Algebra

Multiple Instrumental Case Studies of Inclusive STEM-Focused High Schools: Opportunity Structures for Preparation and Inspiration (OSPrl)

The aim of this project is to examine opportunity structures provided to students by inclusive STEM-focused high schools, with an emphasis on studying schools that serve students from underrepresented groups. The project is studying inclusive STEM-focused high schools across the United States to determine what defines them. The research team initially identified ten candidate critical components that define STEM-focused high schools and is refining and further clarifying the critical components through the research study.

Lead Organization(s): 
Award Number: 
1118851
Funding Period: 
Thu, 09/01/2011 to Mon, 08/31/2015
Full Description: 

The aim of this project is to examine opportunity structures provided to students by inclusive STEM-focused high schools, with an emphasis on studying schools that serve students from underrepresented groups. In contrast to highly selective STEM-focused schools that target students who are already identified as gifted and talented in STEM, inclusive STEM-focused high schools aim to develop new sources of STEM talent, particularly among underrepresented minority students, to improve workforce development and prepare STEM professionals. A new NRC report, Successful K-12 STEM Education (2011), identifies areas in which research on STEM-focused schools is most needed. The NRC report points out the importance of providing opportunities for groups that are underrepresented in the sciences, especially Blacks, Hispanics, and low-income students who disproportionately fall out of the high-achieving group in K-12 education. This project responds specifically to the call for research in the NRC report and provides systematic data to define and clarify the nature of such schools. 

The project is studying inclusive STEM-focused high schools across the United States to determine what defines them. The research team initially identified ten candidate critical components that define STEM-focused high schools and is refining and further clarifying the critical components through the research study. The first phase of the study is focusing on 12 well-established and carefully planned schools with good reputations and strong community and business support, in order to capture the critical components as intended and implemented. Case studies of these high-functioning schools and a cross-case analysis using a set of instruments for gauging STEM design and implementation are contributing toward building a theory of action for such schools that can be applied more generally to STEM education. The second phase of the study involves selecting four school models for further study, focusing on student-level experiences and comparing student outcomes against comprehensive schools in the same district. Research questions being studied include: 1) Is there a core set of likely critical components shared by well-established, promising inclusive STEM-focused high schools? Do other components emerge from the study? 2) How are the critical components implemented in each school? 3) What are the contextual affordances and constraints that influence schools' designs, their implementation, and student outcomes? 4) How do student STEM outcomes in these schools compare with school district and state averages? 5) How do four promising such schools compare with matched comprehensive high schools within their respective school districts, and how are the critical components displayed? 6) From the points of view of students underrepresented in STEM fields, how do education experiences at the schools and their matched counterparts compare? And 7) How do student outcomes compare?

The research uses a multiple instrumental case study design in order to describe and compare similar phenomena. Schools as critical cases are being selected through a nomination process by experts, followed by screening and categorization according to key design dimensions. Data sources include school documents and public database information; a survey, followed by telephone interviews that probe for elaborated information, to provide a systematic overview of the candidate components; on-site visitations to each school provide data on classroom observations at the schools; interviews with students, teachers and administrators in focus groups; and discussions with critical members of the school community that provide unique opportunities to learn such as mentors, business leaders, and members of higher education community that provide outside of school learning experiences. The project is also gathering data on a variety of school-level student outcome indicators, and is tracking the likely STEM course trajectories for students, graduation rates, and college admission rates for students in the inclusive STEM-focused schools, as compared to other schools in the same jurisdiction. Analysis of the first phase of the study aims to develop rich descriptions that showcase characteristics of the schools, using axial and open coding, to determine a theory of action that illustrates interconnections among context, design, implementation, and outcome elements. Analysis of the second phase of the study involves similar processes on four levels: school, student, databases, and a synthesis of the three. Evaluation of the project consists of an internal advisory board and an external advisory board, both of which provide primarily formative feedback on research procedures.

