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Mathematics

Cross-National Comparison of School and District Supports for High-Quality Mathematics Instruction in the US and China

This RAPID project is a cross-national comparative study of U.S. and Chinese instructional support systems, building from earlier data about mathematics teaching and learning in large urban school districts of both the United States and the People's Republic of China. The study uses quantitative methods to compare and contrast the effectiveness of supports (e.g., professional development, teacher networks, school leadership) in improving teachers' instructional practices and student achievement using comparable instrumentation.

Lead Organization(s): 
Award Number: 
1321828
Funding Period: 
Sun, 09/15/2013 - Sun, 08/31/2014
Full Description: 

Since the publication of the result that students from Shanghai, China, outperformed students from all other participating countries on the 2009 Programme for International Student Assessment (PISA) in mathematics, researchers have sought to understand why Chinese mathematics education appears to be both more successful at boosting student learning and more equitably distributed. This RAPID project is a cross-national comparative study of U.S. and Chinese instructional support systems, building from earlier data about mathematics teaching and learning in large urban school districts of both the United States and the People's Republic of China. The work is being conducted by researchers from Vanderbilt University, Virginia Polytechnic Institute and State University and Beijing Normal University. The study uses quantitative methods to compare and contrast the effectiveness of supports (e.g., professional development, teacher networks, school leadership) in improving teachers' instructional practices and student achievement using comparable instrumentation.

The study contributes to research and policy in several ways. First, it is helping to identify supports that have been particularly effective in improving mathematics teaching and learning in China. This should inform current theories about how to best support mathematics education in the United States. Second, the cross-nationally validated instruments used to collect the data can be used by other researchers investigating curricular reform implementation cross-nationally. The findings of this study are especially relevant to district leaders as they develop support and accountability systems to effectively implement the content and practice standards of the Common Core State Standards for Mathematics.

This award is co-funded by NSF's International Science and Engineering Section, Office of International and Integrative Activities.

Cross-National Comparison of School and District Supports for High-Quality Mathematics Instruction in the US and China

ITEAMS Longitudinal Study

The objective of this study is to examine the impact of ITEAMS intervention strategies on student persistence in high school STEM course-taking and career expectations, and the value that students place on STEM careers.

Lead Organization(s): 
Award Number: 
1355323
Funding Period: 
Sun, 09/15/2013 - Wed, 04/30/2014
Full Description: 

The objective of this study at Harvard University is to examine the impact of ITEAMS (Innovative Technology-Enabled Astronomy for Middle Schools) intervention strategies on student persistence in high school STEM course-taking and career expectations, and the value that students place on STEM careers. The central research questions are: 1) does ITEAMS participation boost students' STEM course-taking and their interest in, and valuation of, STEM careers throughout their high school years; 2) to what extent did students' ITEAMS experiences, in terms of knowledge and disposition, have an effect; and 3) which ITEAMS strategies or attributes have been most effective in bringing about positive outcomes? Special focus is on the predictors of persistence for girls and minority students.

The project utilizes a mix of interviews and surveys with current high school students who in previous years participated in ITEAMS (DRL-0833378) as middle-school students, and who are now juniors and seniors. The project surveys a randomly selected cohort of 75 former ITEAMS participants who were enrolled in ITEAMS for two or three years. The project-specific survey instrument includes pertinent demographic questions. The random selection of up to 15 surveyed ITEAMS students for in-depth interviews is also included.

ITEAMS Longitudinal Study

iSTEM: A Multi-State Longitudinal Study of the Effectiveness of Inclusive STEM High Schools

This is a quasi-experimental study of the effects of attending an inclusive STEM high school in three key geographic regions and comparing outcomes for students in these schools with those of their counterparts attending other types of schools in the same states. The study's focus is on the extent to which inclusive STEM high schools contribute to improved academic outcomes, interests in STEM careers, and expectations for post secondary study.

Lead Organization(s): 
Award Number: 
1316920
Funding Period: 
Sun, 09/01/2013 - Thu, 08/31/2017
Full Description: 

Researchers from SRI and George Washington University are studying the effectiveness of inclusive STEM high schools in three key geographic regions including Texas, North Carolina and Ohio. STEM schools continue to be an important policy area and test bed for one indication of what STEM education can accomplish under the most optimal conditions in which STEM is the focus of students' learning experiences. The President has called for the creation of an additional 1,000 STEM schools with relatively little evidence about the impact of such schools or the evidence of which configurations and elements of such schools are important. The study's focus is on the extent to which inclusive STEM high schools contribute to improved academic outcomes, interests in STEM careers, and expectations for post secondary study. The research study engages in implementation research to examine the elements of the STEM schools' design and implementation and other contextual factors, including state policies, which are associated with superior outcomes.

