Statistics

Learning Mathematics of the City in the City

This project is developing teaching modules that engage high school students in learning and using mathematics. Using geo-spatial technologies, students explore their city with the purpose of collecting data they bring back to the formal classroom and use as part of their mathematics lessons. This place-based orientation helps students connect their everyday and school mathematical thinking. Researchers are investigating the impact of place-based learning on students' attitudes, beliefs, and self-concepts about mathematics in urban schools.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1222430
Funding Period: 
Sat, 09/01/2012 to Mon, 08/31/2015
Full Description: 

Learning Mathematics of the City in The City is an exploratory project that is developing teaching modules that engage high school students in learning mathematics and using the mathematics they learn. Using geo-spatial technologies, students explore their city with the purpose of collecting data they bring back to the formal classroom and use as part of their mathematics lessons. This place-based orientation is helping students connect their everyday and school mathematical thinking.

Researchers are investigating the impact of place-based learning on students' attitudes, beliefs, and self-concepts about mathematics in urban schools. Specifically, researchers want to understand how place-based learning helps students apply mathematics to address questions about their local environment. Researchers are also learning about the opportunities for teaching mathematics using carefully planned lessons enhanced by geo-spatial technologies. Data are being collected through student interviews, classroom observations, student questionnaires, and student work.

As the authors explain, "The use of familiar or engaging contexts is widely accepted as productive in the teaching and learning of mathematics." By working in urban neighborhoods with large populations of low-income families, this exploratory project is illustrating what can be done to engage students in mathematics and mathematical thinking. The products from the project include student materials, software adaptations, lesson plans, and findings from their research. These products enable further experimentation with place-based mathematics learning and lead the way for connecting mathematical activities in school and outside of school.

CAREER: Learning to Support Productive Collective Argumentation in Secondary Mathematics Classes

Research has shown that engaging students, including students from underrepresented groups, in appropriately structured reasoning activities, including argumentation, may lead to enhanced learning. This project will provide information about how teachers learn to support collective argumentation and will allow for the development of professional development materials for prospective and practicing teachers that will enhance their support for productive collective argumentation.

Award Number: 
1149436
Funding Period: 
Sun, 07/01/2012 to Sat, 06/30/2018
Full Description: 

Doing mathematics involves more than simply solving problems; justifying mathematical claims is an important part of doing mathematics. In fact, proving and justifying are central goals of learning mathematics. Recently, the Common Core State Standards for Mathematics has again raised the issue of making and critiquing arguments as a central practice for students studying mathematics. If students are to learn to make and critique arguments within their mathematics classes, teachers must be prepared to support their students in learning to argue appropriately in mathematics. This learning often occurs during class discussions in which arguments are made public for all students in the class. The act of creating arguments together in a classroom is called collective argumentation. Teachers need to be able to support students in productively engaging in collective argumentation, but research has not yet shown how they learn to do so. This project will document how mathematics teachers learn to support their students in engaging in productive collective argumentation. The research team will follow a cohort of participants (college students majoring in mathematics education) through their mathematics education coursework, observing their engagement in collective argumentation and opportunities to learn about supporting collective argumentation. The team will continue to follow the participants into their first two years of teaching, focusing on how their support for collective argumentation evolves over time. During their first two years of teaching, the research team and participants will work together to analyze the participants' support for collective argumentation in order to help the participants develop more effective ways to support collective argumentation.

Research has shown that engaging students, including students from underrepresented groups, in appropriately structured reasoning activities, including argumentation, may lead to enhanced learning. This project will provide information about how teachers learn to support collective argumentation and will allow for the development of professional development materials for prospective and practicing teachers that will enhance their support for productive collective argumentation.

Core Math Tools

This project is developing Core Math Tools, a suite of Java-based software including a computer algebra system (CAS), interactive geometry, statistics, and simulation tools together with custom apps for exploring specific mathematical or statistical topics. Core Math Tools is freely available to all learners, teachers, and teacher educators through a dedicated portal at the National Council of Teachers of Mathematics (NCTM) web site.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1201917
Funding Period: 
Sun, 01/15/2012 to Mon, 12/31/2012
Project Evaluator: 
David Barnes, NCTM
Full Description: 

Core Math Tools is a project from Western Michigan University that meets the urgent need of providing mathematical tools that students can use as they explore and learn mathematical concepts that are aligned with the Common Core State Standards in Mathematics (CCSSM). The developers have repurposed and modified tools originally designed for an NSF-funded curriculum project (e.g., Core-Plus Mathematics), creating a suite of tools that supports student learning of mathematics regardless of the curricula choice. Core math Tools is Java-based software that includes a computer algebra system(CAS, interactive geometry, statistics, and simulation tools together with custom apps for exploring specific mathematical and statistical topics. The designers provide exemplary lessons illustrating how the software can be used in the spirit of the new CCSSM. The goal of the project is to provide equitable and easy access to mathematical software both in school and outside of school. The tools are available to all learners and teachers through the web site of the National Council of Teachers of Mathematics (NCTM). The web site includes feedback loops for teachers to provide information about the tools. By using the NCTM website, the tools can be downloaded for use by teachers and students. The dedicated portal on the NCTM website allows supervisors to use the tools in professional development, teachers to use the tools as an integral part of instruction, and students to use the tools for exploring, conjecturing, and problem solving.

