Learning Progression

Empirical Recovery of Learning Progressions Through the Lens of Educators

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).

Author/Presenter

Leanne R. Ketterlin-Geller

Yetunde Zannou

Anthony Sparks

Lindsey Perry

Year
2020
Short Description

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).

NCTM Presentation Line of "Good" Fit in Grade 8 Classrooms

Lead Organization(s)
Year
2018
Short Description

This presntation addreses 4 research cquestions

 

What extant criteria do Grade 8 students use to choose the better line
of fit between two lines “fit” to a set of data, when both lines express
the trend of the data?
 
Is a residual criterion accessible and useful to Grade 8 students when
learning about line of fit?
 
How does introducing a residual criterion impact student
understanding of line of fit and their understanding mathematical
modeling process?
 
What stages of learning do students express as they engage in our
lesson?

LEAP: Learning through an Early Algebra Progression

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.

Author/Presenter

Maria Blanton

Angela Murphy Gardiner

Ana Stephens

Eric Knuth

Lead Organization(s)
Year
2020
Short Description

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.

Length Measurement in the Early Years: Teaching and Learning with Learning Trajectories

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 instructional activities and pedagogical strategies, correlated with each level of the developmental progression. This study evaluated a portion of our learning trajectory, focusing on the instructional component.

Author/Presenter

Julie Sarama

Douglas H. Clements

Jeffrey E. Barrett

Craig J. Cullen

Aaron Hudyma

Yuly Vanegas

Lead Organization(s)
Year
2021
Short Description

This study evaluated a portion of our learning trajectory, focusing on the instructional component. We found that the instruction was successful in promoting a progression from one level to the next for 40% of the children, with others developing positive new behaviors (but not sufficient to progress to a new level).

The Role of Balance Scales in Supporting Productive Thinking about Equations Among Diverse Learners

This research focuses on ways in which balance scales mediate students’ relational understandings of the equal sign. Participants included 21 Kindergarten–Grade 2 students who took part in an early algebra classroom intervention focused in part on developing a relational understanding of the equal sign through the use of balance scales. Students participated in pre-, mid- and post-intervention interviews in which they were asked to evaluate true-false equations and solve open number sentences. Students often worked with balance scales while solving these tasks.

Author/Presenter

Ana Stephens

Yewon Sung

Susanne Strachota

Ranza Veltri Torres

Karisma Morton

Angela Murphy Gardiner

Maria Blanton

Eric Knuth

Rena Stroud

Year
2020
Short Description

This research focuses on ways in which balance scales mediate students’ relational understandings of the equal sign.

Experimental Impacts of the Ongoing Assessment Project on Teachers and Students

In this report, we describe the results of a rigorous two-year study of the impacts of a mathematics initiative called Ongoing Assessment Project (OGAP) on teacher and student learning in grades 3-5 in two Philadelphia area school districts. OGAP is a mathematics program which combines teacher formative assessment practices with knowledge of student developmental progressions to build deeper student understanding of mathematics content. OGAP includes teacher professional development, classroom resources, school-based routines for regular practice, and ongoing school-based supports.
Author/Presenter

Jonathan A. Supovitz

Caroline B. Ebby

Janine Remillard

Robert A. Nathenson

Lead Organization(s)
Year
2018
Short Description

In this report, authors describe the results of a rigorous two-year study of the impacts of a mathematics initiative called Ongoing Assessment Project (OGAP) on teacher and student learning in grades 3-5 in two Philadelphia area school districts.

Pathways for Analyzing and Responding to Student Work for Formative Assessment: The Role of Teachers’ Goals for Student Learning

This study explored how teachers interpreted and responded to their own student work during the process of formative assessment. The study involved a purposefully selected sample of 32 teachers in grades K-5 who had been trained by the Ongoing Assessment Project (OGAP) to use learning progressions to analyze and respond to evidence in student work.

Author/Presenter

Caroline Brayer Ebby

Janine Remillard

Jordan H. D'Olier

Lead Organization(s)
Year
2019
Short Description

This study explored how teachers interpreted and responded to their own student work during the process of formative assessment.

Gina’s mathematics: Thinking, tricks, or “teaching”?

Students with learning disabilities display a diverse array of factors that interplay with their mathematical understanding. Our aim in this paper is to discuss the extent to which one case study elementary school child with identified learning disabilities (LDs) made sense of composite units and unit fractions. We present analysis and results from multiple sessions conducted during a teaching experiment cast as one-on-one intervention.

Author/Presenter

Jessica H.Hunt

Beth L.MacDonald

JuanitaSilva

Year
2019
Short Description

This paper discusses the extent to which one case study elementary school child with identified learning disabilities (LDs) made sense of composite units and unit fractions.

What Can We Learn from Correct Answers?

Dig deeper into classroom artifacts using research-based learning progressions to enhance your analysis and response to student work, even when most students solve a problem correctly.

Ebby, C. B., Hulbert, E. T., and Fletcher, N. (2019). What can we learn from correct answers? Teaching Children Mathematics, 25(6), 346-353.

Author/Presenter

Caroline B. Ebby

Elizabeth T. Hulbert

Nicole Fletcher

Lead Organization(s)
Year
2019
Short Description

This article describes how research-based learning progressions can be used to enhance the analysis and response to student work.