of learning trajectories in early mathematics and possible advantages and disadvantages in the educational application of learning trajectories.

Learning trajectories in early mathematics instruction have received increasing attention from policymakers, educators, curriculum developers, and researchers. They are generally deemed useful for guiding curriculum standards, instructional planning, and assessment. However, the specific contributions of learning trajectories to education and children’s learning are unclear. We review research over the last five years to describe what is known and what still needs to be learned about methods of development, refinement, and validation of the goals, developmental progressions, and instruction of learning trajectories in early mathematics and possible advantages and disadvantages in the educational application of learning trajectories.

We discuss transforming STEM education using three aspects: learning progressions (LPs), constructed response performance assessments, and artificial intelligence (AI). Using LPs to inform instruction, curriculum, and assessment design helps foster students’ ability to apply content and practices to explain phenomena, which reflects deeper science understanding. To measure the progress along these LPs, performance assessments combining elements of disciplinary ideas, crosscutting concepts and practices are needed. However, these tasks are time-consuming and expensive to score and provide feedback for. Artificial intelligence (AI) allows to validate the LPs and evaluate performance assessments for many students quickly and efficiently.

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.

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.

‘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.

In this manuscript, we propose that educators’ perspectives may serve as an independent source of evidence that can be integrated with traditional evidence sources (e.g., cognitive interviews with students, psychometric data). This manuscript describes two studies that used surveys to draw on educator knowledge of students to identify upper and lower bounds of a learning progression (MMaRS study) and to understand the order of intermediary phases of learning (ESTAR study).