Learning Progression

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.

Problematizing and Assessing Secondary Mathematics Teachers’ Ways of Thinking

STEM Categorization: 
Day: 
Thu

Engage with presenters as they discuss assessment and rubrics designed to measure secondary teachers’ mathematical habits of mind.

Date/Time: 
9:30 am to 11:00 am
Session Materials: 

Work in secondary mathematics education takes many approaches to content, pedagogy, professional development and assessment. This session aims to illuminate the richness of hte content of secondary mathematics and the field of secondary mathematics education by sharing two such approaches and reflecting on the differences and commonalities between the two.   

Session Types: 

Levels of Participatory Conceptions of Fractional Quantity Along a Purposefully Sequenced Series of Equal Sharing Tasks: Stu's Trajectory

Current intervention research in special education focuses on children's responsiveness to teacher modeled strategies and not conceptual development within children's thinking. As a result, there is a need for research that provides a characterization of key understandings (KUs) of fractional quantity evidenced by children with learning disabilities (LD) and how growth of conceptual knowledge may occur within these children's mathematical activity.

Author/Presenter: 
Jessica Hunt
Arla Westenskow
Juanita Silva
Jasmine Welch-Ptak
Lead Organization(s): 
Year: 
2016
Short Description: 
Current intervention research in special education focuses on children's responsiveness to teacher modeled strategies and not conceptual development within children's thinking. As a result, there is a need for research that provides a characterization of key understandings (KUs) of fractional quantity evidenced by children with learning disabilities (LD) and how growth of conceptual knowledge may occur within these children's mathematical activity. This case study extends current literature by presenting KUs of fractional quantity, evidenced through problem solving strategies, observable operations, and naming/quantification of one fifth grader with LD before, during, and after seven instructional sessions situated in equal sharing.

Webinar on the Common Guidelines for Education Research and Development

Author/Presenter: 
Edith Gummer
Year: 
2014
Short Description: 
This webinar, led by Edith Gummer (formerly of NSF), discusses the guidelines outlined in the report co-authored by the Institute of Education Sciences, U.S. Department of Education and the National Science Foundation.

Teaching Viable Argumentation and Measuring the Effects

Day: 
Tues

How do we encourage referent-based mathematical argumentation without encouraging students to request that examples accompany otherwise viable arguments? Assessment concerns are explored and discussed.

Date/Time: 
1:45 pm to 3:45 pm
2014 Session Types: 
Feedback Session (Work in Development)
Presenters: 

The LAMP project has developed a sequence of lessons in a hypothetical learning trajectory that targets students’ ability to write viable arguments in algebraic contexts. Most of the lessons encourage students to produce a referent (e.g., variable expression or equation, generic example, diagram) as the foundation of their argument. Students come to the lessons with a predisposition for example production in support of their claims and to augment arguments.

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