Learning Progression

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: 
Award Number: 
0733272
Funding Period: 
Sat, 09/01/2007 to 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.

Quality Cyber-enabled, Engineering Education Professional Development to Support Teacher Change and Student Achievement (E2PD)

In this project, a video and audio network links elementary school teachers with researchers and educators at Purdue to form a community of practice dedicated to implementing engineering education at the elementary grades. The research plan includes identifying the attributes of face-to-face and cyber-enabled teacher professional development and community building that can transform teachers into master users and designers of engineering education for elementary learners.

Lead Organization(s): 
Award Number: 
0822261
Funding Period: 
Mon, 09/15/2008 to Tue, 08/31/2010
Project Evaluator: 
Rose Marra, University of Missouri-Columbia

The Inquiry Project

This project is developing a learning progression in scientific inquiry about the nature of matter. The effort will result in a research-guided system of curriculum, assessment and professional development focusing on the transition from a macroscopic to a microscopic understanding of matter that occurs in upper elementary and middle school. The project has a close collaboration with scientists and urban schools.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
0628245
Funding Period: 
Sun, 10/01/2006 to Thu, 03/31/2011
Project Evaluator: 
John Zuman
Full Description: 

The Inquiry Project is a partnership between teachers, TERC and Tufts University. The project builds an understanding of science in grades 3–5 that lays a foundation for students’ later understanding of matter in terms of molecules and atoms. The Inquiry Project focuses on material, weight, volume, density and related ideas that we know are important and challenging for today’s students. Unique characteristics of this work are the integration of mathematics and science content, and the focus on inquiry through investigation.

The Inquiry Project brings research, curriculum, assessment, and professional development together in one coherent system with each components vital to preparing learners for this challenging learning progression.

 

The Inquiry Project is Asking:

  • What do young children think about matter, material kinds, and their properties?
  • What understandings at the macroscopic level are pivotal for helping children to move towards a microscopic understanding of matter?
  • What kinds of mathematical knowledge and representations are important to their understanding of matter?
  • What kinds of metaconceptual knowledge are needed to support inquiry and theory building about matter?

What understanding do students develop and why is this important?

Inquiry is central to science learning. As described in the National Science Education Standards (NRC, 1996), a classroom having the essential features of inquiry is one in which learners:

  • engage in scientifically oriented questions
  • give priority to evidence in responding to questions
  • formulate explanations from evidence
  • connect explanations to established scientific knowledge
  • justify and communicate explanations.

The Inquiry Project curriculum is designed with these features in mind, and with three content-specific dimensions of inquiry: measurement of matter, change and conservation, and scale.

Measurement of matter

Students with balance

Many middle school students can calculate density as the ratio of mass to volume, but lack a deeper intuitive sense that density is related to number of particles within a specific volume and the mass of those particles. In The Inquiry Project, students learn to measure weight and volume using a variety of methods and use their measurements as evidence to support explanations. They begin to understand that all matter (in solid, liquid, or gaseous form) has weight and volume. With a firm grasp of the measurement of weight and volume, students are able to build mental models of matter and density that will help them understand the particulate nature of matter later on.

Conservation and Transformation

The Inquiry Project helps students deepen their understanding of matter and materials through investigations of what changes and what stays the same when matter changes state, is reshaped, divided, heated, and mixed. In these investigations students need to isolate variables that are important to their investigations and control their experimentation to measure these variables. They use their measurements and their emerging models of matter to understand that some quantities, such as the total mass of a system, do not change.

Scale

Students build an intuitive sense of scale of space (volume), weight, and density that will later assist them in developing a particulate model of matter. Moving from macroscopic to microscopic thinking requires the ability to construct mental models about things and processes we cannot observe. Students who gain a strong understanding of quantities of volume, weight, and density through observation, measurement, and modeling are poised to understand quantities and phenomena at a scale that they cannot observe.

A Longitudinal Examination of Children's Developing Knowledge of Measurement: Mathematical and Scientific Concept and Strategy Growth from Pre-K through Grade 5

The project proposes a longitudinal study that investigates the development of an understanding of measurement across seven grades-from pre-K through Grade 5. Specifically, the project will establish clear cognitive accounts of the development of students' strategic and conceptual knowledge of measurement on increasingly demanding sets of length, perimeter, and area measurement tasks.