CAREER: Investigating Middle and Secondary Mathematics Teachers' Transformative Learning of Statistics Within Professional Development

The project will examine how teachers reason about variation subsequent to focused instruction and contribute knowledge to in-service middle and secondary mathematics teacher education by targeting characteristics of professional development that might support teachers' reasoning about variation in increasingly sophisticated ways. The project will produce a coherent collection of shareable instructional materials for use in introductory statistics education and teacher education in statistics.

Award Number: 
1149403
Funding Period: 
Fri, 06/01/2012 to Wed, 05/31/2017
Full Description: 

This CAREER project addresses the professional development of middle and secondary mathematics teachers by investigating teachers' statistical reasoning and targeting characteristics of professional development that support teachers' development of increasingly sophisticated ways to reason about variation. Statistical variation plays a critical role throughout statistical investigation.

The project integrates educational and research activities in its design and implementation of a professional development program and research on the professional development. The research addresses three interrelated questions: In a professional development program that encourages reasoning about variation from multiple perspectives and that encourages dilemma, critical reflection, and rational discourse:

1. How do middle and secondary mathematics teachers reason about variation from design, data-centric, and modeling perspectives?

2. In what ways do dilemma, critical reflection, and rational discourse affect teachers' reasoning about variation?

3. How do teachers differently engage with and benefit from dilemma, critical reflection, and rational discourse?

The project relies on multiple data sources and strategically chosen combinations of qualitative and quantitative methods to answer the three research questions. Data sources from two cohorts of teachers include statistics assessments, interviews, video-recordings of program activities, reflective journals, and classroom observations.

The project will examine how teachers reason about variation subsequent to focused instruction and contribute knowledge to in-service middle and secondary mathematics teacher education by targeting characteristics of professional development that might support teachers' reasoning about variation in increasingly sophisticated ways. The project will produce a coherent collection of shareable instructional materials for use in introductory statistics education and teacher education in statistics.

Teacher Education: Learning the Practice of Statistics

This exploratory project is to enhance the ability of teachers to provide high quality STEM education for all students by developing research-based materials that enable teachers to facilitate students' progress toward statistical understanding.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1119016
Funding Period: 
Tue, 11/01/2011 to Thu, 10/31/2013
Full Description: 

This exploratory project is to enhance the ability of teachers to provide high quality STEM education for all students by developing research-based materials that enable teachers to facilitate students' progress toward statistical understanding. The exploratory project has two phases. The first phase will focus on modeling student learning of difficult statistical concepts by constructing and developing a set of student learning progressions. Informed by the first phase, the second phase will focus on developing, implementing, supporting, and pilot testing instructional materials for teachers aimed at increasing knowledge and effective practice of statistical concepts. Formative and summative assessments will be used to evaluate (a) the materials, (b) the participant activities and experiences with the materials, and (c) the implementation process.

Both Common Core State Standards for Mathematics and National Council of Teachers of Mathematics standards clearly recommend the emphasis of statistics education in K-12 schools. In recent years, researchers have started to explore issues related to statistics education in Grades K-8, but little work has been done at the high school level. This exploratory project addresses a critical need in mathematics education and fills an important gap in teacher education related to high school statistics.

Levels of Conceptual Understanding in Statistics (LOCUS)

LOCUS (Levels of Conceptual Understanding in Statistics) is an NSF Funded DRK12 project (NSF#118618) focused on developing assessments of statistical understanding. These assessments will measure students’ understanding across levels of development as identified in the Guidelines for Assessment and Instruction in Statistics Education (GAISE). The intent of these assessments is to provide teachers and researchers with a valid and reliable assessment of conceptual understanding in statistics consistent with the Common Core State Standards (CCSS).

