Digital Media

Transition to College Mathematics and Statistics

This project will develop a mathematics course for the fourth year of high school. The new course is being designed for students who will enter post-secondary education and will major in programs not requiring Calculus. The new course includes mathematics from a problem-solving or applications perspective, and serves as a bridge to college mathematics and statistics. Unit topics include functions, modeling, algebraic strategies, binomial distributions, and information processing.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1020312
Funding Period: 
Wed, 09/01/2010 to Fri, 08/31/2012
Project Evaluator: 
Steven Ziebarth
Full Description: 

The Transitions to College Mathematics and Statistics project is developing a mathematics course for the fourth year of high school. The course builds on the NSF-supported Core-Plus Mathematics curriculum and provides an alternative to the Calculus course that is now in place. The new course is being designed for students who will enter post-secondary education and will major in programs not requiring Calculus. The new course includes mathematics from a problem-solving or applications perspective, and serves as a bridge to college mathematics and statistics. Unit topics include functions, modeling, algebraic strategies, binomial distributions, and information processing.

The project is creating both a print version and a digital version of the course. Students are taught to use software tools such as spreadsheets, data analysis tools, interactive geometry programs, and computer algebra systems. These tools are embedded in the curriculum and allow students to apply the mathematics they are learning in interesting and relevant problems. The lessons include hyperlinks that allow students to have immediate access to related text. The designers are exploring the incorporation of video, access to language translation software, and the use of public domain, learner-centered software tools. One goal of the course is to increase student access to needed tools and information and to promote flexibility in how the materials are used. The project will conduct field tests of the materials and will implement an extensive formative evaluation plan where staff will visit classrooms and interview students. The summative evaluation will be conducted by an evaluator at the University of Missouri, and will focus on student achievement as measured by ACT/SAT scores, GPA, placement data, and course-taking.

The Transitions to College Mathematics and Statistics course provides a mathematics course that prepares high school students to transition into college mathematics and statistics courses that are designed to support non-scientific fields. It provides a viable, interesting, and useful technology-based course in the fourth year of high school. The course will also provide an effective way to help schools meet the college and career readiness standards that states have adopted.

SimScientists Human Body Systems: Using Simulations to Foster Integrated Understanding of Complex, Dynamic, Interactive Systems

This project leverages curricular module development to design, develop, and test new cyberlearning modules that integrate multiple (circulation, respiration, and digestion) systems of the human body. The project aims to deepen science content knowledge, science inquiry skills, and model-based reasoning skills for high school biology students. The project will use simulations showing how individual systems function, how they work together, and how the integration of all three creates a dynamic and reactive biological system.

Lead Organization(s): 
Award Number: 
1020264
Funding Period: 
Wed, 09/15/2010 to Sun, 08/31/2014
Project Evaluator: 
Gargani + Company
Full Description: 

This research and development project leverages curricular module development to design, develop, and test new cyberlearning modules that integrate multiple (circulation, respiration, and digestion) systems of the human body. The project aims to deepen science content knowledge, science inquiry skills, and model-based reasoning skills for high school biology students. The project will use simulations showing how individual systems function, how they work together, and how the integration of all three creates a dynamic and reactive biological system. It is expected that the presentation of this dynamic system will result in a deeper understanding of the materials and enhanced performance on student achievement measures. The goals of the project are to: 1. Develop an integrated simulation of the human digestive, circulatory and respiratory systems that allows students to develop productive inquiry strategies. 2. Embed the simulation in online instructional modules that provide immediate, individualized coaching as students are challenged with a series of investigative tasks. 3. Provide reports of students' performances during the activities to students and teachers. 4. Develop follow-up online collaborative investigations that provide differentiated instruction to strengthen students' understanding and support transfer and opportunities to engage in scientific discourse. 5. Develop one benchmark assessment that measures outcomes across all three body systems and reports to students and teachers. 6. Develop and deploy professional development to support teachers as they use these materials. 7. Provide evidence of the technical quality, feasibility, and usability of the new materials. 8. Study the influence of these materials on complex science and inquiry learning of the integration of the three human body systems modeled. A small scale randomized, controlled trial will be performed at the end of the project. The project is grounded in model-based learning, cognitive learning research, and an evidence-centered design. Universal Design for Learning is factored into all simulation designs. Questions asked during the evaluation include: Is the project progressing as planned? Are the modules useable? Are the users satisfied? Are the modules used as intended in a typical high school setting? Does this improve teaching and learning of key content? The primary investigator is WestEd; the American Association for the Advancement of Science is a partner and three teachers from nearby schools serve as co-developers. The project has an external evaluator as well as a strong advisory board. The project will create multi-leveled instructional cyber-modules. These modules will contain embedded assessments that provide students and teachers immediate and individualized coaching. Professional development will also provide teachers tools and guidance to increase their learning of human body systems. Dissemination strategies include featuring the modules on WestEd's award-winning website as well as submission of academic papers to journals and national conferences targeted at science educators and education researchers. Because these modules supplement classroom curricula and use online technology, they could potentially be used to teach millions of high school biology students.