This is a quasi-experimental study of the effects of attending an inclusive STEM high school comparing outcomes for students in these schools with those of their counterparts attending other types of schools in the same states. The study includes all students in the 9th or 12th grade in the inclusive STEM high schools and students in samples of same-state comparison schools identified through propensity score matching. Data are collected longitudinally using student records and surveying students at regular intervals. The study follows the 12th grade students after graduation into postsecondary study and the workforce. The states identified in this study have the requisite administrative data systems to support the proposed study. By using a combination of data available in state-level data bases and new information obtained through project surveys, the researchers are identifying students who are matched not only on demographic variables and academic achievement before high school entry, but also on indicators of pre-existing interest and expectation such as self-efficacy and prior participation in informal STEM-related activities. Impacts on student achievement are analyzed separately for each state. Data on the elements of STEM schools are collected through teacher and administrator surveys and interviews. State STEM school history and policy data are collected through document analysis and interviews. The study utilizes hierarchical regression models, with separate models of each outcome measure and adjustments for tests of multiple comparisons. Student attrition is monitored and findings are examined to determine influence of attrition.

This project focuses on inclusive rather than selective STEM schools so that the population of students more typically represents the population of the students locally. The study provides a source of evidence about not only the effectiveness of STEM schools, but also contextual evidence of what works and for whom and under what conditions.

iSTEM: A Multi-State Longitudinal Study of the Effectiveness of Inclusive STEM High Schools

Teacher's Guide to the Mathematics and Science Resources of the ELPD Framework

This two-year project will develop, pilot, validate, and publish a Teacher's Guide to the Science and Mathematics Resources of the ELPD Framework. This guide and related materials will translate the key science and mathematics concepts, ideas, and practices found within the ELPD Framework into classroom resources for direct use by teachers, schools, and districts to support English learners (ELs).

Lead Organization(s): 
Award Number: 
1346491
Funding Period: 
Sun, 09/01/2013 - Mon, 08/31/2015
Full Description: 

The Council of Chief State School Officers (CCSSO) coordinated the development of a document addressing the implementation of Standards as guided by a framework for English Language Proficiency Development Standards (ELPD Framework). The expressed purpose of the ELPD Framework is to provide guidance to states on how to develop and use tools for the creation and evaluation of ELP standards. Once published, it became immediately apparent that the ELPD Framework would be of great help to teachers. However, the Framework was written specifically for those tasked with the responsibility to develop, adopt, or adapt state ELPD standards and assessments that support the language demands of STEM education grounded in learning performances that cojoin concepts with practices. That is, it has a technical focus rather than an instructional focus. There is an immediate need to develop and validate such a tool in states that have adopted Standards-based models, since educational agencies are now building teachers capacities to implement these standards.

This two-year project will develop, pilot, validate, and publish a Teacher's Guide to the Science and Mathematics Resources of the ELPD Framework. This guide and related materials will translate the key science and mathematics concepts, ideas, and practices found within the ELPD Framework into classroom resources for direct use by teachers, schools, and districts to support English learners (ELs).

Resources supporting ELs at different language proficiency levels in science and mathematics classrooms are sparse. Classroom-based resources supporting ELs' academic language development in science and mathematics based on career and college readiness standards are non-existent. The development of such a resource would have significant impact on science and mathematics teachers' teaching of ELs. Understanding how teachers' practice in supporting content-based academic language changes by using such a resource would be of great value for teachers, administrators, and researchers. Arguably, the ELPD Framework (and the proposed teacher's guide) has applications beyond ELs. Many challenges "at-risk" students face in science and mathematics classes may not be due to a lack in content knowledge, per se, but a lack of ability to communicate in the language of the content. The proposed teacher's guide could help teachers support all students in the language underlying the science and mathematics standards in the CCSS and NGSS.

Teacher's Guide to the Mathematics and Science Resources of the ELPD Framework

CAREER: Scaffolding Engineering Design to Develop Integrated STEM Understanding with WISEngineering

The development of six curricular projects that integrate mathematics based on the Common Core Mathematics Standards with science concepts from the Next Generation Science Standards combined with an engineering design pedagogy is the focus of this CAREER project.

