Measurement

Studying Topography, Orographic Rainfall, and Ecosystems (STORE) with Geospatial Information Technology

This project is using innovative Geospatial Information Technology-based learning in high school environmental science studies with a focus on the meteorological and ecological impacts of climate change. The resources developed are using ArcGIS Explorer Desktop and Google Earth software applications to increase students' learning and interest in science and careers and will be adaptable for teachers to improve classroom implementation.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1019645
Funding Period: 
Wed, 09/01/2010 to Sat, 08/31/2013
Project Evaluator: 
Haynie Research and Evaluation
Full Description: 

STORE is developing and piloting classroom uses of GIS-based interactive data files displaying climatological, topographical, and biological data about an especially ecologically and topographically diverse section of mid-California and a section of western New York State, plus projected climate change outcomes in 2050 and 2099 from an IPCC climate change model. Both areas contain weather stations. The participating students and teachers live in those areas, hence the place-based focus of the project.

To help teachers make curricular decisions about how to use these data with their students, the project has, with input from six design partner teachers, produced a curriculum module exemplar consisting of six lessons. The lessons start with basic meteorological concepts about the relationship between weather systems and topography, then focus on recent climatological and land cover data. The last two lessons focus on IPCC-sanctioned climate change projections in relation to possible fates of different regional species. Technology light versions of these lessons send students directly to map layers displaying the data for scientific analysis. Technology-heavy versions address the additional goal of building students' capacities to manipulate features of geographic information systems (GIS). Hence, the technology-heavy versions require use of the ARC GIS Explorer Desktop software, whereas the technology light versions are available in both the ARC software and in Google Earth. Google Earth makes possible some student interactivity such as drawing transects and studying elevation profiles, but does not support more advanced use of geographic information system technology such as queries of data-containing shape files or customization of basemaps and data representational symbology.

Answer keys are provided for each lesson. Teachers have in addition access to geospatial data files that display some storm systems that moved over California in the winter of 2010-2001 so that students can study relationships between actual data about storm behavior and relationship to topography and the climatological data which displays those relationships in a summary manner. This provides the student the opportunity to explore differences between weather and climate.

To increase the likelihood of successful classroom implementation and impact on student learning, the professional development process provides the conditions for teachers to make good adaptability decisions for successful follow-through. Teachers can implement the six lessons or adapt them or design their own from scratch. The project requires that they choose from these options, explain on content representation forms their rationales for those decisions, and provide assessment information about student learning outcomes from their implementations. The project provides the teachers with assessment items that are aligned to each of the six lessons, plus some items that test how well the students can interpret the STORE GIS data layers.

All of this work is driven by the hypothesis that science teachers are more likely to use geospatial information technology in their classrooms when provided with the types of resources that they are provided in this project. In summary, these resources include:

1.     tutorials about how to use the two GIS applications

2.     sufficiently adaptive geospatial data available in free easily transportable software applications

3.     lessons that they can implement as is, adapt, or discard if they want to make up their own (as long as they use the data)

4.     supportive resources to build their content knowledge (such as overview documents about their states' climates and information about the characteristics of each data layer and each data set available to them).

 

The growth and evolution of the teachers' technological pedagogical content knowledge is being tracked through interviews, face-to-face group meetings, and classroom observations. Also being tracked is the extent to which the teachers and students can master the technology applications quickly and on their own without workshops, and how well teachers provide feedback to the students and assess their learning outcomes when implementing STORE lessons. As the project moves into its third and final year, we will be studying outcomes from the first classroom implementation year (i.e. year two of the project) and determining to what extent the professional development strategies need to be revised in relation to how the teachers are responding to the project resources and forms of professional support. In the end, the project will contribute to the knowledge base about what professional development strategies are appropriate for getting teachers to use these types of resources, what decisions teachers make about how to use the resources for different courses and student groups they teach, and what are the outcomes of those uses in terms of curricular material, instructional strategies, and student learning.

Pre-K Early Algebra Through Quantitative Reasoning (PreKEA)

This project is initiating an innovative approach to pre-K students' development of quantitative reasoning through measurement. This quantitative approach builds on measurement concepts and algebraic design of the pre-numeric stage of instruction found in the Elkonin-Davydov (E-D) elementary mathematics curriculum from Russia. The project team is adapting and refocusing the conceptual framework and learning tasks of the E-D pre-numeric stage for use with four-year-olds.

Lead Organization(s): 
Award Number: 
1212766
Funding Period: 
Wed, 09/01/2010 to Sat, 08/31/2013
Full Description: 

This is an exploratory project that endeavors to initiate an innovative approach to preK students’ development of quantitative reasoning through measurement. This quantitative approach builds on measurement concepts and algebraic design of the pre-numeric stage of instruction found in the successful Elkonin-Davydov (E-D) elementary mathematics curriculum from Russia. The PreKEA project will adapt and refocus the conceptual framework of the E-D pre-numeric stage with respect to early algebra in the context of teaching experiments with preK and kindergarten students. A primary goal of the project is to obtain a proof-of-concept and lay down a conceptual and empirical foundation for a subsequent full research and development DR K-12 proposal.

