Jere Confrey - US grants

This project will conduct research on the development of students' conceptions of exponential functions. These Principal Investigators have selected exponential functions, a particularly rich and useful set of concepts, because of its propensity for misconceptions and its widespread and significant, applications in mathematics, the sciences and engineering. Through, the use of clinical interviews and the teaching experiment, these investigators will examine students' conceptions, the relationships between their informal and formal knowledge, their interjections and use of concepts across a variety of contexts and the development of metacognitive strategies in the application of these concepts. The project will explore the design and use of a multi-representatival (Laser Disc) instructional systems, to explore options for using its vast memory storage for tracking student problem-solving strategies and student control of instruction. Thus, these investigators hope to significantly advance our understanding of the development of student concepts and create a prototype unit in exponential functions for a precalculus course for high school and college students.

This project examines the development of students' schemes for multiplication and multiplicative rate of change that will enable students to understand the crucial societal and environmental issues of exponential growth. Through the use of teaching experiments, historical analysis and the design of software incorporating new representational and visual forms, the research team seeks to investigate how to improve students' insight in issues of scale, functions, multiplicative rate of change and biological forms of growth. To facilitate the research on secondary students, preliminary work will be undertaken into young children's concepts of multiplication, similarity and growth in relation to a primitive construct labelled "splitting" which is conjectured to be the basis of an approach to multiplication independent of counting. Initial studies will also include an ethnomathematical investigation of scientists' and social scientists' use of exponential functions. Informed by the interview studies, research on whole classroom implementation will be undertaken towards the preparation of applied research products including curricula, case studies of teacher development and software products.

9453876 "Algebra by Design" is a three year project in which researchers and teachers will create design activities for middle school students introducing them to functions and algebraic thinking. Researchers will study students engaged in open-ended design challenges requiring them to use their creativity to build structures, design devices and create vidual displays form the fields of mechanical engineering,physics, art geometry and environmental sciences. these design challenges will present middle school students with a problem, a purpose, constraints, materials and means of evaluation. Interactive technological tools such as function Probe, Shape Shifter, Macmotion, Interactive Physics and Geometer's Sketchpad will be available for students to analyze their projects. Review panels of peers and experts will provide feedback on the projects. projects will be selected for their appeal to success in assisting students in learning to work effectively in algebra. Small group interactions among groups of students and teachers will be studied first as researchers find ways to bridge from design activities to algebraic thinking and back. A set of selected projects will then be used in a year long teaching experiment in a combined technology and algebra class with heterogeneous grouping. Research will be conducted on effective policies for implementing reform, necessary teacher development and improving student outcomes.

9705623 Confrey Quest Mulitmedia Math and Science, Inc. of Ithaca, NY is developing a complete precalculus course to be delivered initially on CD-ROM in a Netscape container. The product has an emphasis on problem solving and modeling using families of functions and transformations. Computer-based quantitative tools and a rich set of interactive diagrams are available and complement the product's use of multimedia resources, including text, graphics, video, photographs, animations, and sound. The product is derived from precalculus materials which have been tested and used with secondary school and undergraduate students as well as preservice and inservice secondary teachers.

ABSTRACT REC 972552 The University of Texas at Austin will accomplish the preliminary planning for a new educational center, called the Center for the Improvement of Science, Technology, and Mathematics Education. The Center, when established, will develop the national infrastructure for research on systemic improvement of science, mathematics and technology instruction. The primary discipline focus would be on the implementation of standards-based instruction, with supporting policy and technology. The planning phase will establish the infrastructure necessary to support the Center. The activities undertaken will include: forging partnerships, within the University and with the state; developing organizational and managerial strategies; establishing sites for implementation activities; and developing a corresponding graduate program. Much of the planning will be accomplished through a series of small conferences, each with a focus on a particular aspect of the Center infrastructure.

This proposal is for support of a multifaceted and comprehensive center for research in systemic reform. The proposal identifies four goals, namely: a) to build capacity and leadership in the domain of system reform research; b) to stimulate other researchers to engage in educational system change theory-based inquiry; c) to increase the base of usable knowledge on effective system practice; and d) to design and field test technological and curricular enablements to high-quality learning of mathematics and science for all students.

This proposal will address the four goals above, in part by establishing national research clusters in various domains of system change (such as complexity and systems as learning organizations).

The project focuses on an analysis of the trigonometric concepts and skills needed to successfully traverse a "knowledge supply chain" towards three technologically reliant fields: semi-conductor fields, graphic arts, and acoustic analysis and design. The study is designed to examine how to establish an explicit linkage between career preparation for high technology positions ranging from technician to engineer or artist and the academic preparation of a high school in the particular instance of trigonometric reasoning. It is believed that such redesign of school practice will be necessary to support a larger segment of the population in pursuing and mastering mathematics-related concepts and skills.