Project Email: 
Award Number: 
0732217
Funding Period: 
Wed, 08/15/2007 to Tue, 07/31/2012
Project Evaluator: 
Richard Lesh
Full Description: 

The Children's Measurement Project examines children's developing knowledge from PreKindergarten through Grade 5 as they develop the capacity and strategies they need to measure geometric space (length, area and volume), investigating number concepts, early algebra, or variability. We investigate ways children learn to use measures as evidence for scientific or mathematical claims. We began by examining the literature on learning trajectories and progressions to interpret existing research on children's understanding of length, area and volume. Our work engages both Rasch modeling and learning/teaching experiments within clinical and classroom contexts to collect data for longitudinal accounts of children's development of measurement concepts and strategies. The work is being conducted as a collaboration of Illinois State University and the University at Buffalo (State University of New York). We are beginning the fourth year of our project (2010).

Project Publications and Presentations:

Barret, J.; Clements, D.; Sarama, J.; Cullen, C.; Witkowski, C. & Klanderman, D. (2010, May). Addressing the Challenge of Learning and Teaching Measurement: Curricular, Learning, and Teaching Analyses (Barrett et al.). Presented at 2010 AERA Annual Meeting, Denver, CO.

Smith, J.P.; Dietiker, L.; Chang, K.; Mosier, A.; Gonulates, F.; Clements, D.; Battista, M.; Barret, J.; Cullen, C. & Zhou, W. (2010, May). Assessing the Alignment of Written Curricula and State Standards for Length Measurement (Smith et al.). Presented at 2010 AERA Annual Meeting, Denver, CO.

Barret, J.; Confrey, J.; Maloney, A.; Knuth, E.; Clements, D.; Sarama, J.& Daro, P. (April 2010) Defining and Implementing Learning Trajectories as Research Tools (Barrett et al.). Presented at 2010 NCTM Research Precession.

Barrett, J. E. (2009). Length Measurement Learning Trajectory: Validation of Learning Trajectories with Longitudinal Research. Presented at Consortium for Policy Research in Education and Friday Institute for Educational Innovation. Raleigh, NC.

McCool, J. K. & Barrett, J. E. , 2010-10-28 "Incorporating a Measurement Learning Trajectory into a Teacher's Toolbox for Facilitating Student Understanding of Measurement" Paper presented at the annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, The Ohio State University, Columbus, OH Online <PDF>. 2012-06-19 from http://www.allacademic.com/meta/p428027_index.html

Cullen, C.J.&  Barret, J.E. (2010). Strategy use indicative of an understanding of units and length. Unpublished.

Cullen, C. , Witkowski, C. , Miller, A. L., Barrett, J. E., Clements, D. H. and Sarama, J. , 2010-10-28 "The Key Components for Measurement Tasks" Paper presented at the annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, The Ohio State University, Columbus, OH Online <APPLICATION/PDF>. 2012-06-19 from http://www.allacademic.com/meta/p422400_index.html

Researching Mathematics Leader Learning

This project studies mathematics professional development leaders' understandings and practices associated with developing mathematically rich learning environments. It investigates this issue by considering: How can leaders cultivate professional development environments in which teachers have a greater opportunity to grapple with and deeply understand mathematics? The project studies how explicit attention to the cultivation of sociomathematical norms influences leaders' understanding of the process of creating mathematically rich environments and the impacts on their practices.

Lead Organization(s): 
Award Number: 
0554186
Funding Period: 
Mon, 05/01/2006 to Sat, 04/30/2011
Full Description: 

Our research and development work focuses on one aspect of mathematics professional development, when teachers are engaged in solving, discussing, and sharing mathematical work. Although mathematics professional development may include other activities, we specifically focus on how leaders learn to attend to doing mathematics with teachers because it is a primary time during PD that teachers may be developing deeper understandings of mathematics. To support their learning about cultivating rich teacher learning environments, leaders explored two frameworks: sociomathematical norms (norms for mathematical reasoning) and a set of practices for orchestrating productive mathematical discussions. The staff of RMLL created and facilitated seminars as learning opportunities for leaders, studied what and how leaders learned about facilitation, and investigated how leaders facilitated PD in their schools and districts.