Lead Organization(s): 
Award Number: 
1253523
Funding Period: 
Mon, 07/01/2013 - Sat, 06/30/2018
Full Description: 

The development of six curricular projects that integrate mathematics based on the Common Core Mathematics Standards with science concepts from the Next Generation Science Standards combined with an engineering design pedagogy is the focus of this DRK-12 CAREER project from the University of Virginia. Research on the learning sciences with a focus on a knowledge integration perspective of helping students build and retain connections among normative and relevant ideas and existing knowledge structures the development of the WiseEngineering learning environment, an online learning management system that scaffolds engineering design projects. WiseEngineering provides support for students and teachers to conduct engineering design projects in middle and high school settings. Dynamic virtualizations that enable learners to observe and experiment with phenomena are combined with knowledge integration patterns to structure a technology rich learning environments for students. The research focuses on the ways in which metacognition, namely self-knowledge and self-regulation interact with learning in these technology-enhanced environments.Embedded assessments and student pre and post-testing of key science and mathematics constructs provide evidence of the development of student understanding.A rubric that examines knowledge integration is used to examine the extent wo which students understand how multiple concepts interact in a given context. A mixed-methods research design will examines how students and teachers in middle school mathematics and science courses develop understanding of the underlying principles in STEM. The PI of this award has integrated research and education in this proposal by connecting her research on engineering design and technology-enabled learning environments with the preservice secondary education methods course that she teachs. In addition, she has folded the research into the instructional technology graduate courses of which she is the instructor.

Engineering design is a key area of the Next Generation Science Standards that requires additional curricular materials development and research on how students integrate concepts across mathematics and science to engage in these engineering practices. The technology-rich learning environment, WISEngineering, provides the context to examine how student engineering design principles evolve over time. The opportunitiy for students to provide critiques of each others' work provides the context in which to examine crucial metacognitive principles. Classroom observations and teacher interviews provides the opportunity to examine how the technology-rich engineering design learning environment integrates STEM knowledge for teachers as well as students.

CAREER: Scaffolding Engineering Design to Develop Integrated STEM Understanding with WISEngineering

Electronic Communities for Mathematics Instruction (e-CMI)

This exploratory project builds on twelve years of successful experience with the summer program for secondary mathematics teachers at PCMI. It addresses the following two needs in the field of professional development for secondary mathematics teachers: increase content knowledge and understanding of the Common Core State Standards for Mathematics; and investigate and develop alternative models to conduct content-based professional development that meets the recommendations of the MET-II report.

Award Number: 
1316246
Funding Period: 
Thu, 08/01/2013 - Fri, 07/31/2015
Full Description: 

This 2-year Exploratory project, Electronic Communities for Mathematics Instruction (eCMI), is designed and conducted by the Education Development Center (EDC) in collaboration with the Institute for Advanced Study and the Park City Mathematics Institute (PCMI). It builds on EDC's successful experience over the last twelve years with the design and implementation of the summer program for secondary mathematics teachers at PCMI. It addresses the following two needs in the field of professional development for secondary mathematics teachers: increase content knowledge and understanding of the Common Core State Standards for Mathematics; and investigate and develop alternative models to conduct transformative, content-based professional development that meets the recommendations of the MET-II report. Addressing the need to find affordable, effective professional development models, particularly given the enormous task of helping teachers understand the implications of the Common Core, the project eCMI will design and conduct a research study and pilot a professional development design, centering on the following two questions: (1) How can tools, experiences, and facilitation be structured in order to build an authentic and vibrant multisite community of learners? (2) To what extent and in what ways does participation in eCMI lead to increases in secondary teachers' knowledge of mathematics, particularly the knowledge and use of mathematical habits of mind? The long-term goal is for eCMI to evolve into a common large-scale national professional development program that helps secondary teachers implement the Common Core, with special focus on the Standards for Mathematical Practice.

To create a context for investigating the two questions above, eCMI will develop and pilot a blended program using online and local mathematics facilitation in a course focused on deepening knowledge of mathematics using the Common Core as a blueprint. The project team will refine and extend the "e-table" concept, developed over the past few years at PCMI, in which teachers in different sites work together with a facilitator via sophisticated electronic conferencing technology. The mathematics course will consist of nine three-hour sessions conducted online during the academic year. Each session will integrate challenging mathematics content, carefully designed and focused on developing mathematical habits of mind through problem solving, with explicit opportunities that ask teachers to reflect on the implications of these experiences for their learning and beliefs. Teachers will be asked to spend time between sessions in deeper discussions online by sharing responses to reflective prompts and responding to each other's prompts. Sessions will be delivered to tables of five or six participants and a table leader meeting live at the same site and connected electronically to other sites. Table leaders will be teachers or university faculty experienced with the following style of delivery: serious and challenging mathematics that is driven by problem-based experience. The project team will collect information on teachers' beliefs about the nature of mathematics and their strategies for approaching mathematics.

