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 Sat, 06/30/2018
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.

Formative Assessment Delivery System (FADS)

This project uses new psychometric techniques to create a technological tool that could evaluate how well students in the 4th-8th mathematics and science classrooms respond to complex performance tasks. The purpose of this tool is to improve the instruction of teachers in mathematics and science. It will produce real-time individualized diagnoses of instructional needs to help teachers plan instruction that specifically addresses the learning needs of each student in that class.

Project Email: 
Award Number: 
0733334
Funding Period: 
Wed, 08/15/2007 to Sat, 07/31/2010
Project Evaluator: 
Julie Koppich
Full Description: 

This project addresses the Measurement goal under the Mathematics and Science Education research program. Specifically, we propose developing and refining an assessment development, delivery, scoring, and report-generating system in the area of mathematics, centered on statistics and modeling.  We have been engaged with colleagues at Vanderbilt University in designing a formative assessment system to support (and help evaluate) their innovative curriculum in this area: the Assessing Data Modeling and Statistical Reasoning (ADM) system developed by Rich Lehrer and his colleagues (Lehrer & Schauble, 2007).  This assessment system has been created using the principles of the BEAR Assessment System (BAS; Wilson, 2005), and it and the curriculum it supports is currently being used in several states (WI, AK, TN), and is being adopted into a broader curriculum that is widely used.  The aim of the current project is: (a) to refine a set of software programs that the Berkeley Evaluation and Assessment Research (BEAR) Center has been developing over the last 10 years that support the development, calibration, use and training for the assessment system, and to develop software interconnections among those programs to allow them to operate seamlessly for users whose roles range from assessment developers to teachers to school administrators, to those who provide professional development for teachers; (b) as a first full trial of that software,  to embed the existing ADM materials in the software, construct computer-deliverable and computer-scorable task equivalents of the current  item bank, and develop new computerized reports and support materials for teachers; and (c) to investigate the usefulness of this new software in the context of the ADM curriculum.

The positive effects of innovative assessments are widely acknowledged (Black & Wiliam, 1998), and we are happy that the BAS is seen as one such innovation.  But we are strongly concerned that the good effects that one can find from early-adopters of such innovations will not be sustained unless the considerable burden of teacher scoring of their students’ formative assessments is lightened.  We believe that it is essential that teachers become experts in interpreting their student’s responses to assessments.  But, equally, we see that it is wise to then relieve them of the burden of continual scoring of large amounts of student work.  Hence, the strategy we have adopted is to involve teachers early on in a deep program of professional development that will include close work with curriculum materials, assessments and student responses to assessments (preferably including a large proportion of work from their own students).  However, once teachers have shown their mastery of the role of scorer and interpreter of such student products, we then provide the teacher with computerized assessments that will deliver and score equivalent assessments for their students, and generate rich interpretational materials to help them with diagnosis and planning.  We expect that teachers will still be called upon to evaluate unusual student responses, and also will need to carry out occasional hand-scoring to keep up their mastery and to adapt to innovations in the curriculum.

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

This project is developing 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, conjecture improved strategies, and test their strategies in another round of the game.

Award Number: 
0918653
Funding Period: 
Tue, 09/01/2009 to Fri, 08/31/2012
Project Evaluator: 
Jim Hammerman
Full Description: 

Students playing computer games generate large quantities of rich, interesting, highly variable data that mostly evaporates into the ether 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 being 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, conjecture improved strategies, and test their strategies in another round of the game.

 

The video games are embedded in TinkerPlots and Fathom, two data analysis learning environments widely used in grades 5–8 and 8–14 respectively. The game data appear in graphs in real time, allowing several cycles of strategy improvement in a short time. The games are designed so that these cycles im- prove understanding of specific data modeling and/or mathematics concepts. Lessons will be embedded in LessonLink from Key Curriculum Press to facilitate their integration into standard curricula. The three- year project expands research in students’ understanding of data modeling and their ability to learn mathematical content embedded in data-rich contexts.

