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Learning Progression

Mapping Developmental Trajectories of Students' Conceptions of Integers

This project is using data from interviews with 160 K-12 students and 20 adults to describe common understandings and progressions of development for negative number concepts and operations. The project is motivated by the widely acknowledged finding that students have difficulty mastering key concepts and skills involved in work with integers.

Project Email: 
Lisa.Lamb@sdsu.edu
Lead Organization(s): 
Award Number: 
0918780
Funding Period: 
Sat, 08/15/2009 - Sun, 07/31/2011
Project Evaluator: 
West Ed (Juan Carlos Bojorquez)
Full Description: 

The project Mapping Developmental Trajectories of Students' Conceptions of Integers, led by faculty from San Diego State University, is using data from 160 interviews with K-12 students and 20 adults to describe common understandings and progressions of development for negative number concepts and operations. The project is motivated by the widely acknowledged finding that students have difficulty mastering key concepts and skills involved in work with integers.

Two questions frame and guide the proposed research:

* What are students' conceptions of integers and operations on integers?

* What are possible developmental trajectories of students' understandings?

The investigators are seeking answers to those questions through structured interviews with students in elementary grades prior to instruction about negative numbers (Grades 2 and 4), students in middle grades whose formal learning experiences have already included explicit instruction about integers (Grade 7), high school students who are expected to use prior knowledge about integers in more advanced mathematics (Grade 11 PreCalculus and Calculus students), and adults who use integers in their work.

In addition to providing an empirically-based picture of ways that students reason about negative numbers, the project is producing useful interview protocols and a reliable and valid assessment instrument for describing the understanding and skill of students at various stages on such a progression.

Both the characterization of common learning progressions and the assessment instruments will be broadly useful to curriculum and test developers and teachers in K-12 mathematics classrooms.

Mapping Developmental Trajectories of Students' Conceptions of Integers

Developing an Empirically-tested Learning Progression for the Transformation of Matter to Inform Curriculum, Instruction and Assessment Design

A principled framework is created for the development of learning progressions in science that can demonstrate how their use can transform the way researchers, educators and curriculum developers conceptualize important scientific constructs. Using the construct of transformation of matter, which requires understanding of both discrete learning goals and also the connections between them, a hypothetical learning progression is constructed for grades 5-12.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
0822038
Funding Period: 
Mon, 09/15/2008 - Fri, 08/31/2012
Full Description: 

A principled framework is created for the development of learning progressions in science that can demonstrate how their use can transform the way researchers, educators and curriculum developers conceptualize important scientific constructs. Using the construct of transformation of matter, which requires understanding of both discrete learning goals and also the connections between them, a hypothetical learning progression is constructed for grades 5-12. Assessments are developed that link to the learning progression and require students to use cognitively challenging activities such as construction of models and scientific explanation to demonstrate their understanding of topics related to transformation of matter. The resultant set of assessment items can be used to place students along the transformation of matter learning progression, regardless of curriculum. The learning progression is empirically tested in grades 6-8 using mainly, but not exclusively, the chemistry units of the IQWST curriculum in a three year longitudinal study that measures the longitudinal progression of students and the cross-sectional development of teachers as they gain experience with the curriculum. The framework developed for creating the tools can inform the learning of other core ideas in science in emergent sciences that are inherently interdisciplinary. Also investigated is the relationship between student and teacher factors and different levels of students' developmental learning.

Developing an Empirically-tested Learning Progression for the Transformation of Matter to Inform Curriculum, Instruction and Assessment Design

Shifting Mindsets: A Study of a First-year Implementation of "New Technology High School"

This grant examines the changes teachers and students go through in their first year of implementing a New Technology High School project-based curriculum for ninth graders in two high schools. This first year of implementation is part of a phased-in implementation for subsequent grades. The NTHS approach calls for moving from more traditional approaches to mathematics and science education to project-based curricula that posits mathematics and science in the context of real-world issues and problems.

