Learning Progression

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: 

Improving Student Learning and Teacher Practice in Mathematics: A Focus on Formative Assessment

STEM Categorization: 
Day: 
Thu

Join a discussion with panelists from several projects about project model designs, initial findings, and implementation challenges associated with formative assessment in mathematics.

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

In this session, four projects will share their work on formative assessment and mathematics learning trajectories, and participants will discuss the implications for formative assessment practices in mathematics.

Session Types: 

Argumentation and Discourse

STEM Categorization: 
Day: 
Thu

Join a discussion about models for teaching and learning argumentation and discourse in mathematics, including implications for teacher practice, classroom structure, and the nature of students’ learning.

Date/Time: 
11:15 am to 12:00 pm
Facilitators: 
Session Materials: 
Presenter Reflections: 

David Yopp, University of Idaho | June 22, 2016

This session’s conversation focused on ways of viewing argumentation and how argument produces as the content to be learned.

Participants discussed examples (e.g., rational and irrational numbers, solving equations, and natural number operations) in Common Core where the argument students produce is the content. Understanding these concepts included understanding arguments that represent the concept, and these arguments provide access to mathematical notions that have no physical expression.

For example, numbers are classified as rational or irrational through an argument. An arguer might classify a radical as an irrational number by arguing that the radical cannot be expressed as the quotient of integers. When a linear equation is solved and a solution is found, the solution process can be viewed as an argument: that there exist a unique solution. The concept of "solving equations" is represented by this argument.

Following discussion of these examples, participants asked themselves what other areas of content could be viewed as an argument.

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