Research findings, as well as case studies, records of instrument and rubric development and use, annual reports, and conference proposals and papers are being provided on a website, in order to provide an immediate and ongoing resource for education leaders, researchers and policymakers to learn about research on these schools and particular models. An effort is also being made to give voice to the experiences of high school students from the four pairs of high schools studied in the second phase of the study. Findings are also being disseminated by more traditional means, such as papers in peer-reviewed journals and conference presentations.

Children's Understanding of Functions in Grades K-2

This project is studying how young children in grades K-2 understand mathematical concepts that are foundational for developing algebraic thinking. Researchers are contributing to an ongoing effort to develop a learning trajectory that describes how algebraic concepts are developed. The project uses teaching experiments, with researchers talking directly to students as they explore algebraic ideas. They explore how students think about and develop concepts related to covariation, representations of functions, relationships among variable, and generalization.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1154355
Funding Period: 
Mon, 08/01/2011 to Thu, 07/31/2014
Full Description: 

The researchers in the Children's Understanding of Functions project are studying how young children in grades K-2 understand mathematical concepts that are foundational for developing algebraic thinking. Researchers at University of Massachusetts at Dartmouth and Tufts University are contributing to an ongoing effort to develop a learning trajectory that describes how algebraic concepts are developed. Most research has focused on student development at the upper elementary and middle school levels, but this project will add information about early elementary learners.

The project's research methodology uses teaching experiments which allow researchers to talk directly to students as they explore algebraic ideas. They explore how students think about and develop concepts related to covariation, representations of functions, relationships among variable, and generalization. Researchers have designed tasks that help students explain their thinking and solve problems where some quantities vary and others are constant. They are analyzing videos and students' written work as they build case studies about the development of algebraic thinking. External evaluation of this exploratory project is one of the responsibilities of its advisory board.

This project is connecting the algebraic thinking of younger children to what has been documented for older children. This process enables them to build an evidence-based learning trajectory about students' development of algebraic thinking. The products of this research can be used to build curricula and lessons that are aligned with what students know and can learn at various points in their development. Project findings, tasks and videos are being disseminated not only to researchers, but also to practitioners through professional publications and the DRK-12 Resource Network.

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.

Mathematical Argumentation in Middle School: Bridging from Professional Development to Classroom Practice

This exploratory project is working in collaboration with teachers to increase their knowledge of mathematics for teaching in middle school. In addition to geometry and algebra, the research component of the project is providing insights into how teachers use their mathematical knowledge to increase argumentation in the classroom and to help students build skills in mathematical argumentation.

Lead Organization(s): 
Award Number: 
1119518
Funding Period: 
Sat, 10/01/2011 to Mon, 09/30/2013
Project Evaluator: 
SRI International evaluation team
Full Description: 

Mathematical Argumentation in the Middle School is an exploratory project that is working in collaboration with teachers to increase their knowledge of mathematics for teaching in middle school. In addition to geometry and algebra, the professional development is focusing on the role of mathematical argumentation in the middle school and strategies for increasing argumentation. The research component of the project is providing insights into how teachers use their mathematical knowledge to increase argumentation in the classroom and to help students build skills in mathematical argumentation. In addition, the project is studying student outcomes such as reasoning, communication skills, and mathematical knowledge.

The project researchers are using both qualitative and quantitative methodologies to ensure that they have high quality data and analysis that will provide insights into the following research questions: 1) How do teachers use what they learn from the professional development (PD) experiences when they teach in the classroom? 2) To what extent does teachers? use of the project materials and what they learn in the PD result in mathematical argumentation in their classroom discourse? 3) Do students gain conceptual understanding of the mathematics as a result of their participation in argumentation in the classroom? Based on previous research, there is adequate evidence to believe that argumentation in the classroom does increase for participants in the workshop, but the researchers are seeking a better understanding of how teachers use their knowledge and the project materials to enact such an important change in mathematics lessons and in student learning. The professional development uses the dynamic software Geometers' Sketchpad, a carefully-designed, geometry curricular unit, and student materials to help teachers see how to set up a classroom environment that supports mathematical conjectures, arguments, and discussion. The research is done in the classroom and assesses the various components of the professional development in promoting argumentation.