Lead Organization(s): 
Award Number: 
0738247
Funding Period: 
Wed, 08/15/2007 - Sat, 07/31/2010
Shifting Mindsets: A Study of a First-year Implementation of "New Technology High School"

Diagnostic E-learning Trajectories Approach (DELTA) Applied to Rational Number Reasoning for Grades 3-8

This project aims to develop a software diagnostic tool for integrating diagnostic interviews, group administered assessments, and student data in real-time so that teachers can enter and view student status information. This project would concentrate on rational number learning in grades 3-8. The design is based on a model of learning trajectories developed from existing research studies.

Project Email: 
gismo.fi@gmail.com
Lead Organization(s): 
Partner Organization(s): 
Award Number: 
0733272
Funding Period: 
Sat, 09/01/2007 - Tue, 08/31/2010
Project Evaluator: 
William Penuel (SRI)
Full Description: 

This project aims to develop a software diagnostic tool for integrating diagnostic interviews, group administered assessments, and student data in real-time so that teachers can enter and view student status information. This project would concentrate on rational number learning in grades 3-8. The design is based on a model of learning trajectories developed from existing research studies.

The diagnostic system to be developed for teachers would be used in assessing their students' knowledge and would identify difficulties in understanding five key clusters of concepts and skills in rational number reasoning. It would also investigate the diagnostic system's effects on student and teacher learning in relation to state standards, assessments, and curricular programs. The five areas include understanding: (1) multiplicative and division space; (2) fractions, ratio, proportion and rates; (3) rectangular area and volume; (4) decimals and percents; and (5) similarity and scaling.

The diagnostic measures will include diagnostic interviews collecting data using a handheld computer, two types of group-administered assessments of student progress, one set along learning trajectories for each of the five sub-constructs and one composite measurement per grade. The diagnostic system will produce computer-based progress maps, summarizing individual student and class performance and linking to state assessments.

Diagnostic E-learning Trajectories Approach (DELTA) Applied to Rational Number Reasoning for Grades 3-8

Cyber-enabled Design Research to Enhance Teachers' Critical Thinking Using a Major Video Collection on Children's Mathematical Reasoning (Collaborative Research: Maher)

This project is working to create a cyber infrastructure that supports development and documentation of additional interventions for teacher professional development using the video collection, as well as other videos that might be added in the future by teacher educators or researchers, including those working in other STEM domains.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
0822204
Funding Period: 
Mon, 09/15/2008 - Fri, 08/31/2012
Full Description: 

The Video Mosaic Collaborative features  videos of student mathematics reasoning,  tools and services to encourage learning, research and practices fostering the development of student reasoning.  The VMC is a collection and service portal intended to support three primary audiences—teacher educators and their pre-service and in-service students, practicing teachers, and researchers.  The Video Mosaic Collaborative features a 22-year longitudinal study of students’ mathematical reasoning skills as they are developed from elementary through high school grades.  The VMC has been carefully designed to leverage the insights and strategies that can be mined in this extensive and unique video collection featuring observations, interventions and interviews with students solving mathematics problems in the classroom and in informal learning settings.  A careful metadata strategy was designed by the library and education research partners in collaboration to capture elements for searching that include forms of reasoning and heuristics, math strand, math problem, NCTM standards, grade level and type of educational environment.  Students and researchers are identified and can be individually tracked through the collection.  Transcripts, student work and dissertations resulting from the videos are linked in metadata.  Tools, such as the VMCAnalytic, a video annotation and analysis tool, are provided to enable registered participants to reuse the videos for instruction, study and research by creating personal clips and combining clips to accomplish research goals such as demonstrating changes in reasoning for an individual student studying probability over several video sessions.  Unlike other video annotation tool, the VMC analytic creates  XML-based independent resources that can be kept private in the researcher’s workspace but that can also be shared.  Shared analytics will be mined for keywords, which will retrieve the video(s) being analyzed, thus adding user tagging to the metadata for the videos.  The analytic resources created are not independently searched and displayed but will display as part of the context for the videos in the collection, along with student work, dissertations, and ultimately published articles, etc., all of which form the critical context of research and study surrounding each video.