Secondary teachers who immplement the standards for mathematical practice require extensive experiences in the practice of mathematics. Several professional development programs, including PCMI, have been able to provide such experiences but they are expensive in cost and labor. eCMI will adapt the proven PCMI design, one that uses carefully designed problem sets in which significant mathematical results emerge from reflection on numerical and geometric experiments, to blend online and face-to-face platforms in a way that has the potential to increase the reach of the program by orders of magnitude. The exploratory project, through pilot and research programs, will lay the foundation for such a scale up by working with 15-30 secondary mathematics teachers. Results of the research will inform the field about ways in which teachers can be provided with genuine mathematical experiences through the use of online media paired with local facilitation.

Electronic Communities for Mathematics Instruction (e-CMI)

Developing Rich Media-Based Materials for Practice-Based Teacher Education

This research and development project is premised on the notion that recent technological developments have made it feasible to represent classroom work in new ways. In addition to watching recorded videos of classroom interactions or reading written cases, teacher educators and teachers can now watch animations and image sequences, realized with cartoon characters, and made to depict activities that happened, or could have happened, in a mathematics classroom.

Lead Organization(s): 
Award Number: 
1316241
Funding Period: 
Thu, 08/15/2013 - Fri, 07/21/2017
Full Description: 

The 4-year research and development project, Developing Rich Media-based Materials for Practice-based Teacher Education, is premised on the notion that recent technological developments have made it feasible to represent classroom work in new ways. In addition to watching recorded videos of classroom interactions or reading written cases, teacher educators and teachers can now watch animations and image sequences, realized with cartoon characters, and made to depict activities that happened, or could have happened, in a mathematics classroom. Furthermore, teacher educators and teachers can react to such animations or image sequences by making their own depictions of alternative moves by students or teachers in classroom interaction. And all of that can take place in an on-line, cloud-based environment that also supports discussion fora, questionnaires, and the kinds of capabilities associated with learning management systems. Such technologies offer important affordances to teacher educators seeking to provide candidates with course-based experiences that emphasize the development of practice-based skills. The focus of the project is on mathematics teacher education. This joint project of the University of Maryland Center for Mathematics Education and the University of Michigan will produce 6 to 8 field-tested modules for use in different courses that are a part of mathematics teacher preparation programs. The following two-pronged research question will be resolved: What are the affordances and constraints of the modules and the environment as supports for: (1) practice based teacher education and (2) a shift toward blended teacher education?

The project involves the following activities: (1) a teacher education materials development component; (2) a related evaluation component; and (3) two research components. The development phase seeks to develop both the LessonSketch.org platform and six to eight mathematics teacher education modules for use in preservice teacher education programs from around the country. The modules will be written with practice-based teacher education goals in mind and will use the capacities of the LessonSketch.org platform as a vehicle for using rich-media artifacts of teaching with preservice teacher candidates. LessonSketch Teacher Education Research and Development Fellows will be chosen through a competitive application process. They will develop their respective modules along with teams of colleagues that will be recruited to form their inquiry group and pilot the module activities. The evaluation activity will focus on the materials development aspect of the project. Data will be collected by the LessonSketch platform, which includes interviews with Fellows and their teams, perspectives of module writers, descriptive statistics of module use, and feedback from both teacher educator and preservice teacher end-users about the quality of their experiences. The first research activity of the project is design research on the kinds of technological infrastructure that are useful for practice-based teacher education. The PIs will identify tools that teacher educators need and want beyond the current capabilities for web-based support for use of rich media and will produce prototype tools inside the LessonSketch environment to meet these needs. The second research activity of the project will supplement the evaluation activity by examining the implementation of two of the modules in detail. This aspect of the research will examine the goals of the intended curriculum, the proposed modes of media use, the fidelity of the implemented curriculum, and learnings produced by preservice teachers. This research activity will help the field understand the degree to which practice-based teacher education that is mediated by an online access to rich media would be a kind of practice that could be easily incorporated into existing teacher education structures.