UTeach is a collaboration between the Colleges of Natural Sciences and Education at The University of Texas at Austin, in conjunction with the Austin Independent School District, to improve the preparation of secondary science and mathematics teachers. Anticipating a projected steady state of 500 students, it is becoming one of the largest programs for secondary science and mathematics teacher preparation housed in a research university. The UTeach program includes extensive recruitment among students in the Colleges of Natural Sciences and Engineering and at Austin Community College, financial support for students, and revised pedagogy and content courses for prospective teachers. Project goals include: 1) expansion of guided early field experiences supervised by master teachers; 2) development of exemplary undergraduate courses that model Standards-based instruction and reform of large service courses in science and mathematics that pose particular barriers to students with weak backgrounds; 3) increased use of modern information and communications technologies in both education and subject-matter courses; and 4) attention to issues of equity, including student recruitment and support, as well as program content. While the design of the program addresses the immediate needs of the state of Texas, the project is producing a set of teacher education programs and products that can be used and replicated nationally.

The focus of this research is on parents in poor urban communities and the relationships they establish and the roles they play in elementary schools that are active in implementing reform-based science education. We intend to move the research around parents and science education beyond the underdeveloped belief that parent participation is good for students. We want to know what this participation looks like in centers of urban poverty involved in school science reform efforts, how parents negotiate their actions and understandings with others involved in school science reform, and how a relational systems model might help to shed new insights on the roles parents play in school science reform in poor urban areas. Because we are focusing on parents in urban poverty and because we intend to understand the complexity and depth of parent participation in school science reform, we will make a concerted effort to draw half of the parent participant pool from community, family homeless shelters. These questions are significant given that 20% of all children attend school in urban poverty, and the city represented in this study supports large numbers of homeless families.

Specifically, this REPP proposal outlines a program of research designed to analyze the nature, qualities, and impact of parental relationships and interactions in elementary schools serving poor urban children in Austin, TX that are working to improve science instruction within the scope and spirit of current science education reform initiatives. While it is generally acknowledged that where you find good urban schools you will find caring and motivated parents, it has been difficult to construct an account of parental interaction, grounded in everyday practice, that goes beyond either a general belief that caring and motivated parents matter in effective school reform or a laundry list of things that "good parents" do for their children's education. Using qualitative research methodology, we will research the following questions:

- BELIEFS AND ACTIONS. How do parents in poor urban settings perceive "best practice" in science education in schools initiating science education reform, and what do they see as their role in helping to enact such a process? How do such parental beliefs "measure up" against expectations held by others in the science education reform process (children, teachers, administrators, community leaders) about best practice and parents' roles in such a process? What do parents do to enact their beliefs: at home? in the community? at schools?
- SUSTAINING RELATIONSHIPS. How do parents in poor urban settings negotiate common understandings about beliefs and practices and build sustaining relationships with each other and with actors within the school (teachers, administrators, and their children) in school districts acting to reshape science education in line with current ideas of best practice, especially if and when their beliefs and practices differ from expectations held by these audiences? What are the nature and qualities of these relationships? What kinds of support structures (institutional, material, intellectual) sustain these interactions and relationships?
- SCIENCE EDUCATION REFORM. In what ways does documenting and analyzing the formation, nature, and qualities of sustaining relationships between parents and actors within schools- and the kinds of beliefs and actions those relationships support-shed light on what it means to enact school reform in science education for children in poor urban centers? How might we develop, refine, and implement this model in science education reform?

This is a proposal for a two-day meeting. The meeting will host system reform researchers in science, mathematics emphasizing technology. These researchers represent a number of distinct disciplines including mathematics and science education, organization research, technology and policy. The goal of the meeting is to produce a working research framework by taking stock of the research from these cross-disciplinary fields. The framework will bring some coherence to the systemic movement from the perspective of research. The deliverable will be a report that compares and contrasts what research models work and don't work in an effort to better map this now burgeoning field. The ultimate deliverable will be a series of adaptation studies that will shed light on the possibility for research based systemic studies fundable in ROLE's quadrant IV.

The St. Louis Center for Inquiry in Science Teaching and Learning (CISTL) combines a focus on research into science teaching and learning with a focus on professional development and support needed to bring inquiry-based teaching and learning into K-12 science education in both formal and informal settings. Joining together in this effort are three informal science institutions, two universities, five school districts, one community college system and the Association of Science-Technology Centers (ASTC). CISTL will address the full continuum of science educators -- those entering the field, those in the field and those retooling from one area of expertise to another. Their research agenda focuses on the effect of varying types of collaboration on professional development and the interfaces among the collaborators (education and scientific; formal and informal). A diagnostic tool for assessing strengths and weaknesses in science and inquiry backgrounds will be developed for teachers and other science educators. In addition, the project will create a synergy between research and practice through research based in practice, practice based on research and the translation of results into practical suggestions for educators.

