Learning Progression

Analyzing Early Algebra Learning Progressions for Grades 3-8

Day: 
Thu

This session will critically examine conjectured Early Algebra Learning Progressions for grades 3–8 for coherence, alignment, and completeness.

Date/Time: 
8:30 am to 9:45 am
Session Type: 
Product Feedback Session
Session Materials: 

This session will critically examine conjectured Early Algebra Learning Progressions for grades 3–8 for coherence, alignment, and completeness.

A Learning Progression-Based System for Promoting Understanding of Carbon-Transforming Processes

This project builds on prior efforts with learning progressions, and is focused on key carbon-transforming processes in socio-ecological systems at multiple scales, including cellular and organismal metabolism, ecosystem energetics and carbon cycling, carbon sequestration, and combustion of fossil fuels. The primary project outcomes will be coordinated instructional tools that are useful to professionals at all levels in the science education system--classroom teachers, professional developers, and developers of curricula, standards and assessments.

Lead Organization(s): 
Award Number: 
1020187
Funding Period: 
Wed, 09/15/2010 to Mon, 08/31/2015
Project Evaluator: 
Rose Shaw
Full Description: 

This project--led by science educators at Michigan State University, the National Geographic Society, the Natural Resource Ecology Laboratory (NREL) at Colorado State University, the Berkeley Evaluation and Assessment Research (BEAR) Center, and AAAS Project 2061, and including schools in California, Colorado, Maryland, Michigan, and Washington--builds on prior efforts with learning progressions, and is focused on key carbon-transforming processes in socio-ecological systems at multiple scales, including cellular and organismal metabolism, ecosystem energetics and carbon cycling, carbon sequestration, and combustion of fossil fuels.

The project uses an iterative design research process to develop and refine a suite of tools for reasoning and test efficacy of those tools in geographically and culturally diverse schools. The project team is:

1. Refining and validating a detailed learning progression framework covering the middle and high school years; ultimately, the framework will describe the development of students' capacity to use fundamental principles such as conservation of matter and energy to reason about carbon-transforming processes at multiple scales.

2. Refining 'Tools for Reasoning' that make hidden scientific principles - matter, energy, and scale - visible to students; the power of these tools lies in their flexible use for different processes, systems, scales, and curricular contexts.

3. Developing and refining flexible teaching strategies that engage students in cognitive apprenticeship in the practices of environmental science literacy: a) inquiry and argumentation, b) explanations and predictions, and c) decision-making about environmental issues.

4. Using and refining existing summative assessments, and developing and testing formative assessment tools; these assessment tools will provide teachers and researchers with immediate information about their students' intellectual resources and will be linked to the learning progression framework.

5. Developing, field testing, and assessing the effectiveness of six middle school and six high school units that use project tools and enact project principles; the units introduce students to fundamental principles, engage them in reasoning about carbon-transforming processes at organismal scale, and at landscape and global scales. Each unit includes a) an online formative assessment and b) activity sequences that use tools for reasoning and teaching strategies.

6. Developing, field testing, and assessing professional development materials in both face-to-face and facilitated online forms; the materials introduce teachers to learning progressions in environmental science literacy, assessment tools, tools for reasoning, teaching strategies, and teaching materials and activities, and also address difficulties that teachers encounter in using learning progressions and enacting teaching strategies.

The primary project outcomes will be coordinated instructional tools that are useful to professionals at all levels in the science education system--classroom teachers, professional developers, and developers of curricula, standards and assessments.

Efficacy Study of Metropolitan Denver's Urban Advantage Program: A Project to Improve Scientific Literacy Among Urban Middle School Students

This is an efficacy study to determine if partnerships among formal and informal organizations demonstrate an appropriate infrastructure for improving science literacy among urban middle school science students. The study aims to answer the following questions: How does participation in the program affect students' science knowledge, skills, and attitudes toward science; teachers' science knowledge, skills, and abilities; and families engagement in and support for their children's science learning and aspirations?