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.

ScratchEd: Working with Teachers to Develop Design-Based Approaches to the Cultivation of Computational Thinking

This project is designing, developing, and studying an innovative model for professional development (PD) of teachers who use the Scratch computer programming environment to help their students learn computational thinking. The fundamental hypothesis of the project is that engagement in workshops and on-line activities of the ScratchEd professional development community will enhance teacher knowledge about computational thinking, their practice of design-based instruction, and their students' learning of key computational thinking concepts and habits of mind.

Project Email: 
Award Number: 
1019396
Funding Period: 
Sun, 08/15/2010 to Wed, 07/31/2013
Project Evaluator: 
Education Development Center
Full Description: 

The ScratchEd project, led by faculty at the Massachusetts Institute of Technology and professionals at the Education Development Center, is designing, developing, and studying an innovative model for professional development (PD) of teachers who use the Scratch computer programming environment to help their students learn computational thinking. The fundamental hypothesis of the project is that engagement in workshops and on-line activities of the ScratchEd professional development community will enhance teacher knowledge about computational thinking, their practice of design-based instruction, and their students' learning of key computational thinking concepts and habits of mind.

The effectiveness of the ScratchEd project is being evaluated by research addressing four specific questions: (1) What are the levels of teacher participation in the various ScratchEd PD offerings and what do teachers think of these experiences? (2) Do teachers who participate in ScratchEd PD activities change their use of Scratch in classroom instruction to create design-based learning opportunities? (3) Do the students of teachers who participate in the ScratchEd PD activities show evidence of developing an understanding of computational thinking concepts and processes? (4) When the research instruments developed for the evaluation are made available for teachers in the Scratch community to use for self-evaluation, how do teachers make use of them? Because both computational thinking and design-based instruction are complex activities, the project research is using a combination of survey, interview, and artifact analysis methods to answer the questions.

The ScratchEd professional development and research work will provide important insight into the challenge of helping teachers create productive learning environments for development of computational thinking. Those efforts will also yield a set of evaluation tools that can be integrated into the ScratchEd resources and used by others to study development of computational thinking and design-based instruction.

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Expanding PhET Interactive Science Simulations to Grades 4-8: A Research-Based Approach

Colorado’s PhET project and Stanford’s AAALab will develop and study learning from interactive simulations designed for middle school science classrooms. Products will include 35 interactive sims with related support materials freely available from the PhET website; new technologies to collect real-time data on student use of sims; and guidelines for the development and use of sims for this age population. The team will also publish research on how students learn from sims.