Successful preparation for and passage of algebra remains a major gateway to pursuit of science, mathematics and technology related careers. Students in urban settings in rational number reasoning (RNR), including multiplication and division, fractions, ratio reasoning, scaling, similarity, and the related ideas of decimal and percents. This configuration of topics is also known as the Multiplicative Conceptual Field (Vergnaud, 1983). This project will synthesize the research literature in this area to strengthen urban practitioners' knowledge of how to prepare students for this critical filter (Sells, 1973). It will implement an innovative approach to construct a new resource base composed of three interrelated elements: a) a bibliographic database of studies with coded and searchable characteristics and abstracts, organized into a visual web of authors, works, and topics, b) a data cube of RNR topics, types of reasoning skills, and grade bands that maps the rich array of assessment items used in these studies to national standards, and c) a synthesis of the work into a conceptual corridor in both visual and narrative formats. The project will interlink these databases to permit teachers to follow an effective conceptual sequence as much as can be identified, while generating relevant assessment items for their students, and identifying related readings for their own professional development.

The purpose of this project is to develop technologies for improving laboratory experiences in advanced technical education through the use of internet-accessible, virtual laboratory facilities. Laboratory experiences are a central component of advanced technical education, allowing students to see how what they are learning in the classroom can be put it into practice, enabling them to appreciate the real-world implications of what can seem like very abstract concepts. While the importance of labs is taken for granted by university faculty, the quality of laboratory experiences is highly variable. Reasons for this include the limited understanding of how students learn from lab assignments and the kinds of experiences that are most effective in achieving educational objectives, the time demands that lab assignments place on both faculty and students and the high cost of laboratory facilities, which makes it difficult to maintain adequate facilities for advanced courses. The project seeks to address these issues in the context of advanced technical courses in networking, using an existing facility, called the Open Network Laboratory (ONL). ONL has proved to be a valuable educational tool that allows students in advanced networking and information technology courses to have a substantial laboratory experience that builds upon and strengthens their classroom instruction. ONL is built around a set of extensible, gigabit routers and allows remote users to perform a wide range of experiments and demonstrations, allowing them to directly observe the effects of various parameters on system behavior. This allows them to compare observed behavior with behavior predicted by analytical methods or simulation, helping them to solidify their understanding of the underlying principles, and helping them appreciate the difference between analytical predictions and measurements of real systems. The project activities include a detailed educational study of how sophisticated internet-accessible virtual laboratories such as ONL can enhance the quality of advanced education, and the development of a series of technical enhancements to ONL that will make it more useful as an educational tool. The educational research component will involve faculty at two universities, who are using ONL to teach courses in networking to advanced undergraduates and graduate students, and who will work together with researchers specializing in learning and in evaluation of educational methods. The planned technical enhancements include tools to facilitate instructor observation and interaction with students engaged in laboratory exercises, enable collaboration and information-sharing among students, recording and playback of laboratory sessions to enable asynchronous review and automated analysis, and tools to enable students to contribute to an on-line knowledge base accessible to other students. The intellectual merit of the activity lies in its expected contributions to improved understanding of how laboratory experiences affect student learning and on how specific technical features of internet-accessible virtual laboratories such as ONL, contribute to the overall learning experience. The broader impact of the project lies in its potential use as a nation-wide education resource for educating network engineers.

Confrey, Berger and Wilson propose to develop a software diagnostic tool for integrating diagnostic interviews, group administered assessments, and student data in real-time so that teachers can enter and view student status information. This project would concentrate on rational number learning in grades 3-8. The design is based on a model of learning trajectories developed from existing research studies.

The diagnostic system to be developed for teachers would be used in assessing their students' knowledge and would identify difficulties in understanding five key clusters of concepts and skills in rational number reasoning. It would also investigate the diagnostic system's effects on student and teacher learning in relation to state standards, assessments, and curricular programs. The five areas include understanding: (1) multiplicative and division space; (2) fractions, ratio, proportion and rates; (3) rectangular area and volume; (4) decimals and percents; and (5) similarity and scaling.

The diagnostic measures will include diagnostic interviews collecting data using a handheld computer, two types of group-administered assessments of student progress, one set along learning trajectories for each of the five sub-constructs and one composite measurement per grade. The diagnostic system will produce computer-based progress maps, summarizing individual student and class performance and linking to state assessments.