As our research project has evolved, we have revised our frameworks for supporting leader development to include a focus on identifying the purposes for doing mathematics with teachers.  We have used Deborah Ball and her colleagues' work at the University of Michigan to draw a distinction between common content knowledge that teachers hold in common with other professional using mathematics and specialized content knowledge that teachers need to know because of their unique role in   We engage in mathematics with teachers in professional development to help them develop not just common content knowledge but specialized knowledge as well. To develop specialized mathematical knowledge, teachers need to engage in explanations that make taken-for-granted ideas in mathematics explicit. Norms for explanation and representational use are vital. These norms are fostered through the orchestration of discussions. In redesigning seminars according to these ideas, we aim to have leaders select and design tasks that engage teachers more comprehensively with the mathematical knowledge they need to teach. Leaders need to know how to specify purposes for doing mathematics in ways that develop teachers’ SCK and identify tasks and discussion prompts that immerse teachers in SCK. They need to know how to pursue this purpose when orchestrating discussions and support the development of sociomathematical norms in ways that unpack teachers’ highly symbolic or incomplete reasoning. In short, we augmented our initial emphasis on sociomathematical norms with this new emphasis on SCK. supporting learners in the classroom.

We are completing analyses of the experiences of leaders in our revised seminars to understand what they gained from our revised frameworks in planning for and enacting professional development.

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): 
Partner Organization(s): 
Award Number: 
0822016
Funding Period: 
Mon, 09/15/2008 to Fri, 08/31/2012
Project Evaluator: 
Jim Minstrell

A Study of the Struggling Learner's Knowledge and Development for Number and Operation

This project targets first- and second-grade children who struggle to develop a deeper understanding of the mathematical strand of number and operation. The research team will (a) identify the various specific cognitive obstacles of first- and second-grade students who are struggling in number and operation, and (b) explore how instructional tasks designed to address specific cognitive obstacles affect the learning trajectory of struggling learners in number and operation.

Lead Organization(s): 
Award Number: 
0918060
Funding Period: 
Tue, 09/01/2009 to Fri, 08/31/2012
Project Evaluator: 
Dr. Jeff Barrett

Change Thinking for Global Science: Fostering and Evaluating Inquiry Thinking About the Ecological Impacts of Climate Change

This project draws from the expertise of a fully collaborative educator-scientist team to create learning progressions, curricular units and assessment instruments towards large scale research on the teaching and learning of climate change and impacts by 7-12th graders in primarily under-resourced schools. Products include eight week curricular units, IPCC-compliant simplified future scenarios, an online interface with guided predictive distribution modeling, and research results.

Project Email: 
Lead Organization(s): 
Award Number: 
0918590
Funding Period: 
Sat, 08/01/2009 to Wed, 07/31/2013
Project Evaluator: 
Dr. Amelia Gotwals
Full Description: 

Overview

It is increasingly important for all American students to become sophisticated thinkers of science. The Center for Essential Science at the University of Michigan is conducting educational research to engage and support complex thinkers of science and to improve science learning in high-poverty, urban, elementary and middle school classrooms, with particular focus on the Detroit Public Schools. Our previous work focused on fourth through sixth grades, a period when the performance of American science students falls significantly behind that of students in other countries. In this grant, we extend our learning progressions and associated curricular materials, visualization technologies and educational research from fourth to the tenth grade. In particular, this grant is focused in two areas:

  • the development and empirical evaluation of eight to twelve-week curricular units and associated technologies to promote students' deep understandings of the impact of climate change on ecosystems dynamics and animal interactions, and
  • the exploration of new ideas in educational assessment leading to tests that evaluate students' complex reasoning with science.

A Sense of Urgency on Learning Ecological Impacts of Global Climate Change

The modern world is experiencing substantial and rapid changes that are reshaping not only human societies but natural ecosystems worldwide. During the lifetimes of our current middle and high school students, it is likely that our planet will undergo more anthropogenic change than it has during all of human history to date.  While scientists from many disciplines are modeling, monitoring, predicting, and analyzing climate change, understanding the impacts and consequences of climate change cannot be left to scientists alone.