The project is providing insights into how teachers use their mathematical knowledge to implement changes in the classroom. The project is creating effective professional development strategies, a middle school curriculum unit on geometry that emphasizes argumentation, and associated materials. The research is explaining how teachers use their knowledge and the materials and providing information on how students' conceptual knowledge develops through argumentation.

Modeling Engineered Levers for the 21st Century Teaching of STEM (Collaborative Research: Schunn)

This project will develop three replacement units for biology and refine them through classroom testing. The units will be models of STEM integration by using the important concepts of proportional reasoning and algebraic thinking and engineering re-design to address big ideas in science while also promoting the learning of 21st century skills. The materials will be educative for teachers, and the teacher materials and professional development methods will work at scale and distance.

Project Email: 
Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1027629
Funding Period: 
Wed, 09/01/2010 to Sun, 08/31/2014
Project Evaluator: 
Bill Bickel
Full Description: 

Research in biology has become increasingly mathematical, but high school courses in biology use little mathematics. To address this concern, this project will develop three replacement units for biology and refine them through classroom testing. The units will be models of STEM integration by using the important concepts of proportional reasoning and algebraic thinking and engineering re-design to address big ideas in science while also promoting the learning of 21st century skills. The materials build on existing work on the use of model eliciting activities and focus science and technology instruction on high-stakes weaknesses in mathematics and science. They address the scaling issue as part of the core design work by developing small units of curriculum that can be applied by early adopters in each context. The materials will undergo many rounds of testing and revision in the early design process with at least ten teachers each time. The materials will be educative for teachers, and the teacher materials and professional development methods will work at scale and distance.

Learning of science content will be measured through the use of existing instruments in wide use. Existing scales of task values, achievement goals and interest are used to measure student motivation. The work performed is guided by a content team; a scaling materials team; a scaling research team; the PI team of a cognitive scientist, a robotics educator, and a mathematics educator specializing in educational reform at scale; and the summative evaluation team lead by an external evaluator.

There is great interest in understanding whether integrated STEM education can interest more students in STEM disciplines. The focus on mathematics integrated with engineering in the context of a science topic is interesting and novel and could contribute to our understanding of integrating mathematics, engineering and science. The development team includes a cognitive scientist, a mathematics educator, teachers and scientists. The issues and challenges of interdisciplinary instruction will be investigated.

Changing Curriculum, Changing Practice

This project is studying the impact of implementing a NSF-funded, high school mathematics curriculum that emphasizes mathematical habits of mind. This curriculum focuses on ways of thinking and doing mathematics in contrast with curricula that focus on mathematical topics. The project is studying the development of teachers' mathematical knowledge for teaching and their capacity to align their instruction with the new curriculum.

Award Number: 
1019945
Funding Period: 
Wed, 09/01/2010 to Fri, 08/31/2012
Full Description: 

The CME Project Mathematical Practices Implementation Study project (formerly called "Changing Curriculum, Changing Practice"), led by mathematics educators at the Education Development Center, is studying the impact of implementing a NSF-funded, high school mathematics curriculum that emphasizes mathematical habits of mind. This curriculum focuses on ways of thinking and doing mathematics in contrast with curricula that focus on mathematical topics. The project is studying the development of teachers' mathematical knowledge for teaching and their capacity to align their instruction with the new curriculum. The project includes a moderate level of professional development and the development of valid and reliable instruments to assess teachers' mathematical knowledge for teaching and their instructional practices.

