Learning Progression

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.

Children’s Measurement: A Longitudinal Study of Children’s Knowledge and Learning of Length, Area, and Volume

Quantitative reasoning and measurement competencies support the development of mathematical and scientific thinking in children in the early and middle grades and are fundamental to science, technology, engineering, and mathematics (STEM) education. The sixteenth Journal for Research in Mathematics Education (JRME) monograph is a report on a four-year-long multisite longitudinal study that studied children’s thinking and learning about geometric measurement (i.e., length, area, and volume).

Author/Presenter: 
Jeffrey E. Barrett
Douglas H. Clements
Julie Sarama
Year: 
2017
Short Description: 

This monograph is a report on a four-year-long multisite longitudinal study that studied children’s thinking and learning about geometric measurement (i.e., length, area, and volume).

Evaluation of three interventions teaching area measurement as spatial structuring to young children

We evaluated the effects of three instructional interventions designed to support young children’s understanding of area measurement as a structuring process.

Author/Presenter: 
Douglas H. Clements
Julie Sarama
Jeffrey E. Barrett
Craig J. Cullen
Aaron Hudyma
Ron Dolgin
Amanda L. Cullen
Cheryl L. Eames
Year: 
2018
Short Description: 

In this article, authors evaluated the effects of three instructional interventions designed to support young children’s understanding of area measurement as a structuring process.

Scientific Modeling across the K–12 Continuum: Alignment between Theoretical Foundations and Classroom Interventions

STEM Categorization: 
Day: 
Thu

Explore methods and challenges associated with supporting and evaluating scientific modeling in K–12 classrooms in this structured poster session.

Date/Time: 
2:15 pm to 3:45 pm
Session Materials: 

In this interactive panel symposium, presenters will draw from a set of active DR K-12 projects to explore a diverse array of resources, models, and tools (RMTs) designed to operationalize varying perspectives on scientific modeling in elementary, middle, and secondary classrooms across disciplinary domains.

Session Types: 

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