Learning Progression

Student Mathematics Learning Through Self-Explanation, Peer Tutoring and Digital Media Production

This project engages high-school students as student-tutors who create screen-capture videos that demonstrate step-by-step solutions to mathematical problems and explicate the use of interactive applets. The project tests whether the mathematical and communication skills of student-tutors improve in the process of making the video materials. It also tests whether teachers and student users benefit from the videos. The project will examine whether the process of creating and disseminating the videos is replicable and scalable.

Lead Organization(s): 
Award Number: 
1119654
Funding Period: 
Mon, 08/15/2011 - Thu, 07/31/2014
Full Description: 

Watch a video report on the Teachers Create/Media Making Research effort.

This exploratory research and development project engages high-school students as student-tutors who create screen-capture videos that demonstrate step-by-step solutions to mathematical problems and explicate the use of interactive applets. The project has three development goals (a model for creating the media, a model for collaboration with teachers, and enhancements to a Lesson Study model) and three research goals (to test conjectures about student change, to analyze reconfigured roles for teachers and students, and to advance a theory of personalized learning communities.) The project tests whether the mathematical and communication skills of student-tutors improve in the process of making the video materials. It also tests whether teachers and the student users of the videos benefit from them. Further, the project will examine whether the process of creating and disseminating the videos is replicable and scalable.

The project uses design research methods as well as both formative and summative evaluations to achieve the research and development goals. The investigators pose a series of thoughtful research questions and plan to use a variety of research methods to collect and analyze data to answer them.

The project is potentially transformative. The advances in technology present opportunities and challenges for improving student learning. Built on strong theoretical and empirical foundations and prior work, the project takes full advantages of the opportunities of tutoring using 21st-century technologies - marrying screen-capture video with a model of student-delivered tutoring. The project will contribute to an understanding of how teachers and student-tutors change and exercise creativity through participating in digital media production. The findings of the project will have broader impact in at least three dimensions: (1) The videos created by students will be helpful for other students' learning; (2) The research on engaging students in creating videos can not only help us understand the effective use of technology, but also help us understand the mechanism for developing students' generative thinking and creativity; and (3) This project can provide insights about how to integrate 21st-Century technology into regular classrooms.

Student Mathematics Learning Through Self-Explanation, Peer Tutoring and Digital Media Production

Supporting Scientific Practices in Elementary and Middle School Classrooms

This project will develop a learning progression that characterizes how learners integrate and interrelate scientific argumentation, explanation and scientific modeling, building ever more sophisticated versions of practice over time using the three common elements of sense-making, persuading peers and developing consensus. The learning progression is constructed through students’ understanding of scientific practice as measured by their attention to generality of explanation, clarity of communication, audience understanding, evidentiary support, and mechanistic versus descriptive accounts.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1020316
Funding Period: 
Wed, 09/01/2010 - Fri, 08/31/2012
Full Description: 

Research on student learning has developed separate progressions for scientific argumentation, explanation and scientific modeling. Engaging Learners in Scientific Practices develops a learning progression that characterizes how learners integrate and interrelate scientific argumentation, explanation and scientific modeling, building ever more sophisticated versions of practice over time using the three common elements of sense-making, persuading peers and developing consensus. The learning progression is constructed through improvements in students' performance and understanding of scientific practice as measured by their attention to generality of explanation, attention to clarity of communication and audience understanding, attention to evidentiary support, and attention to mechanistic versus descriptive accounts. The project is led by researchers at Northwestern University, the University of Texas, Wright State University, Michigan State University, and the BEAR assessment group. Two cohorts of 180 students each are followed for two years from 4th to 5th grade in Illinois and two cohorts of 180 students each are followed for two years from 5th to 6th grade in Michigan The elementary school students will work with FOSS curriculum units modified to embed supports for scientific practices. Two cohorts of 500 middle school students are followed for three years from 6th to 8th grade as they work with coordinated IQWST units over three years. The outcome measures include analyses of classroom discourse, pre- and pos-test assessments of student learning, and reflective interviews grounded in students' own experiences with practices in the classroom to assess their growth across the dimensions. The BEAR team is responsible for validation and calibration of the frameworks and instruments, and design of the scheme for analysis of the data. Horizon Research performs the formative and summative evaluation. The project will produce an empirically-tested learning progression for scientific practices for grades 4-8 along with tested curriculum materials and validated assessment items that support and measure students' ability in the scientific practices of explanation, argumentation and modeling. In the process of development, an understanding is gained about how to design and test this learning progression. The framework is articulated on a website for use by other researchers and developers. The project also builds capacity by educating several graduate students.