Project Email: 
Lead Organization(s): 
Award Number: 
1020362
Funding Period: 
Wed, 09/01/2010 to Sat, 08/31/2013
Project Evaluator: 
Stephanie Chasteen
Full Description: 

In this DRK12 project, the PhET Interactive Simulations group at the University of Colorado and the AAALab at Stanford University are working together to produce and study learning from interactive simulations designed for middle school science classrooms. We are developing a suite of 35 high-quality, interactive simulations covering physical science topics. These simulations include innovative technologies that provide teachers with real-time, formative feedback on how their students are using the simulations.  The research investigates how various characteristics of the simulation design influence student engagement and learning, and how this response varies across grade-level and diverse populations. The research also includes an investigation of different ways of using simulations in class, and how these approaches affect student preparation for future learning when they are no longer using a given simulation.

      The original PhET simulations were designed for college use, but overtime, they have migrated to lower grades.  The current suite of free research-based, interactive PhET science simulations are used over 10 million times per year.  To optimize their utility for middle school science, we are conducting interviews with diverse 4-8th graders using 25 existing PhET simulations to help identify successful design alternatives where needed, and to formulate generalized design guidelines. In parallel, pull-out and classroom-based studies are investigating a variety of lesson plans to identify the most promising approach. These studies include controlled comparisons that collect both qualitative and quantitative data.

      On the basis of our emerging design principles, we are developing 10 new simulations in consultation with teachers, who are helping to identify high need areas for simulations. These new simulations also include a back-end data collection capability that can collect, aggregate, and display student patterns of simulation use for teachers and researchers. The design of the data collection and presentation formats depends on an iterative process done in collaboration with teachers to identify the most useful information and display formats. A final evaluation compares student learning with and without this back-end formative assessment technology.   

This project is working to transform the way science is taught and learned in Grades 4-8 so that it is more effective at promoting scientific thinking and content learning, while also being engaging to diverse populations. The project is expected to impact many, many thousands of teachers and students through its production of a suite of 35 free, interactive science simulations optimized for Grades 4-8 along with “activity templates”, guidance, and real time feedback to teachers to support pedagogically effective integration into classrooms. Finally, the intellectual merit of the project is its significant contributions to understanding when, how, and why interactive simulations can be effective learning and research tools.

Embodied STEM Learning Across Technology-Based Learning Environments

This project conducts interdisciplinary research to advance understanding of embodied learning as it applies to STEM topics across a range of current technology-based learning environments (e.g., desktop simulations, interactive whiteboards, and 3D interactive environments). The project has two central research questions: How are student knowledge gains impacted by the degree of embodied learning and to what extent do the affordances of different technology-based learning environments constrain or support embodied learning for STEM topics?

Lead Organization(s): 
Award Number: 
1020367
Funding Period: 
Sun, 08/15/2010 to Sun, 07/31/2011
Project Evaluator: 
Susan Haag
Full Description: 

This project conducts interdisciplinary research to advance understanding of embodied learning as it applies to STEM topics across a range of current technology-based learning environments (e.g., desktop simulations, interactive whiteboards, and 3D interactive environments). The project builds on extensive research, including prior work of the PIs, regarding both embodied learning and statistical learning. The PIs describe embodied learning as engaging the neuromuscular systems of learners as they interact with the world around them visually, aurally, and kinesthetically in order to construct new knowledge structures. Statistical learning is described as the ability to learn, often without intent, which sequences of stimuli are consistent with a set of rules. An example of statistical learning is pattern recognition, which is central to mastery of complex topics in many STEM disciplines including physics and mathematics.

The project has two central research questions: How are student knowledge gains impacted by the degree of embodied learning and to what extent do the affordances of different technology-based learning environments constrain or support embodied learning for STEM topics? To investigate these questions, the PIs are conducting three series of experiments in five phases using two physics topics. The first four phases are developmental and the final phase implements and assesses the two modules in schools (20 plus teachers, 700 plus K-12 students) in Arizona and New York (15 total sites, 10 plus public schools, minimum one Title I school).

The aim of this project is to meld these two research trajectories to yield two key outcomes: 1) basic research regarding embodiment and statistical learning that can be applied to create powerful STEM learning experiences, and 2) the realization of exemplary models and principles to aid curriculum and technology designers in creating learning scenarios that take into account the level of embodiment that a given learning environment affords.