The goal of this study is to develop a conceptual model for Learning-Trajectory Based Instruction (LTBI). LTBI refers to the ways in which teachers use their own knowledge of a learning trajectory to organize their instructional practice and participate in their professional communities. The study explores the concept of LTBI within a specific content domain termed equipartitioning. Within the study the PIs identifies four distinct cases (e.g., sharing a collection, sharing a single whole, sharing multiple wholes with more persons than objects, and more objects than persons) to be studied. The PI determines that "equipartitioning" is a more mathematically satisfactory descriptor for the overall construct, because, unlike breaking, fracturing, and segmenting; equipartitioning pertains to behaviors that create equal-sized groups.

The PI builds the work on prior findings on equipartitioning, refines the initial working definition of LTBI, and investigates: (1) the ways teachers' knowledge of equipartitioning learning trajectory (EPLT) develops; (2) the ways teachers use their knowledge of EPLT in instruction; (3) the ways teachers use their knowledge of EPLT for participation in a professional development learning community; and (4) the ways in which teachers' knowledge of EPLT is disseminated in teachers' daily interactions at the school.

The study will be implemented in two parts. Part one consists of a design experiment about teacher knowledge development, practice, and participation. Part Two consists of a social network analysis to help determine key connectors that exist in the school network, the extent to which they are effective and how they change over time.

The intervention will focus on an extensive professional development (PD) program where K-5 teachers will participate in 16, six-hour days of professional development over a 12-month period. Multiple venues will be used for PD that will impact approximately 100 teachers and 1200 to 1500 students. A design experiment will be used to focus on both the process of learning and the means that are designed to support that learning. The main form of data analysis will be constant comparison methods in search for grounded theory. Additionally, the proposed methods include initial conjectures for each research question to guide the ways in which data is collected and analyzed.

Partners in this effort include local schools in Durham, NC. Outcomes include a conceptual model of Learning Trajectory-Based Instruction and insight about how teachers use social networking to improve instructional practices.

This project will build and validate learning trajectories (LTs) in mathematics for fraction, ratio, and for decimal and percent to represent learning by grades 3-7 students. A system will be developed to automate data collection for field testing assessment items to determine students' attainment of proficiency levels. Three LTs will be produced and validated along with over 125 assessment items for each of these three trajectories. These assessment items will be useful for diagnosing student learning. Technologies such as mobile phones, tablets, and computers will be used to deliver, analyze, and report diagnostic data on students. The learning trajectories will be available both electronically and in print. The levels of proficiencies will be provided with the outcome spaces, the exemplary items, the student work, and videos of student responses. Publications will provide data on analysis of the diagnostic items and assessments. The project will be done by researchers at the North Carolina State University in collaboration with RoleModel Software Inc.,and the University of Maryland.

The learning trajectories will be developed through literature reviews, whole class teaching experiments, clinical interviews, and large-scale assessments. Students in grade 3 will be observed and interviewed while engaging in work on fractions, ratios, decimal, and precents. Some of these students will be observed longitudinally over the two years. Other students from grades 4 through 8 will be interviewed. For each of the three trajectories, about 150 assessment items will be developed and field tested with a large group.

Three learning trajectories will be developed and made available electronically with supporting materials. The learning trajectories will be done in coordination with the Common Core State Standards (CCSS) in mathematics. Because the learning trajectories and materials will be informative to teachers who will be implementing the CCSS, the work has the potential to appeal to and reach a very large audience. Publications will provide data on analysis of the diagnostic items and assessments. The researchers will seek ways for a greater audience to have access to the software for accessing and retrieving items.

The Discovery Research K-12 program (DRK-12) seeks to significantly enhance the learning and teaching of science, technology, engineering and mathematics (STEM) by preK-12 students and teachers, through research and development of innovative resources, models and tools (RMTs). Projects in the DRK-12 program build on fundamental research in STEM education and prior research and development efforts that provide theoretical and empirical justification for proposed projects. This proposal seeks to design a next generation diagnostic assessment using learning progressions and other research (in the learning sciences) to support middle grades mathematics teaching and learning. It will focus on nine large content ideas, and associated Common Core State Standards for Mathematics. The PIs will track students over time, and work within school districts to ensure feasibility and use of the assessment system.

The research will build on prior funding by multiple funding agencies and address four major goals. The partnership seeks to address these goals: 1) revising and strengthening the diagnostic assessments in mathematics by adding new item types and dynamic tools for data gathering 2) studying alternative ways to use measurement models to assess student mathematical progress over time using the concept of learning trajectories, 3) investigating how to assist students and teachers to effectively interpret reports on math progress, both at the individual and the class level, and 4) engineering and studying instructional strategies based on student results and interpretations, as they are implemented within competency-based and personalized learning classrooms. The learning map, assessment system, and analytics are open source and can be used by other research and implementation teams. The project will exhibit broad impact due to the number of states, school districts and varied kinds of schools seeking this kind of resource as a means to improve instruction. Finally, the research project contributes to the nationally supported move to create, use, and apply research based open educational resources at scale.