Supporting Scientific Practices in Elementary and Middle School Classrooms

Reasoning Tools for Understanding Water Systems

This project builds on current learning progression research to study the effects of teaching Tools for Reasoning on development of middle school students' capacities to understand the Earth's hydrologic systems. The project applies a design-based research approach using iterative cycles of Tool design/revision, teacher workshops, and small-scale pilot tests of Tools through classroom experiments with teachers and students in Montana and Arizona.

Lead Organization(s): 
Award Number: 
1020176
Funding Period: 
Wed, 09/15/2010 - Sat, 08/31/2013
Full Description: 

This exploratory project, led by faculty at the University of Montana, Michigan State University, and the University of Arizona, collaborating with teachers from the Missoula, MT schools, builds on current learning progression research to study the effects of teaching Tools for Reasoning on development of middle school students' capacities to understand the Earth's hydrologic systems. The project applies a design-based research approach using iterative cycles of Tool design/revision, teacher workshops, and small-scale pilot tests of Tools through classroom experiments with teachers and students in Montana and Arizona.

The central research question being addressed is: How can learning progression-based Reasoning Tools support students in using models and representations to engage in principled reasoning about hydrologic systems? This question will be answered by analysis of data from assessments of student learning, student clinical interviews, teacher assessments, classroom observations, and teacher focus groups.

The Reasoning Tools project will contribute insight into the challenge of developing students' environmental science literacy and the reasoning skills needed to make informed citizenship decisions about 21st century water issues. Project outcomes will include materials for teaching middle school students to reason about hydrologic systems, theoretical and practical insights into the effects of teaching Tools for Reasoning, strategies for supporting students and teachers in use of the Tools, and refinements of a water systems learning progression framework.

Reasoning Tools for Understanding Water Systems

Rethinking How to Teach Energy: Laying The Foundations in Elementary School (Collaborative Research: Lacy)

This project is a collaborative effort that aims to develop a grade 3-5 Learning Progression that will provide a coherent approach to teaching energy in elementary school and lay a strong foundation for further learning in middle school. The project will identify a network of core concepts and principles about energy that are fundamental and general enough to be compatible with scientific ideas about energy, yet within reach of 5th graders.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1020013
Funding Period: 
Wed, 09/01/2010 - Fri, 08/31/2012
Full Description: 

This project is a collaborative effort involving scientists, science educators, and teachers from TERC, Clark University, Tufts University,and urban Massachusetts schools that aims to develop a grade 3-5 Learning Progression that will provide a coherent approach to teaching energy in elementary school and lay a strong foundation for further learning in middle school. The work draws on and complements the learning progression and curriculum for matter developed and tested in the Inquiry Project (NSF award 0628245). The project will identify a network of core concepts and principles about energy that are fundamental and general enough to be compatible with scientific ideas about energy, yet within reach of 5th graders.

This project explores the hypothesis that, while the scientific concept of energy is too abstract and difficult to understand in early grades, useful foundations can be established early on by elaborating a learning progression for energy. Clinical interviews will be administered to 24 pairs of 3rd, 4th, and 5th graders recruited from urban after-school programs, to identify precursors to the core ideas as well obstacles to learning them. This research will help the investigators design key learning experiences that could allow students to progress from initial ideas toward a scientific understanding of energy. Those learning designs will then be tested in teaching interviews with 3 small groups of students in the same settings.