The project will produce 6 to 8 LessonSketch modules for use in teacher education classes. Each module will be implemented in at least eight teacher education classes across the country, which means that between 720 and 960 preservice teacher candidates will study the materials. The project aims to shift the field toward practice-based teacher education by supporting university programs to implement classroom-driven activities that will produce mathematics teachers with strong capabilities to teach mathematics effectively and meaningfully.

Developing Rich Media-Based Materials for Practice-Based Teacher Education

Smarter Together Working Conference: Developing a Shared Curriculum of Complex Instruction for Elementary Mathematics Methods Courses

This working conference will help university professors who teach elementary mathematics methods courses learn to use Complex Instruction, a research-proven pedagogy for building mathematical content knowledge and supporting the learning of diverse students.

Award Number: 
1316235
Funding Period: 
Thu, 08/01/2013 - Fri, 07/31/2015
Full Description: 

This working conference will help university professors who teach elementary mathematics methods courses learn to use Complex Instruction, a research-proven pedagogy for building mathematical content knowledge and supporting the learning of diverse students. In Complex Instruction, educators design tasks that require multiple mathematical abilities to solve. For example, solving a particular task might require computational skills as well as the ability to visualize a 3-dimensional object and represent that object on paper. Through this mathematical complexity, the tasks demand that students engage deeply with mathematics and draw on each others' mathematical strengths. In addition, in Complex Instruction teachers use strategies that minimize status differences in the classroom that impact participation, ensuring that all students - regardless of their popularity, first-language, race, or income level - participate equitably. During the conference, 28 university instructors from across the country will design tasks to be used in mathematics methods courses for prospective elementary teachers. Mathematics educators from University of Georgia, University of Arizona, University of Michigan, and Michigan State University will work together to design and host the conference. The conference is expected to produce a cohort of mathematics educators knowledgeable about Complex Instruction, and who can then support colleagues at their home institutions in learning to use the pedagogy as well as promoting the use of Complex Instruction in mathematics classrooms in U.S. elementary schools.

After learning the essential elements of Complex Instruction, conference participants will design Complex Instruction curriculum modules to implement at their home institutions. Evaluation of the conference will include surveys and phone interviews with conference participants to assess their knowledge of and use of Complex Instruction. In addition, some participants will be selected for more extensive follow-up, including the collection of videos of Complex Instruction lessons in their courses and surveys of their students. Data will be analyzed to identify major themes related to the knowledge of the participants and their students, the supports and obstacles present in various contexts in relation to adopting a new pedagogy, and the impact of Complex Instruction on the methods courses.

All of the tasks and the activities designed during the conference will be available not only to the conference participants but also to anyone interested in Complex Instruction through the website, www.ci.org. In addition, by developing experts in Complex Instruction at more than a dozen universities across the country, the conference will play an important role in disseminating this relatively new, but effective, pedagogy. Evidence about the effectiveness of Complex Instruction suggests that large-scale incorporation of this practice into mathematics methods classrooms will increase the mathematics understandings of prospective elementary teachers and ultimately their students, particularly those in schools with significant numbers of marginalized students.

Smarter Together Working Conference: Developing a Shared Curriculum of Complex Instruction for Elementary Mathematics Methods Courses

From Undergraduate STEM Major to Enacting the NGSS

The Colorado Learning Assistant (LA) model, recognized nationally as a hallmark teacher recruitment and preparation program, has run a national workshop annually for four years to disseminate and scale the program. This project expands the existing annual workshop to address changing needs of participants and to prepare eight additional faculty members to lead new regional workshops.

Lead Organization(s): 
Award Number: 
1317059
Funding Period: 
Thu, 08/01/2013 - Fri, 07/31/2015
Full Description: 

The Colorado Learning Assistant (LA) model, recognized nationally as a hallmark teacher recruitment and preparation program, has run a national workshop annually for four years to disseminate and scale the program. This project expands the existing annual workshop to address changing needs of participants and to prepare eight additional faculty members to lead new regional workshops. Workshop sessions integrate crosscutting concepts, scientific practices, and engineering design as articulated in the Framework for K-12 Science Education (NRC, 2012). Infusing the Frameworks into the workshop helps STEM faculty better understand their role in preparing future K-12 teachers to implement the new standards, by transforming their own undergraduate courses in ways that actively engage students in modeling, argumentation, making claims from evidence, and engineering design. The National Science Foundation (NSF), the Howard Hughes Medical Institute (HHMI), the American Physical Society's PhysTEC project, and University of Colorado-Boulder, provide resources for national workshops in 2013 and 2014 allowing 80 additional math, science, and engineering faculty from a range of institutions to directly experience the LA model and to learn ways to implement, adapt, grow, and sustain a program on their own campuses. Evaluation of the project focuses on long-term effects of workshop participation and contributes to efforts to strengthen networks within the international Learning Assistant Alliance. The launching of 10 - 12 new LA programs is anticipated, and many existing programs will expand into new STEM departments as a result of the national workshops.