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1118168
Funding Period: 
Thu, 09/01/2011 to Fri, 08/31/2012
Project Evaluator: 
TERC, Jim Hammerman
Full Description: 

The goal of this project is to develop two tests (instruments) to assess conceptual understanding of statistics. The instruments are based on the levels A/B and on level C of statistical understanding development as described in the American Statistical Association Guidelines for Assessment and Instruction of Statistics Education (GAISE) framework. These instruments will be used to assess knowledge of statistics by grades 6-12 students. The instruments will have multiple-choice and constructed response (CR) items. The CR items will have scoring rubrics. The assessments will be pilot tested in school districts in six states. The instruments will be used by teachers to analyze students' growth in understanding of statistics and will be useable for both formative and summative purposes. An assessment blueprint will be developed based on the GAISE framework for selecting and constructing both fixed-choice and open-ended items. An evidenced-based designed process will be used to develop the assessments. The blueprint will be used by the test development committee to develop items. These items will be reviewed by the advisory board considering the main statistics topics to be included on the assessments. Through a layering process, the assessments will be piloted, revised, and field tested with students in grades 6-12 in six states. A three-parameter IRT model will be used in analyzing the items. The work will be done by researchers at the University of Florida with the support of those at the University of Minnesota, the Educational Testing Service, and Kenyon College. Researchers from TERC will conduct a process evaluation with several feedback and redesign cycles.

The assessments will be aligned with the Common Core State Standards for mathematics (CCSSM) and made available as open-source to teachers through a website. The research team will interact with the state consortia developing assessments to measure students' attainment of the CCSSM. As such, the assessments have the potential of being used by a large proportion of students in the country. The more conceptually-based items will provide teachers with concrete examples of what statistics students in grades 6-12 should know.

Continuous Learning and Automated Scoring in Science (CLASS)

This five-year project investigates how to provide continuous assessment and feedback to guide students' understanding during science inquiry-learning experiences, as well as detailed guidance to teachers and administrators through a technology-enhanced system. The assessment system integrates validated automated scorings for students' written responses to open-ended assessment items into the "Web-based Inquiry Science Environment" (WISE) program.

Award Number: 
1119670
Funding Period: 
Thu, 09/01/2011 to Mon, 08/31/2015
Full Description: 

This five-year project investigates how to provide continuous assessment and feedback to guide students' understanding during science inquiry-learning experiences, as well as detailed guidance to teachers and administrators through a technology-enhanced system. The assessment system integrates validated automated scorings for students' written responses to open-ended assessment items (i.e., short essays, science narratives, concept mapping, graphing problems, and virtual experiments) into the "Web-based Inquiry Science Environment" (WISE) program. WISE is an online science-inquiry curricula that supports deep understanding through visualization of processes not directly observable, virtual experiments, graphing results, collaboration, and response to prompts for explanations. In partnership with Educational Testing Services (ETS), project goals are: (1) to develop five automated inquiry assessment activities that capture students' abilities to integrate their ideas and form coherent scientific arguments; (2) to customize WISE by incorporating automated scores; (3) to investigate how students' systematic feedback based on these scores improve their learning outcomes; and (4) to design professional development resources to help teachers use scores to improve classroom instruction, and administrators to make better informed decisions about teacher professional development and inquiry instruction. The project targets general science (life, physical, and earth) in three northern California school districts, five middle schools serving over 4,000 6th-8th grade students with diverse cultural and linguistic backgrounds, and 29 science teachers. It contributes to increase opportunities for students to improve their science achievement, and for teachers and administrators to make efficient, evidence-based decisions about high-quality teaching and learning.

A key research question guides this effort: How automated scoring of inquiry assessments can increase success for diverse students, improve teachers' instructional practices, and inform administrators' decisions about professional development, inquiry instruction, and assessment? To develop science inquiry assessment activities, scoring written responses include semantic, syntax, and structure of meaning analyses, as well as calibration of human-scored items with a computer-scoring system through the c-rater--an ETS-developed cyber learning technology. Validity studies are conducted to compare automated scores with human-scored items, teacher, district, and state scores, including sensitivity to the diverse student population. To customize the WISE curriculum, the project modifies 12 existing units and develops nine new modules. To design adaptive feedback to students, comparative studies explore options for adaptive guidance and test alternatives based on automated scores employing linear models to compare student performance across randomly assigned guidance conditions; controlling for covariates, such as prior science scores, gender, and language; and grouping comparison studies. To design teacher professional development, synthesis reports on auto-scored data are created to enable them to use evidence to guide curricular decisions, and comments' analysis to improve feedback quality. Workshops, classroom observations, and interviews are conducted to measure longitudinal teachers' change over time. To empower administrators' decision making, special data reports, using-evidence activities, individual interviews, and observation of administrators' meetings are conducted. An advisory board charged with project evaluation addresses both formative and summative aspects.

A research-informed model to improve science teaching and learning at the middle school level through cyber-enabled assessment is the main outcome of this effort. A total of 21 new, one- to three-week duration standards-based science units, each with four or more automatically scored items, serve as prototypes to improve students' performance, teachers' instructional approaches, and administrators' school policies and practices.