The importance of early algebra (EA) in mathematics education has been acknowledged by the publication of a separate chapter solely devoted to early algebra and algebraic reasoning in the second Handbook of Research on Mathematics Teaching and Learning (Lester, 2007). Given that “much prior research highlights the difficulties that middle and high school students have with algebra,” the proponents of EA argue that “the weaving of algebra throughout the K-12 curriculum could lend coherence, depth, and power to school mathematics, and replace late, abrupt, isolated, and superficial high school algebra courses” (Carraher & Schliemann, 2007, pp. 670-671). At the same time, “quantitative thinking is unavoidable in EA” as it “does not seem realistic to first introduce youngsters to the algebra of number and then proceed to problems steeped in quantities as ‘applications’ of algebra” (ibid., p. 671). While the E-D curriculum with its proven track record focuses on the development of quantitative and measurement reasoning among elementary-aged children in grades 1–6, it is feasible that much younger children, even four-year-olds, can access the pre-numeric ideas. This is supported by research by Baillargeon (2001) and Wynn (1997) who showed that infants as young as two-months old demonstrate the development of number and measurement concepts. The PreKEA project will identify key concepts of the E-D pre-numeric stage relevant to four-year-olds and develop and explore lesson units which can be integrated into US preK settings. The project team combines the international expertise of PI Berkaliev who served as project coordinator and international liaison for an NSF-funded international project US-Russian Working Forum on Elementary Mathematics: Is the Elkonin-Davydov Curriculum a Model for the US? and who also brings the perspective of a mathematician, with the theoretical, methodological, and empirical expertise of co-PI Dougherty who has been one of the leading figures in working with, adapting, and studying the implementations of the E-D curriculum in the US, as well as a group of five leading Russian experts who developed, implemented, and studied the original E-D curriculum. The project resources include the E-D curriculum materials and articles only available in Russian.

The PreKEA (PreK Early Algebra through Quantitative Reasoning) project has the potential to make contributions beyond the preK early algebra curriculum that it will develop and implement. The PreKEA project can benefit disadvantaged students by using an innovative approach to EA instruction that has the potential to broaden access and at an early stage change the situation when disproportionately many disadvantaged students are not prepared adequately for learning quantitative reasoning and algebra. With research in preK narrowly focused on particular topics, the results of this project have the potential to inform a broader field including mathematics education and early childhood education with evidence that young children can access and interact with more complex mathematics, extending beyond counting.

Developers and researchers at the Illinois Institute of Technology and Iowa State University are initiating an innovative approach to pre-K students' development of quantitative reasoning through measurement. This quantitative approach builds on measurement concepts and algebraic design of the pre-numeric stage of instruction found in the Elkonin-Davydov (E-D) elementary mathematics curriculum from Russia. The project team is adapting and refocusing the conceptual framework and learning tasks of the E-D pre-numeric stage for use with four-year-olds. The adaptation is being done in collaboration with experts in Russia who were involved in the original E-D development. A primary goal of the project is to obtain a proof-of-concept and lay down a conceptual and empirical foundation for a subsequent research and development.

The research progresses using teaching experiments involving six students. Each student is engaged in 15 minute one-on-one sessions twice each week. Sessions are videotaped and transcribed for further analysis. The analysis of the data is conducted by the project team in collaboration with Russian consultants.

The research findings and methodology will provide grounds for supporting more complex and sophisticated mathematical ideas that will inform curriculum development for pre-K students and teachers. Results will be published and reported widely.

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.

Math Snacks: Addressing Gaps in Conceptual Mathematics Understanding with Innovative Media

This project is developing and evaluating effectiveness of 15 - 20 short computer mediated animations and games that are designed to: (1) increase students' conceptual understanding in especially problematic topics of middle grades mathematics; and (2) increase students' mathematics process skills with a focus on capabilities to think and talk mathematically.

Lead Organization(s): 
Award Number: 
0918794
Funding Period: 
Tue, 09/01/2009 to Fri, 08/31/2012
Project Evaluator: 
Sheila Cassidy WEXFORD INC.
Full Description: 

View a project spotlight on Math Snacks.