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.

Zydeco: A Mobile "Nomadic Inquiry" System to Support and Bridge Science Inquiry Between Classroom and Museum Contexts

This project will explore how new mobile and web-based technologies can support content-rich nomadic inquiry; that is, science inquiry that takes place on-the-go, across integrated K-12 formal and informal settings. Students will begin the inquiry process in the classroom using curricular activities and the Zydeco web software developed in the project to help define goals and questions and to design data collection strategies and categories for use on a field trip to an informal setting.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1020027
Funding Period: 
Sun, 08/01/2010 to Wed, 07/31/2013
Project Evaluator: 
The Learning Partnership
Full Description: 

Although students may engage in scientific inquiry in their classrooms, it is also essential for them to practice scientific inquiry in real-world settings outside the classroom context to build enduring skills and deep, meaningful understanding of core science content ideas. The goal of the Zydeco project is to explore how new mobile and web-based technologies can support content-rich nomadic inquiry; that is, science inquiry that takes place on-the-go, across integrated K-12 formal and informal settings. Students will begin the inquiry process in the classroom using curricular activities and the Zydeco web software developed in the project to help define goals and questions and to design data collection strategies and categories for use on a field trip to an informal setting. With a mobile device and the Zydeco mobile software populated with the students' preparatory work, students will continue their inquiry in the museum, collecting relevant data and information in an organized, scaffolded manner, in the form of tagged, captioned, and voice-annotated photographs, video, and text. The Zydeco system will store the students' collected data on a web server, which students can access upon their return to the classroom. Thus students can access, sort, and analyze their collected data, using curricular and web-based scaffolds to help evaluate and explain their findings to complete the inquiry process.

The project will involve middle school teachers and students from the Ypsilanti and Detroit Public Schools; educators, researchers, and scientists at the University of Michigan Exhibit Museum of Natural History and the Detroit Science Center; and researchers from the University of Michigan School of Education and Department of Electrical Engineering and Computer Science. The science content will be tailored to both the museum partners' foci and the teachers' curricula: biology, earth science, and physical science.

The Zydeco project explores three major research questions:

(1) How can mobile and web technologies coordinate with school curricula to scaffold nomadic inquiry and enhance student learning?

(2) How can scaffolded mobile technologies support teachers and students to connect classroom and museum experiences more closely in order to enhance science inquiry and content learning?

(3) What impacts do scaffolded nomadic inquiry experiences have on classroom-based science inquiry and science learning?

The collaborative team will use an iterative, learner-centered approach to develop the Zydeco web and mobile systems and the associated student activities. For each iteration, the researchers will videotape and audio-tape students' discussions and activities, and collect artifacts and logs of student work as they engage with the curriculum the web and mobile systems in the classroom and museum. This data will be analyzed using rubrics designed to gauge the quality and variety of students' inquiry, the scientific content of their discussions and work, and their engagement throughout the process. In addition, pre-and post-program assessment tasks will be used to gauge the program's short-term and long-term impacts on targeted inquiry skills and content understanding. Student and teacher interviews will be administered to gather feedback about the program content and usability. Technology evaluation rubrics will be used to evaluate the different scaffolding features in the Zydeco mobile and web systems to gauge how well those systems help students overcome the complexities of scientific inquiry in multiple settings.

The products of this research will include a web-based software application that will support pre-visit and post-visit inquiry activities and applications for the mobile device to support student inquiry on their visit to an informal learning environment. The project will produce documentation to enable teachers and museum educators to use the developed nomadic inquiry system. Research papers about scaffolding nomadic inquiry, developing adaptable technologies to help teachers connect classroom curricula and field trip experiences, curriculum design for learning across formal and informal settings, and developing technologies to enhance learning and inquiry in informal settings will be written.