Award Number: 
1020386
Funding Period: 
Wed, 09/15/2010 to Wed, 08/31/2011
Project Evaluator: 
Maggie Miller
Full Description: 

This is an efficacy study through which the Denver Museum of Nature and Science, the Denver Zoo, the Denver Botanic Gardens, and three of Denver's urban school districts join efforts to determine if partnerships among formal and informal organizations demonstrate an appropriate infrastructure for improving science literacy among urban middle school science students. The Metropolitan Denver Urban Advantage (UA Denver) program is used for this purpose. This program consists of three design elements: (a) student-driven investigations, (b) STEM-related content, and (c) alignment of schools and informal science education institutions; and six major components: (a) professional development for teachers, (b) classroom materials and resources, (c) access to science-rich organizations, (d) outreach to families, (e) capacity building and sustainability, and (e) program assessment and student learning. Three research questions guide the study: (1) How does the participation in the program affect students' science knowledge, skills, and attitudes toward science relative to comparison groups of students? (2) How does the participation in the program affect teachers' science knowledge, skills, and abilities relative to comparison groups of teachers? and (3) How do families' participation in the program affect their engagement in and support for their children's science learning and aspirations relative to comparison families?

The study's guiding hypothesis is that the UA Denver program should improve science literacy in urban middle school students measured by (a) students' increased understanding of science, as reflected in their science investigations or "exit projects"; (b) teachers' increased understanding of science and their ability to support students in their exit projects, as documented by classroom observations, observations of professional development activities, and surveys; and (c) school groups' and families' increased visits to participating science-based institutions, through surveys. The study employs an experimental research design. Schools are randomly assigned to either intervention or comparison groups and classrooms will be the units of analysis. Power analysis recommended a sample of 18 intervention and 18 comparison middle schools, with approximately 72 seventh grade science teachers, over 5,000 students, and 12,000 individual parents in order to detect differences among intervention and comparison groups. To answer the three research questions, data gathering strategies include: (a) students' standardized test scores from the Colorado Student Assessment Program, (b) students' pre-post science learning assessment using the Northwest Evaluation Association's Measures for Academic Progress (science), (c) students' pre-post science aspirations and goals using the Modified Attitude Toward Science Inventory, (d) teachers' fidelity of implementation using the Teaching Science as Inquiry instrument, and (e) classroom interactions using the Science Teacher Inquiry Rubric, and the Reformed Teaching Observation protocol. To interpret the main three levels of data (students, nested in teachers, nested within schools), hierarchical linear modeling (HLM), including HLM6 application, are utilized. An advisory board, including experts in research methodologies, science, informal science education, assessment, and measurement oversees the progress of the study and provides guidance to the research team. An external evaluator assesses both formative and summative aspects of the evaluation component of the scope of work.

The key outcome of the study is a research-informed and field-tested intervention implemented under specific conditions for enhancing middle school science learning and teaching, and supported by partnerships between formal and informal organizations.

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.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1020316
Funding Period: 
Wed, 09/01/2010 to 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.


Project Videos

2019 STEM for All Video Showcase

Title: Science Storylines

Presenter(s): Brian Reiser, Kelsey Edwards, Barbara Hug, Tara McGill, Jamie Noll, Michael Novak, Bill Penuel, Trey Smith, & Aliza Zivic


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 to 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.

Measurement Approach to Rational Number (MARN)

This project is designing, developing, and testing an innovative approach to elementary students' learning in the critical areas of multiplicative reasoning, fractions, and proportional reasoning. The project is building on the successful El'Konin-Davydov (E-D) elementary mathematics curriculum that originated in Russia to develop a curriculum framework that can be implemented in U. S. schools. The ultimate product of the research will be a rational number learning progression consisting of carefully articulated and sequenced learning goals.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1020154
Funding Period: 
Thu, 07/15/2010 to Tue, 06/30/2015
Full Description: 

The Measurement Approach to Rational Number (MARN) project is a collaborative effort by faculty at New York University, Iowa State University, and the Illinois Institute of Technology that is designing, developing, and testing an innovative approach to elementary students' learning in the critical areas of multiplicative reasoning, fractions, and proportional reasoning. The project team is building on the successful El'Konin-Davydov (E-D) elementary mathematics curriculum that originated in Russia to develop a curriculum framework that can be implemented in U. S. schools.