While scientists are aware of the sense of urgency to develop scientific understanding of the impacts of global climate changes, science education resources and sound research on students’ development of complex reasoning about ecological impacts of global climate change are scarce, despite recognition from scientists and policy makers of the importance of this topic. Several factors contribute to this absence. First, global climate change is an extremely multi-disciplinary domain that does not easily fit into existing K-12 disciplinary boundaries of earth science, life science, and physical science. The American Institute for Global Change Research defines global change as “the interactions of biological, chemical and physical processes that regulate changes in the function on the Earth system, including the particular ways in which these changes are influenced by human activities” (American Institute for Global Change Research, 2008). Second, scientific information associated with global climate change is relatively new and emergent, disallowing strong representation in science standards, high stakes tests, textbooks or curricular units utilized in classrooms. Our previous research suggests that the complexity of content coupled with almost no representation on high stakes tests leads to a low priority for many classroom teachers and consequently little to no classroom time. (S. Blum, personal communication 11.6.08). Third, global climate change is a dynamic topic that might be best addressed with resources that couple curricular activities which guide the development of complex inquiry reasoning and modeling/simulation resources to represent the dynamic nature of the science. While modeling and simulation resources exist for professional scientists (e.g., Lifemapper designed by proposal co-PI), neither the guided curricular activities nor the modeling and simulation resources are widely available for middle and high school audiences.

Together, a sense of urgency exists to build a solid, research-based foundation about a new and essential focus area within pre-college science education: students’ complex inquiry reasoning about the impact of global changes on ecosystem dynamics. This sense of urgency can be addressed through the combination of three research-based activities addressed in this proposal: (1) the extension of existing 4-6th grade curricular units towards the development and empirical evaluation of a 4-10th grade curricular progression focused on complex reasoning about biodiversity and the impact of global changes on populations of animals and ecosystem dynamics; (2) the development and evaluation of ecological simulation and modeling resources to accompany the middle and high school units; and (3) sound educational research to provide strong empirical evidence of both growth spurts and plateaus, as well as documentation of how and when complex inquiry reasoning occurs among middle and early high school students in these focus areas.

The program outlined will serve as the major research vehicle for research questions in several interrelated areas. We propose a research design with a series of quasi-experimental studies that will complement each other and provide multiple lenses for understanding complex questions such as these. Our research questions are:

1. Which scientific content and reasoning skills are essential for 7-10th graders’ complex reasoning and modeling of the ecological impacts of climate change? How are these manifested in content and inquiry reasoning progressions?

2. What dynamic visualization and modeling resources support the development of deep thinking about the ecological impacts of climate change?

3. What scaffolding and instructional activities support the development of deep thinking about the ecological impacts of climate change, including both content (ecological impacts) and complex reasoning components (science practices) of this knowledge, within cohorts of 7-10th graders in two new curricular units?

4. Utilizing quantitative (growth curve models, cross sectional studies) and qualitative (think aloud interviews) analyses, what learning outcomes and growth trajectories are realized by 7-10th intervention and control students as measured by both traditional standardized items and assessments focusing on complex thinking about ecological impacts of climate change?

We believe the greatest contribution of our work will be clear empirical information (growth spurts, growth plateaus and achievement information) associated with middle and high school students’ learning of complex and dynamic science associated with the ecological impacts of global climate change. We see the empirically driven development of learning progressions, curricular units, assessment instruments and professional development resources as important secondary contributions. The hypotheses we wish to test are the following:  Do Detroit, rural and small city students who work with coordinated scaffold-rich inquiry programs and visualization resources focusing on impacts of global climate change develop deep conceptual understandings as compared to matched cohorts students?  As determined by growth curve analyses, what do their learning trajectories look like? What new insights about the design of scaffold-rich curricular units and visualization technologies can be gleaned from an analysis of students’ growth trajectories and summative achievement results?  What kinds of assessment instruments are needed to provide reliable and valid measurement of learning progressions in these focus areas? What can we learn about the design of a series of multi-year, coordinated learning resources from the empirically driven development of learning progressions associated with an important emerging science, the ecological impacts of climate change? 

 

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