CAREER: Engaging Elementary Students in Data Analysis Through Study of Physical Activities

This project is investigating the learning that can take place when elementary school students are directly involved in the collection, sense-making, and analysis of real, personally-meaningful data sets. The hypotheses of this work are that by organizing elementary statistics instruction around the study of physical activities, students will have greater personal engagement in data analysis processes and that students will also develop more robust understandings of statistical ideas.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1054280
Funding Period: 
Fri, 07/01/2011 to Thu, 06/30/2016
Full Description: 

This CAREER awardee at Utah State University is investigating the learning that can take place when elementary school students are directly involved in the collection, sense-making, and analysis of real, personally-meaningful data sets. The project responds to increasing attention to data collection and analysis in elementary grades and aims to make important contributions to the knowledge base on effective approaches to these topics. The hypotheses of this work are that by organizing elementary statistics instruction around the study of physical activities, students will have greater personal engagement in data analysis processes and that students will also develop more robust understandings of statistical ideas. Students and teachers from fifth grade classrooms from several elementary schools from northern Utah, are participating in the project. This work is co-funded by the EPSCoR program.

Statistics topics include measures of center and variation. Students use pedometers, heart rate monitors, other probeware, and the TinkerPlots software. The research team investigates the influence of personal ownership and relationships to data on students' understanding of learning of elementary statistics concepts and their ability to analyze data. The research involves multi-year clinical interviews and video-recorded classroom design experiments.

Research results are expected to be published in appropriate journals and are expected to be presented at professional meetings. Lesson plans and student instructional materials related to physical activity, measures of center, and data distributions are made available for use in partner elementary schools.

Teachers Empowered to Advance Change in Mathematics (TEACH MATH): Preparing Pre K-8 Teachers to Connect Children's Mathematical Thinking and Community-Based Funds of Knowledge

This project will modify the teacher preparation program for preK-8 teachers. The program is designed to help pre-service teachers learn mathematics well, learn to access students' cultural funds of knowledge, and learn to encourage students' mathematical thinking. The developers are designing (a) modules that can be used in teacher preparation courses, (b) a mentoring program for new teachers, and (c) on-line networks to facilitate collaboration among participating teachers and institutions.

Lead Organization(s): 
Award Number: 
1228034
Funding Period: 
Thu, 09/01/2011 to Thu, 08/31/2017
Project Evaluator: 
Research Institute for Studies in Education
Full Description: 

This research and development project will modify the teacher preparation program for preK-8 teachers at six universities located in different regions of the U.S. The new program is designed to help pre-service teachers learn mathematics well, learn to access students' cultural funds of knowledge in ways that will help them teach mathematics, and learn to encourage students' mathematical thinking. By integrating these important bodies of knowledge, pre-service teachers should be better prepared to teach mathematics to the variety of students in their classes. The developers are designing (a) modules that can be used in teacher preparation courses, (b) a mentoring program for new teachers, and (c) on-line networks to facilitate collaboration among participating teachers and institutions.

The project includes a study of how pre-service teachers learn to apply the knowledge they have gained in the program. The research team has planned a longitudinal collection of data that will track the pre-service teachers into their careers. Their goal is to document teachers' understandings of children's mathematical thinking and children's cultural funds of knowledge and to understand the relationship between teachers' understandings and the learning and disposition of preK-8 students. The study will be implemented at all six universities with staggered start dates allowing for analysis and revisions between cohorts.

These research and development efforts have the potential to impact preK-8 teacher preparation through (1) the development of modules that integrate several relevant proficiencies in mathematics teaching, and (2) the research that studies the impact of such a program on the mathematical learning and disposition of preK-8 students.

Data Games: Tools and Materials for Learning Data Modeling (Collaborative Research: Finzer)

The Data Games project has developed software and curriculum materials in which data generated by students playing computer games form the raw material for mathematics classroom activities. Students play a short video game, analyze the game data, develop improved strategies, and test their strategies in another round of the game.

Project Email: 
Lead Organization(s): 
Award Number: 
0918735
Funding Period: 
Tue, 09/01/2009 to Fri, 08/31/2012
Project Evaluator: 
James Hammerman
Full Description: 

Students playing computer games generate large quantities of rich, interesting, highly variable data that mostly evaporate when the game ends. What if in a classroom setting, data from games students played remained accessible to them for analysis? In software and curriculum materials developed by the Data Games project at UMass Amherst and KCP Technologies, data generated by students playing computer games form the raw material for mathematics classroom activities. Students play a short video game, analyze the game data, develop improved strategies, and try their strategies in another round of the game.

 

The video games are embedded in an online data analysis learning environment that is based on desktop software tools Fathom® Dynamic Data and Tinkerplots® Dynamic Data Exploration, widely used in grades 5–8 and 8–14 respectively. The game data appear in graphs and tables in real time, allowing several cycles of strategy improvement in a short time. The games are designed so that these cycles improve understanding of specific data modeling and/or mathematics concepts.

 

The research strand of the Data Games project focuses on students’ creation of data representations that model a real-world context. Findings from this research have been incorporated into the design of the data structures in the software.

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