The MARN project addresses five core research questions about how rational number learning can be developed from a measurement perspective and how sociocultural theory and constructivism can contribute to design of effective learning trajectories based on that perspective. The project begins with careful analysis of the E-D curriculum embodied in Russian mathematics materials, of classroom data from a Hawaii implementation of the E-D curriculum, and of relevant prior curriculum development projects in other U. S. contexts. Work is proceeding from development of an initial curriculum framework through intensive teaching experiments to implementation and modification of the framework in the course of classroom design experiments.

The ultimate product of the research and development effort will be a rational number learning progression consisting of carefully articulated and sequenced learning goals. The curriculum framework will also include mathematical tasks to foster learning of each concept, description of predicted student learning in the context of the tasks, a set of assessment items related to each concept, and guidelines for relevant teacher interventions. Thus, the framework will provide a foundation for development of curriculum units.

DRK12-Biograph: Graphical Programming for Constructing Complex Systems Understanding in Biology

This project will investigate how complex systems concepts supported by innovative curricular resources, technology applications and a comprehensive research and development structure can assist student learning in the domain of biology by providing a unifying theme across scales of time and space. The project seeks to address four areas of critical need in STEM education: biological sciences, complex systems, computational modeling, and equal access for all.

Award Number: 
1019228
Funding Period: 
Wed, 09/01/2010 to Sun, 08/31/2014
Project Evaluator: 
David Reider
Full Description: 

This proposal outlines a research and development project that investigates how complex systems concepts supported by innovative curricular resources, technology applications and a comprehensive research and development structure can assist student learning in the domain of biology by providing a unifying theme across scales of time and space. The project seeks to address four areas of critical need in STEM education: biological sciences, complex systems, computational modeling, and equal access for all. This proposal explores how these needs are addressed through a curricular and technological intervention that structures biology learning through the framework of complex systems and computational modeling. The primary partners are the Massachusetts Institute of Technology and the University of Pennsylvania, working with eight teachers in four schools in the Boston area.

The project integrates graphical programming and simulation software, StarLogo TNG, into the standard high school biology curriculum to improve learning of biology concepts through the introduction and understanding of core complex systems processes. Instead of learning biology in discrete chunks, the chosen biological topics are connected through the framework of complex systems, and successively build in complexity from the basic building blocks of life to the interdependence and sustainability of life forms. This approach is designed to help students understand how processes at one level are connected to those at another level. The research is designed to answer the following questions: 1. Does a learning progression based on the complex systems ideas of scale and emergence enable students to make connections across biological topics, remediate known misconceptions, and apply core complex systems principles better than traditional instructional sequences? 2. What are the on-going affordances and constraints of implementation taking into consideration structural, functional and behavioral variables and what changes to project activities yield increased implementation and learning capacities? 3. Does programming of simulations increase understanding of complex systems and biology concepts compared to use of previously constructed simulations? The evaluation is designed to collect data and provide feedback on the adherence to the plan, the implementation challenged, and how research informs development.

The project anticipates a number of deliverables towards the end of the project and beyond. These include the creation of a unified high school biology curricular sequence that builds in increasing spatial and temporal scales to deepen student understanding of four core biology topics; the production, implementation and testing of curricular activities that acknowledge and ameliorate known implementation challenges; and the development of curricular strategies and tools to help teachers and students improve knowledge and skills in computational modeling, computer programming and participation in the cyberinfrastructure. In order to increase ease of integration into schools, and enhance scalability, the simulation activities are facilitated by a new web-based version of StarLogo TNG that integrates the curricular materials all of which will be distributed freely. Additional dissemination strategies include a website, conferences, a newsletter, community activities, active dissemination, and academic presentations.

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 to 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.

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: 
1743356
Funding Period: 
Mon, 03/15/2010 to Fri, 06/30/2017
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.

This project was previously funded under award #0952415.

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 to 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.

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