This project Math Snacks: Addressing Gaps in Conceptual Mathematics Understanding with Innovative Media, led by mathematics and education faculty at New Mexico State University, is developing and evaluating effectiveness of 15 - 20 short computer mediated animations and games that are designed to: (1) increase students' conceptual understanding in especially problematic topics of middle grades mathematics; and (2) increase students' mathematics process skills with a focus on problem-solviing and communicating mathematically. The basic research question for this project is whether the planned collection of computer-mediated animations and games can provide an effective strategy for helping students learn core middle grades mathematics concepts in conceptual areas that research suggests are difficult for these students.  A second question relates to types of delivery that are effective for mathematics learning using these tools including in classrooms during extended learning time at home or in informal educational settings. The project is developing and testing the effectiveness of a set of such learning tools and companion print materials, including student and teacher guides, and short video clips documenting best practices by  teachers using the developed materials with students. A pilot study in year 3 and a substantial randomized control trial in year 4 will test the effects of using the Math Snacks web-based and mobile technologies on student learning and retention of identified core middle school mathematics concepts, as measured by performance on disaggregated strands of the New Mexico state standardized mathematics assessments. Thus the project will produce animations and games using the web and new mobile technologies, and useful empirical evidence about the efficacy of their use. One of the key features of the Math Snacks project is development of the mediated games and simulations in a form that can be used by students outside of normal classroom settings on media and game players that are ubiquitous and popular among today's young people. Thus the project holds the promise of exploiting learning in informal settings to enhance traditional school experiences.

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.

Project M2: Maturing Mathematicians -- Advanced Curriculum for Primary Level Students

Project M2 is producing and disseminating curriculum materials in geometry and measurement for students in grades K-2. This builds on success of the M3 U.S. Department of Education curriculum grant for students in Grades 3-5. (www.projectm3.org). Project M2 units are advanced units for all students designed using research-based practices in mathematics, early childhood, and gifted education. Curricular materials focus on promising discourse and hands-on inquiry of rich problem-situations.  

Project Email: 
Lead Organization(s): 
Partner Organization(s): 
Award Number: 
0733189
Funding Period: 
Wed, 08/15/2007 to Sun, 07/31/2011
Full Description: 

Project Publications and Presentations:

Gavin, M. K.; Casa, Tuita, M.; Chapin, S. & Sheffield, L. (2010). Designing a Shape Gallery: Geometry with Meerkats.

Gavin, M. K.; Casa, Tuita, M.; Chapin, S. & Sheffield, L. (2010). Designing a Shape Gallery: Geometry with the Meerkats Student Mathematician's Journal. Student Mathematician's Journal.

Casa, T.; Firmender, J. & Gavin, M. K. (2010, April). Designing a Shape Gallery: Making Geometry Connections for Primary Students. Presented at National Council of Teachers of Mathematics Annual Meeting, San Diego, CA.

Casa, T. & Gavin, M. K. (2010, March). Exploring Shapes in Space: Geometry with the Frogonauts. Presented at Keefe Bruyette Symposium, Saint Joseph College, West Hartford, CT.

Gavin, M. K. (2009, November). Mentoring Young Mathematicians: New Advanced Curriculum for Primary-level Students. Presented at the National Association for Gifted Children Annual Meeting, St. Louis, MO.

Gavin, K. M. (2010, April). Nurturing Mathematically Promising and Creative Students, Project M2: Mentoring Young Mathematicians. Presented at National Council of Supervisors of Mathematics Annual Conference, San Diego, CA.

Gavin, M. K.; Firmender, J. M. & Casa, Tuita, M. (2010, April). Project M2's Approach: Connecting Math and Language Arts through Communication. Presented at the National Council of Teachers of Mathematics Annual Meeting, San Diego, CA.

Gavin, M. K.; Casa, T. M., Chapin, S. & Sheffield, L. (2011). Using Everyday Measures: Measuring with the Meerkats.

Calipers II: Using Simulations to Assess Complex Science Learning

This project has pioneered simulation-based assessments of model-based science learning and inquiry practices for middle school physical and life science systems. The assessment suites include curriculum-embedded, formative assessments that provide  immediate, individualized feedback and graduated coaching with supporting reflection activities as well as summative end-of-unit benchmark assessments. The project has documented the instructional benefits, feasibility, utility, and technical quality of the assessments with over 7,000 students and 80 teachers in four states.

Project Email: 
Lead Organization(s): 
Award Number: 
0733345
Funding Period: 
Mon, 10/01/2007 to Thu, 09/30/2010
Project Evaluator: 
CRESST

AutoMentor: Virtual Mentoring and Assessment in Computer Games for STEM Learning

This project is developing a system for producing automated professional mentoring while students play computer games based on STEM professions. The project explores a specific hypothesis about STEM mentoring: A sociocultural model as the basis of an automated tutoring system can provide a computational model of participation in a community of practice, which produces effective professional feedback from nonplayercharacters in a STEM learning game.

Award Number: 
0918409
Funding Period: 
Tue, 09/01/2009 to Fri, 08/31/2012

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

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