Biocomplexity: Transforming an Innovative High School Curriculum with UDL Scaffolds and Multimedia Resources

This project transforms an already-useful curriculum to reach a wider population of students and teachers. The curriculum effectively builds on a base of core science and math concepts to bring important current science to high school, using a case-based approach that incorporates authentic scientific inquiry. The Biocomplexity and the Habitable Planet curriculum is designed to provide material for a year-long capstone course in ecology and environmental science, or two individual modules for semester-long electives.

Lead Organization(s): 
Award Number: 
1020089
Funding Period: 
Wed, 09/01/2010 to Sat, 08/31/2013
Project Evaluator: 
PERG
Full Description: 

This project transforms an already-useful and innovative curriculum to reach a wider population of students and teachers than anticipated. The curriculum to be transformed effectively builds on a base of core science and math concepts to bring important current science to high school, using a case-based approach that incorporates authentic scientific inquiry. The Biocomplexity and the Habitable Planet curriculum engages high school students in the science of coupled natural and human systems, exploring the complex fabric of relationships between humans and the environment at all spatial and temporal scales. The curriculum is designed to provide material for a year-long capstone course in ecology and environmental science, or two individual modules for semester-long electives.

Pilot and field tests provide preliminary evidence that this material has produced significant student learning. External evaluation during the pilot has yielded two important findings: 1) Teachers have confronted a much more heterogeneous student population than expected at the capstone level. This offers the opportunity to expand the potential audience for the curriculum. 2) Though the previous project has provided supports for teachers and students that address the innovative pedagogy and novel content of the curriculum, this unexpectedly large heterogeneity provides an exciting opportunity to conduct design research to develop effective new curricular scaffolding and contextual supports. In collaboration with CAST, TERC has identified strategies for a transformation and extension of the materials in order to create an enhanced electronic curriculum infused by the principles of Universal Design for Learning (UDL).

The project will result in the following deliverables:

1. An e-text based on two of the most requested Biocomplexity units, to provide the following UDL scaffolds: a) Contextual supports for student work with complex quantitative and visual data that include structured data sets, smart graphs, smart images, and other scaffolds to support data analysis; and b) Reading supports, including highlighting tools, embedded glossary, and careful linking of visual and textual data.

2. Multimedia resources for students on challenging core science ideas and on techniques of scientific argumentation, and teacher materials that provide both content and pedagogical support, for all four units.

3. Study and assessment materials for all four units, including a study guide, test items, and glossary.

4. A research article on the effectiveness of contextual supports for scaffolding student understanding of complex data.

5. A white paper for curriculum developers including guidelines for scaffolding student work with complex data.

CAREER: Examining the Role of Context in the Mathematical Learning of Young Children

This project involves a longitudinal, ethnographic study of children's mathematical performances from preschool to first grade in both formal classroom settings and informal settings at school and home. The study seeks to identify opportunities for mathematical learning, to map varied performances of mathematical competence, to chart changes in mathematical performance over time, and to design and assess the impact of case studies for teacher education.

Award Number: 
1461468
Funding Period: 
Mon, 06/15/2009 to Tue, 05/31/2011
Full Description: 

This project involves a longitudinal, ethnographic study of children's mathematical performances from preschool to first grade in both formal classroom settings and informal settings at school and home. The proposed site for the study is a small, predominately African-American pk-12 school. The study seeks to identify opportunities for mathematical learning by young children across multiple contexts, to map varied performances of mathematical competence by young children, to chart changes in young children's mathematical performance over time, and to design and assess the impact of case studies for teacher education that explore young children's mathematical competencies. Research questions focus on mathematical opportunities for learning in various contexts, children's development of knowledge, skills, and dispositions over time, the characteristics of competent mathematical performances, and the role of case studies in helping beginning teachers to understand young minority children's mathematical thinking. Data collected will include video tapes of classroom activities, written fieldnotes of formal and informal settings, student work, parent focus group transcripts, and children's interview performances. Analysis will involve both thematic coding and construction of case studies. The overarching goal of this project is to transform the ways that researchers think about and study the mathematical learning of young minority children as well as the quality of schooling these children experience.

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