The Development of Student Cohorts for the Enhancement of Mathematical Literacy in Under Served Populations

This project is developing and conducting research on the Cohort Model for addressing the mathematics education of students that perform in the bottom quartile on state and district tests. The predicted outcome is that most students will remain in the cohort for all four years and that almost all of those who do will perform well enough on college entrance exams to be admitted and will test out of remedial mathematics courses.

Lead Organization(s): 
Award Number: 
0822175
Funding Period: 
Mon, 09/01/2008 to Wed, 08/31/2011
Project Evaluator: 
Inverness Research, Inc.
Full Description: 

Project Summary

This is a Full Research and Development proposal which addresses the Contextual Challenge: How can the learning of significant STEM content be achieved to ensure public literacy and workforce readiness?  Our nation is failing to prepare millions of youth for meaningful and productive participation in an information-based society. The target population are those students performing in the bottom quartile on state and national tests, many of these are children of color living in under resourced communities, and most of these young people do not finish high school and end up diverted into an underground economy, gangs, and prisons.   

This project addresses this failure by further developing and testing an approach that the Algebra Project is developing for high school mathematics, in which students form a cohort that stays together for all four years of high school, study mathematics every day using project-designed curricular materials with teachers who participate in project professional development, and are supported by local community groups. 

The Algebra Project seeks to stimulate a demand for math literacy in those most affected by its absence -- the young people themselves.  It stresses the importance of peer culture, using lessons learned from experiences in the 1960s Civil Rights Movement, as well as in the emergence of project graduates into a group with their own perspectives and initiatives. 

In the 60s, project founders learned how to use the meeting place as a tool to engage and empower the people that the meeting was intended to serve.  In the proposed project, there are two meeting places: the students’ high school mathematics classroom and supplementary education activities; and the network of sites around the country that are communicating and learning how to develop and implement cohorts. Young peoples’ roles in each of these settings are key to creating the motivation and commitment needed for student success as well as developing local interest.  The combination of classroom and professional development work, innovative curriculum materials, and community involvement creates an intervention that can significantly transform the peer culture, even in the face of negative forces.

The Algebra Project has developed a cohort model that we predict will stimulate and enable students to pass the state and district mandated tests in mathematics, to pass the mathematics portions of any graduation test, and to score well enough on the SAT or ACT to enter college, and to place into mathematics courses for college credit (not remedial courses).  Building on previous awards, the project will continue to research and develop the cohort model, and will create a small network of cohorts to establish that our model can be widely successful.

Intellectual merit:  This project will demonstrate how students entering high school performing in the bottom quartile nationally and state-wide can be prepared for college-level mathematics, using lessons learned from many years of past experience working in such communities and in their middle schools, and more recently in their high schools and in collaboration with university mathematicians.  The research results are critical to the nation’s learning how to improve mathematics achievement for all children – to gaining a sense of what such a program “looks and feels like”, and what resources and commitments are required, from which institutions. 

Broader impact:  The results of this discovery research project will advance understanding of how to improve mathematics learning and achievement in low performing districts, so students are prepared to take college mathematics without repeating high school mathematics in early college.  It will also demonstrate the resources and commitments needed to reach this result.

Connecting Content and Pedagogical Education of Pre-service Teachers (CONCEPT)

The primary goal of the project is to enhance secondary mathematics teacher education for pre-service teachers by developing, implementing and disseminating resources from a four-course curriculum that brings together the study of mathematics content and pedagogy. Three of the courses are problem-based technology enhanced (PBTE) courses in Algebra and Calculus, Geometry, and Probability and Statistics. A fourth course is a capstone course in Teaching and Learning Secondary School Mathematics.

Lead Organization(s): 
Award Number: 
0455797
Funding Period: 
Wed, 06/01/2005 to Sun, 05/31/2009

Pages

Subscribe to Statistics