This four-year, mixed-methods study is investigating the conjecture that high school teachers' implementation of a curriculum emphasizing mathematical habits of mind will lead to measurable changes in teachers' mathematical knowledge and their instruction. The investigators are also interested in the relationships among (1) teachers' prior knowledge, (2) their use of the curriculum and (3) the school-level support for implementation. The investigators are studying the implementation of the curriculum by 70 teachers in 12 schools that vary in socio-economic status of the students and geographic location. The research design includes observations of the instruction of a sub-sample of nine teachers to obtain a finer-grained measure of instructional practice. They are developing or adapting existing instruments that measure teachers' knowledge and alignment of instruction with the goals of teaching mathematical habits of mind. Using the Instructional Quality Assessment rubric during visits to the classroom, they are assessing students' opportunities to develop mathematical thinking skills. The use of mixed-methods approaches will allow the researchers to analyze the data from multiple perspectives.

This study is part of a long-term effort to help high school students develop specific mathematical habits of mind. The current study is building on previous curriculum development and also developing insights for future studies investigating students' adoption of mathematical habits of mind. The current project is an important effort to understand the roles teachers play in implementing curricular changes that have the potential for improving student achievement in mathematics. Teachers are the critical bridging agents who connect curriculum and learners. This study will help to explain how teachers' knowledge, teachers' instruction, and teachers' contexts within schools contribute to or detract from the faithful implementation of the goals intended by a curriculum. It will lay a foundation for understanding future efforts to assess what students learn and how they learn it.

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.

Using PISA to Develop Activities for Teacher Education (UPDATE)

This project uses items and data from the Program for International Student Assessment (PISA) to develop two kinds of resources for preparation and professional development of secondary mathematics teachers: one in the form of prototype professional learning materials and a second in the form of PISA-based, research-grounded articles written for mathematics teachers and teacher educators. Work on both resources will focus on algebra and quantitative literacy and on factors influencing educational equity.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1019513
Funding Period: 
Wed, 09/01/2010 to Fri, 08/31/2012
Full Description: 

The UPDATE project seeks to enable significant advances in K-12 teacher and student learning of mathematics by using of items and data from the Program for International Student Assessment (PISA) in ways that enhance the work of mathematics teachers and teacher educators. We hypothesize that PISA can be useful to the field in much the same way as the National Assessment of Educational Progress (NAEP), which has long served as a key source of information for the mathematics education community. In contrast to NAEP and TIMSS, the Program for International Student Assessment (PISA) in the area of mathematics has received little or no attention within the U.S. mathematics education community, beyond noting that the performance of U.S. students is mediocre compared to that of students in many other countries in Asia and Europe. A consequence of the lack of attention to PISA in the U.S. is that we have underutilized a potentially valuable source of information for improvement of mathematics education.

In this project we use PISA as a base to develop resources for mathematics educators to use in teacher education settings. One type of resource comes in the form of prototype professional learning materials that provide opportunities for teachers and students to analyze complex mathematical tasks and student responses to those tasks, focusing on both the mathematics entailed in the task and the understandings of mathematics reflected in students’ responses. The materials will be designed to engage teachers in individual and collaborative inquiry aimed at developing their specialized content knowledge and their pedagogical content knowledge. Materials will be field tested in preservice and inservice teacher professional education settings and also shared at regional and national meetings. A second type of resource comes in the form of PISA-based, research-grounded articles written specifically for mathematics teachers and teacher educators and published in journals that reach these audiences. The articles will be informed not only by our experiences in developing and using the prototype materials, but also by the findings of selected secondary analyses of data collected in the 2003 PISA assessment.

Our work is organized around three distinct focus areas: (1) Algebra – a traditional content topic familiar to mathematics teachers that can be approached in a novel way through PISA tasks; (2) Quantitative Literacy – a nontraditional content topic less familiar to mathematics teachers that can be accessed directly through PISA tasks, and (3) Equity – an issue of import to mathematics educators that can be examined carefully using PISA data. In each component our work blends research inquiry and development, integrating the analysis of tasks and data from the PISA mathematics assessment with the creation of prototype teacher education materials and the preparation of PISA-based, research-grounded articles for teachers and teacher educators.

The results of this exploratory study will be disseminated broadly, and they are likely to generate new activity in research and development related to PISA. Mirroring the tradition of the interpretive reports of NAEP results, we will produce PISA-based resources that can have a significant impact on the mathematics education community as teachers, teacher educators, and graduate students examine the materials and reports we produce and use them to improve the quality of teacher and student learning of mathematics.