The result of the project will be an outline for a grade 3-5 learning progression for energy taking into account the project research findings as well as relevant standards, curricula, and science education literature.

Rethinking How to Teach Energy: Laying The Foundations in Elementary School (Collaborative Research: Lacy)

CAREER: Supporting Students' Proof Practices Through Quantitative Reasoning in Algebra

The aim of this project is to explore the hypothesis that a curricular focus on quantitative reasoning in middle grades mathematics can enhance development of student skill and understanding about mathematical proof. The project is addressing that hypothesis through a series of studies that include small group teaching experiments with students, professional development work with teachers, and classroom field tests of curricular units that connect quantitative reasoning and proof in algebra.

Award Number: 
0952415
Funding Period: 
Mon, 03/15/2010 - Mon, 02/28/2011
Full Description: 

The aim of this CAREER project led by Amy Ellis at the University of Wisconsin is to explore the hypothesis that a curricular focus on quantitative reasoning in middle grades mathematics can enhance development of student skill and understanding about mathematical proof. The project is addressing that hypothesis through a series of studies that include small group teaching experiments with students, professional development work with teachers, and classroom field tests of curricular units that connect quantitative reasoning and proof in algebra.

Work of the project will produce: (a) insights into ways of unifying two previously disconnected lines of research on quantitative reasoning and proof; (b) models describing realistic ways to support development of students' proof competencies through quantitative reasoning; (c) improvement in students' understanding of algebra through engagement in proof practices based on quantitative reasoning; (d) insights into middle-school students' thinking as they negotiate the transition from elementary to more advanced mathematics; and (e) increased understanding of teachers' knowledge about proof and their classroom practices aimed at helping students progress towards understanding and skill in proof.

CAREER: Supporting Students' Proof Practices Through Quantitative Reasoning in Algebra

A Learning Progression for Scientific Modeling

This project will provide an empirically-supported learning progression for a key scientific practice, scientific modeling. The specific instructional materials created as part of the project can serve as a model other developers can use to design materials supporting scientific modeling and other practices. The model for educative curriculum materials as a form of teacher support can be adapted to support teacher learning about modeling or other scientific practices in other curriculum materials.

Project Email: 
Models@sesp.northwestern.edu
Lead Organization(s): 
Award Number: 
0628199
Funding Period: 
Sun, 10/01/2006 - Thu, 03/31/2011
Project Evaluator: 
Horizon Research
Full Description: 

The project is a 42-month research and development effort to develop a learning progression for scientific modeling and investigate its implementation in two grade bands. The project focuses on the scientific practice of modeling because of its centrality in both the practice of science and as a vehicle for science learning. A learning progression characterizes variations of the practice that are appropriate for learners, and a sequence of successively more complex versions of that practice possible for learners. A learning progression for a scientific practice contains; (a) a model of the target practice appropriate for learners, (b) the starting points of learners' intuitive understandings and practices, (c) a sequence of successively more sophisticated understandings and practices, and (d) instructional supports to help learners develop the practice. The theoretical contribution of the proposed work is to develop an empirically-tested learning progression for scientific modeling. The project identifies two related learning goals for modeling that serve as the two major constructs it will track: modeling practices and metamodeling knowledge. Each construct is broken into several progress variables that are tracked across time. The project will provide an empirically-supported learning progression for a key scientific practice, scientific modeling. Although the field has produced snapshots demonstrating the promise of engaging learners in scientific practices, systematic empirical research demonstrating how the practice can develop across years is lacking. The specific instructional materials created as part of the project can serve as a model other developers can use to design materials supporting scientific modeling and other practices. The model for educative curriculum materials as a form of teacher support can be adapted to support teacher learning about modeling or other scientific practices in other curriculum materials.

A Learning Progression for Scientific Modeling

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): 
Partner 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): 
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): 
Partner 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
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
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