Workshop participants are awarded travel grants and in return, provide data each year for two years so that long-term impacts of the workshop can be evaluated. Online surveys provide data about each institution's progress in setting up a program, departments in which the program runs, number of faculty involved, number of courses transformed, numbers of teachers recruited, and estimated number of students impacted. These data provide correlations between workshop attendance and new program development, and allow the computation of national cost per impacted student as well as the average cost per STEM teacher recruited. Anonymous data are made available to International Learning Assistant Alliance partners to promote collaborative research and materials development across sites.

The 2013 and 2014 national workshops train eight faculty members who have experience running LA programs to offer regional workshops for local university and community college faculty members. This provides even greater potential for teacher recruitment and preparation through the LA model and for data collection from diverse institutions. This two-year project has potential to support 320 math, science, and engineering faculty as they transform their undergraduate courses in ways consistent with the Frameworks, in turn affording tens of thousands of undergraduate students (and hundreds of future teachers) more and better opportunities to engage with each other and with STEM content through the use of scientific and engineering practices. STEM faculty who participate in what appears to be an easy to adopt process of course transformation through the LA model, become more aware of issues in educational diversity, equity, and access leading to fundamental transformations in the way education is done in a department and at an institution, ultimately leading to sustained policy changes and shared vision of equitable, quality education.

From Undergraduate STEM Major to Enacting the NGSS

Understanding Space Through Engineering Design

Understanding Space Through Engineering Design investigates how engaging K-5 children from underrepresented populations in the design of packages, maps, and mechanisms supports the development of spatial reasoning and spatial mathematics. The prime conjecture is that engineering design makes spatial mathematics more tangible and purposeful, and that systematic support for spatial reasoning and mathematics, in turn, influences the nature of children's designs and their understanding of how those designs work.

Lead Organization(s): 
Award Number: 
1316312
Funding Period: 
Sun, 09/01/2013 - Wed, 08/31/2016
Full Description: 

Understanding Space Through Engineering Design investigates how engaging K-5 children from underrepresented populations in the design of packages, maps, and mechanisms supports the development of spatial reasoning and spatial mathematics. The prime conjecture is that engineering design makes spatial mathematics more tangible and purposeful, and that systematic support for spatial reasoning and mathematics, in turn, influences the nature of children's designs and their understanding of how those designs work. The project, therefore, serves as a test bed to explore the promises and challenges of an integrated STEM education.

Research methods include intensive close-up study of small groups of children designers led by researchers, followed by larger-scale study of classroom implementations led by elementary teachers. The purpose of the work with small groups of students across grades is to enable the project investigators to learn about the accessibility, challenge, and interest that engineering design holds for youngsters and to inform subsequent steps in revising the instruction for classroom tryouts. The classroom implementations provide data about how engineering design supports mathematical growth and, in turn, how growth in mathematical understanding guides subsequent engineering design. As children design and share their designs, mathematical and engineering practices, such as definition, conjecture, and troubleshooting, emerge in classroom conversation, often when children compare variations in the artifacts that they create. Researchers seek relationships between the emergence of these practices and changes in students' learning; in this way, relations between doing and knowing can be established. Forms of data include video recording of episodes of student design and classroom conversations. In addition, researchers conduct interviews with students to assess their understanding of how the artifacts they create work. The interviews particularly emphasize the role that spatial mathematics plays in students' explanations of device function and in their accounts of design processes. The progress of the project, including curriculum development, interview construction, and data analysis will be overseen by a five-member advisory board that includes a evaluation specialist, a mathematician, a mathematics educator, and a design expert.

The project will contribute to a beginning knowledge base about how integrated STEM education can best be pursued, in particular, by exposing the possibilities and challenges inherent in the proposed emphasis on engineering design. By working closely with 18 teachers and their 500 students, the project investigators aim to develop a practical, yet powerful approach to iSTEM education, that is, a new study of integrated science, technology, engineering, and mathematics. Products include a website featuring a suite of curriculum materials, case episodes of children designing, and formative assessments of children's learning in contexts of everyday classroom activity.

Understanding Space Through Engineering Design
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