Learning Progression

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.

Discussion of Promising Scale-up Strategies for Reaching Classrooms

Day: 
Tues

Participants and the presenters will discuss their experiences—including releasing free and paid apps—and provide suggestions to others for successfully reaching many users.

Date/Time: 
1:45 pm to 3:45 pm
2014 Session Types: 
Feedback Session (Work in Post-development)
Session Materials: 

Over a period of five years the SmartGraphs project developed HTML5 software for teaching and learning STEM subjects that make use of line graphs and scatter plots. SmartGraphs activities help students understand the “story” represented by a graph. The project created dozens of activities for algebra, physical science, and other STEM subjects, as well as an authoring system allowing non-computer-programmers to create and disseminate free online activities.

Building Theory While Supporting Implementation of the NGSS

Day: 
Tues

Implementing the NGSS requires changes in teaching, assessments, and curriculum materials. In this session, participants explore theoretical questions for DR K12 research that are raised by these NGSS implementation challenges.

Date/Time: 
1:45 pm to 3:45 pm
2014 Session Types: 
Mini-plenary Presentation

The Next Generation Science Standards present important shifts for science teaching, assessment, and curriculum materials—focusing on core explanatory ideas, a central role for science and engineering practices, and coherence across time and science disciplines. These challenges for practice require new theoretical advances.

Using Learning Progressions for Classroom Assessment and Teaching

Day: 
Tues

Join a discussion addressing how learning progression-based frameworks, assessments, and instruction can support teachers and students in developing increasingly sophisticated scientific knowledge and practice.

Date/Time: 
9:45 am to 11:45 am
2014 Session Types: 
Collaborative Panel Session

The goal of this session is to discuss possibilities, progress, and problems in using learning progression research to support improved assessment and instruction in middle school and high school classrooms.

In this session, several learning progression-related DR K–12 projects share findings and discuss questions around two issues:

Evaluation of a Learning Trajectory for Length in the Early Years

Author/Presenter: 
Clements, D.
Sarama, J.
Barrett, J.
Van Dine, D.
McDonel, J.
Year: 
2011
Short Description: 

Measurement is a critical component of mathematics education, but research on the learning and teaching of measurement is limited, especially compared to topics such as number and operations. To contribute to the establishment of a research base for instruction in measurement, we evaluated and refined a previously developed learning trajectory in early length measurement, focusing on the developmental progressions that provide cognitive accounts of the development of children’s strategic and conceptual knowledge of measure. Findings generally supported the developmental progression, in that children reliably moved through the levels of thinking in that progression. For example, they passed through a level in which they measured length by placing multiple units or attempting to iterate a unit, sometimes leaving gaps between units. However, findings also suggested several refinements to the developmental progression, including the nature and placement of indirect length comparison in the developmental progression and the role of vocabulary, which was an important facilitator of learning for some, but not all, children.

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