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Past Projects

Browse the list below to read brief summaries about the projects that CRMSE members have worked on in the past. The summaries include links to project websites and personal web pages. 

J. Newlin (PI) and Ricardo Nemirovsky (co-PI)Funded by: National Science Foundation. Funding period: 2009-2015.

Math Core for Museums

Description/Abstract: The Science Museum of Minnesota (SMM) is collaborating with the Museum of Science in Boston (MoS), the North Carolina Museum of Life and Science in Durham (NCMLS), Explora in Albuquerque, the Center for Research in Mathematics and Science Education at San Diego State University (CRMSE), and TERC in Cambridge, MA to develop, create and evaluate "MathCore for Museums," long-term math environments that children can interact with over multiple visits and over several years. The project is prototyping and producing 12 open-source, validated interactive exhibits about proportion: fractions, ratios, similarity, scaling, and percentages, basic concepts for understanding Algebra. The eight best exhibits will be replicated for each MathCore museum and the exhibits will be supported by a limited-access website designed to support and extend repeated use of exhibits and further exploration of ratio and proportion. Selinda Research Associates will conduct a longitudinal evaluation of the project. CRSME will conduct a research study of selected exhibit prototypes to investigate when children start to work on proving relations between similarity and proportion in informal settings, the relationship between children's artwork and mathematical insight, and the roles of bodily activity in learning to see relations in similarity and proportion. Results will be disseminated in peer-reviewed publications, at professional meetings, at the Association of Science and Technology Center's RAP Sessions at the NCMLS, and through the project's website.

 

Lisa Lamb, Jessica Bishop, and Randolph Philipp (co-PIs). Funded by: National Science Foundation, 2009-2014.  Project Z Publications

Project Z: Mapping Developmental Trajectories of Students' Conceptions of Integers 

Making sense of integers is particularly challenging for children and yet is foundational for success with first-year algebra coursework. In this research and development project, we will identify students' conceptions of integers across the K–12 spectrum. We will analyze 160 interviews of students in grades 2, 4, 7, and 11, and 30 interviews of specialized adults (those who have revisited their notions of integers by drawing from one of four perspectives: a formal mathematics perspective, a historical mathematical perspective, a children’s mathematical thinking perspective, and a mathematics teacher perspective). Collectively, the conceptions identified across these interviews will help us to map the terrain from informal to expert conceptions of integers.

We propose to use findings from the interviews to create a framework to identify problem types as well as problem-solving strategies as related to student thinking about integers and integer operations. Because we will identify increasingly sophisticated conceptions, teachers and researchers can use the framework to understand students' thinking about integers and to plan next steps to support students' reasoning. To broaden the applicability of our findings, we will use the results from the interviews and subsequent framework to develop a paper-pencil assessment that can be used by teachers and researchers. 

Visit the Project Z website.


Ricardo Nemirovsky (PI)Funded by: National Science Foundation. Funding period: 2008-2013.

Tangible Math: Tangibility for the Teaching, Learning, and Communicating of Mathematics 

The purpose of this project is to conduct research that will take advantage of technical advances in multi-modal and spatial analysis to develop new theories of embodied mathematical cognition and learning. Three university groups will conduct a coordinated series of empirical and design studies that focus on learning the mathematics of space and motion which is a domain that has wide-ranging relevance for what children need to learn in school, and that presents particularly interesting challenges for a theory of embodied cognition. Studies will be conducted in professional workplaces and formal, academic settings where people learn and teach these subject matter areas; they will include professional mathematicians, graduate students in mathematics, professionals working with mapping and spatial analysis, pre-service high school mathematics teachers, high school students, pre-engineering vocational students, and talented middle and high school youth. The Mathematics Technology/CRMSE Innovation Lab at SDSU was developed in connection with this project. 

 

Randy Philipp and Vicki Jacobs (co-PIs)Funded by: National Science FoundationFunding period:June 2005–May 2012. STEP Publications.

STEP Project: Investigating the Needs of Elementary School Teachers of Mathematics at Different Points During Sustained Professional Development

This research project was funded to map a trajectory for the evolution of elementary school teachers engaged in sustained professional development. In Study 1, we use a cross-sectional design to explore the knowledge, beliefs, and practices of three groups of teachers engaged in sustained professional development for different amounts of time. To provide an anchor for the trajectory, we also investigate prospective teachers. Children’s mathematical thinking and classroom artifacts play prominent roles in our measures, analytic lens, and professional development contexts. In Study 2, we collaborate with facilitators from multiple national projects and track how our findings can inform their work with prospective and practicing teachers.

Visit the STEP Project website

 

Leland Beck (PI) and Alexander Chizhik (co-PI), Cooperative Learning Methods for Java-based CSI Courses, funded by the National Science Foundation, CCLI. 

This project involves the development and evaluation of cooperative learning exercises for an introductory computer science class. The exercises involve students in specific roles to focus their attention on key concepts involved in developing and testing Java programs.

