Learning Progression

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.

Evaluating and Improving a Learning Trajectory for Linear Measurement in Elementary Grades 2 and 3: A Longitudinal Study

We examined children’s development of strategic and conceptual knowledge for linear measurement. We conducted teaching experiments with eight students in grades 2 and 3, based on our hypothetical learning trajectory for length to check its coherence and to strengthen the domain-specific model for learning and teaching.We checked the hierarchical structure of the trajectory by generating formative instructional task loops with each student and examining the consistency between our predictions and students’ ways of reasoning.

Author/Presenter: 
Clements, Douglas
Barrett, Jeffrey
Sarama, Julie
Cullen, Craig
McCool, Jenni
Witkowski-Rumsey, Chepina
Klanderman, David
Year: 
2012

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