Different search strategies, guidance in using videos and opportunities to consult or collaborate with others will be provided for each primary audience of the VMC.  The latest iteration of the portal, with collections and services available for immediate use, will be presented and demonstrated at the DRK12 Principal Investigators’ meeting poster session.  Visitors to the poster will be encouraged to search the portal and to create a small analytic, in a hands-on, interactive one on one demonstration.  We believe that the VMC makes a unique and significant contribution to the efforts of teacher educators, practicing teachers and researchers to discover insights and develop innovative strategies to support the development of student reasoning in mathematics education.

Cyber-enabled Design Research to Enhance Teachers' Critical Thinking Using a Major Video Collection on Children's Mathematical Reasoning (Collaborative Research: Maher)

Learning Progressions for Scientific Inquiry: A Model Implementation in the Context of Energy

The project has had three major areas of focus:  (1) Offering professional development to help elementary and 6th grade teachers become more responsive teachers, attending and responding to their students' ideas and reasoning; (2)  Developing web-based resources (both curriculum and case studies) to promote responsive teaching in science; and (3) research how both teachers and students progress in their ability to engage in science inquiry. 

Project Email: 
fgoldberg@sciences.sdsu.edu
Lead Organization(s): 
Partner Organization(s): 
Award Number: 
0732233
Funding Period: 
Tue, 01/01/2008 - Mon, 12/31/2012
Project Evaluator: 
Lawrence Hall of Science
Learning Progressions for Scientific Inquiry: A Model Implementation in the Context of Energy

Building an Understanding of Science


Understanding Science provides an accurate portrayal of the nature of science and tools for teaching associated concepts. This project has at its heart a public re-engagement with science that begins with teacher preparation. To this end, its immediate goals are (1) improve teacher understanding of the nature of the scientific enterprise and (2) provide resources and strategies that encourage and enable K-16 teachers to incorporate and reinforce the nature of science throughout their science teaching.

Lead Organization(s): 
Award Number: 
0624436
Funding Period: 
Mon, 03/12/2007 - Wed, 05/11/2011
Project Evaluator: 
BSCS
Building an Understanding of Science

High School Mathematics and Science Pipeline Study

This project uses a mixed-methods design to test the hypothesis that key approaches to high school reform grease the mathematics and science pipelines for all students in reforming high schools. This study is intended to provide understanding of pipeline progression in reforming high schools and strategies successful schools employ to ensure timely pipeline progress for all students, particularly those historically underrepresented and underserved in mathematics and science and post-secondary education.

Lead Organization(s): 
Award Number: 
0723412
Funding Period: 
Wed, 08/15/2007 - Sun, 07/31/2011
High School Mathematics and Science Pipeline Study

Scientific Role-playing Games for 21st-Century Citizenship

This project investigates the potential of online role-playing games for scientific literacy through the iterative design and research of Saving Lake Wingra, an online role-playing game around a controversial development project in an urban area. Saving Lake Wingra positions players as ecologists, department of natural resources officials, or journalists investigating a rash of health problems at a local lake, and then creating and debating solutions.

Lead Organization(s): 
Award Number: 
0746348
Funding Period: 
Fri, 08/15/2008 - Sat, 07/31/2010
Scientific Role-playing Games for 21st-Century Citizenship

Tool Systems to Support Progress Toward Expert-like Teaching by Early Career Science Educators

The goal of this project is to accelerate the progress of early-career and pre-service science teachers from novice to expert-like pedagogical reasoning and practice by developing and studying a system of discourse tools. The tools are aimed at developing teachers' capabilities in shaping instruction around the most fundamental science ideas; scaffolding student thinking; and adapting instruction to diverse student populations by collecting and analyzing student data on their thinking levels.

Lead Organization(s): 
Award Number: 
0822016
Funding Period: 
Mon, 09/15/2008 - Fri, 08/31/2012
Project Evaluator: 
Jim Minstrell
Tool Systems to Support Progress Toward Expert-like Teaching by Early Career Science Educators
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