This exploratory project led by faculty from the University of Michigan uses items and data from the Program for International Student Assessment (PISA) to develop two kinds of resources for preparation and professional development of secondary mathematics teachers. One type of resource comes in the form of prototype professional learning materials that provide opportunities for teachers and students to analyze complex mathematical tasks and student responses to those tasks, focusing on both the mathematics entailed in the task and the understandings of mathematics reflected in students' responses. A second type of resource comes in the form of PISA-based, research-grounded articles written specifically for mathematics teachers and teacher educators. Work on both resources will focus on the critical content areas of algebra and quantitative literacy and on factors influencing educational equity.

The project is driven by the hypothesis that PISA assessment instruments and findings can be useful to teachers in much the way that prior analyses of NAEP frameworks, items, and data have been. To address the first project objective, the research team will use selected PISA items and student responses to those items to design, develop, and test a collection of professional learning tasks that engage mathematics teachers in individual and collaborative inquiry aimed at enhancing their specialized content knowledge and their pedagogical content knowledge. To address the second project objective, the research team will prepare articles for practitioner journals that will be informed by experiences in developing and using the prototype materials, but also by the findings of selected secondary analyses of data collected in the 2003 PISA assessment.

The results of this work will be a collection of resources for use in various teacher preparation and professional development settings to stimulate thinking of secondary mathematics teachers about issues of curriculum content, student learning, teaching, and assessment.

Using Routines as an Instructional Tool for Developing Students' Conceptions of Proof

This project will develop and systematically investigate a teaching model to assist teachers in developing ideas about proof in grades 2-5. The teaching model provides both a tool for learning on the part of elementary teachers and a model of practice from which they can learn as they implement it.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1019482
Funding Period: 
Wed, 09/01/2010 to Fri, 08/31/2012
Project Evaluator: 
Megan Franke
Full Description: 

Developers and researchers at TERC, the Education Development Center, and Mount Holyoke College are participating in the development and systematic investigation of a teaching model to assist teachers in developing ideas about proof in grades 2-5. The teaching model provides both a tool for learning on the part of elementary teachers and a model of practice from which they can learn as they implement it.

The project is a teaching experiment in which the model is iteratively implemented and refined, first with teachers experienced in incorporating ideas about proof into their classroom instruction (Phase 1), then with teachers who are relatively inexperienced, both in their own understanding of proof and in their knowledge of how their students can learn about proof (Phase 2). Research questions focus on developing the components of the model, the learning of teachers as they implement the model, and the learning of students as they engage in the instruction that is guided by the model, with particular attention to students with varied histories of achievement in grade-level work on number and operations.

The expected outcome is a teaching model that can be tested on a larger scale as well as instruments for assessing student learning and teacher understanding of proof. The model includes printed material with descriptions of the routines and instructional sequences, guidelines for implementing each component, and a teaching framework as well as written and video case examples.

Algebra: A Challenge at the Crossroads of Policy and Practice

This project is reviewing and analyzing policy documents and studies related to Algebra I learning and teaching, in order to (1) gain a better understanding of algebra education in the United States; and (2) conduct an accounting of research questions that have and have not been taken up by policy documents to date. The results are to be disseminated to both the mathematics education research community and to the education policy community.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
0960581
Funding Period: 
Mon, 03/01/2010 to Mon, 02/28/2011
Full Description: 

A team led by researchers at the University of Pittsburgh is reviewing and analyzing policy documents and studies related to Algebra I learning and teaching, in order to (1) gain a better understanding of algebra education in the United States; and (2) conduct an accounting of research questions that have and have not been taken up by policy documents to date (i.e., what we know and what we need to know). The results are to be disseminated to both the mathematics education research community and to the education policy community. Further discussion and dissemination is planned through an invitational conference in Washington, DC. The findings will also be used to set a research agenda for algebra learning and teaching.

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