Tom Carey. Network Growth Strategy for Statway and Quantway, 2011–2012, funded by the Carnegie Foundation for the Advancement of Teaching.

Kathleen Fisher and Kathy Williams, Springboard To Success! Robert C. Noyce Scholarship Award. 

The Springboard to Success! Noyce Scholarship program at San Diego State University aims to open the science and mathematics education pipeline in middle and high schools in the Sweetwater Union High School District, whose schools serve highly diverse, low socioeconomic populations. The aim is to infuse 24 ethnically diverse, reform-minded science and mathematics teachers into the systems. A related goal is to build a community of practice among science and mathematics teachers and prospective teachers, to enhance and sustain momentum, energy and knowledge about hands-on minds-on learning for understanding. Springboard Scholars are actively recruited, carefully selected, well educated, appropriately placed, and supported by collaborative support providers drawn from the districts and SDSU Colleges of Science and Education. Scholars participate in professional development workshops year-round during their student and teaching years. They engage in action research to monitor and improve both instructional practice and personal growth. They also attend professional meetings with such groups as CSU/NASA and AAAS – Pacific Division. A continuing goal is to promote understanding of the nature of science and of science as a process as well as a body of knowledge. 

Fred Goldberg and Sharon Bendall, Systems and Interactions: Constructing Ideas in Physical Science (now InterActions in Physical Science ), funded by the National Science Foundation. 

The CIPS project has developed an inquiry-based, computer-supported physical science course that engages middle school students in constructing meaningful understandings of important physical science concepts. Topics drawn from the NRC National Science Education Standards and AAAS Benchmarks for Scientific Literacy include the physical science concepts of properties and changes in the properties of matter, the structure of matter, motion and forces, and transfer of energy; the unifying themes of interactions; the nature of science and the scientific enterprise; and some experiences with the history of science and science and societal issues. The program uses a pedagogical model based on two decades of research on science learning, and addresses the importance of checking student understanding and building conceptual knowledge through tangible experiences.  Two editions of the course are published by It’s About Time.  The course is entitled InterActions in Physical Science. 

Fred Goldberg, Sharon Bendall, CIPS Professional Development Project, funded by the National Science Foundation. 

This project has produced a robust professional development (PD) package for school districts to use to support implementation of the InterActions in Physical Science middle school curriculum.  The package engage teachers in substantive and innovative PD over two years, and consists of materials for a Getting Started Workshop, materials for follow-up workshops, online workshops and a comprehensive hyperlinked teachers guide/resource.  Together, these components address national standards in science teaching and learning.  The weeklong Getting Started Workshop introduces teachers to InterActions and to pertinent issues in teaching and learning.  Subsequent workshops address teachers’ emergent needs during their first two years of teaching InterActions.  The PD package was developed by an experienced team of university physical science education researchers, middle school teachers and other experts, and piloted and field tested at three large school systems around the United States.   

Fred Goldberg, Professional Development Materials for Constructing Physics Understanding Among Prospective and Practicing Elementary Teachers, funded by the National Science Foundation. 

Two substantive professional development packages have been developed on this project, each consisting of a curriculum to be used by prospective and practicing teachers and other learners, and a comprehensive set of professional development materials for faculty teaching the course or workshop.  The first curriculum is called Physics and Everyday Thinking (PET, formerly called Physics for Elementary Teachers), and the second curriculum is called Physical Science and Everyday Thinking (PSET). PET and PSET are each one-semester (75-hours of classroom or workshop instruction) general education courses, whose design was guided by research on student learning of physical science.  The PET course content focuses on the themes of interactions, conservation of energy and Newton's Laws, as well as on the skill of writing and evaluating explanations. The PSET course, which includes both physics and chemistry, focuses on the same things plus atomic-molecular theory. Specially designed computer simulators are used in both curricula during class and as part of web-based homework. Each curriculum consists of carefully sequenced sets of activities to help students develop physical science ideas through guided experimentation and extensive small group and whole class discussion. The curricula also include a series of Learning About Learning activities, in which students are asked to reflect on their own learning, the learning of younger children (using videos from classrooms where students are discussing physics or chemistry ideas), or the learning of scientists (the history and nature of science). The professional development materials that support faculty teaching the course or workshop consist of substantive on-line teacher guides and separate teacher resources CDs. The CDs include implementation information as well as classroom videos illustrating the pedagogy used in teaching the course.  In addition to PET and PSET, a separate book called Elementary Children and Everyday Thinking (ESET) provides sample activities, a teacher guide and classroom videos that elementary teachers can use to implement the activities in their own classrooms.  PET, PSET and ESET are all published by It's About Time, Herff Jones Education Division.  

Fred Goldberg (PI).  Developing a Large Enrollment Physical Science Curriculum (LEP). Funded by the National Science Foundation.

This project developed an inquiry-based physical science curriculum for large enrollment, general education settings. The work addressed needs that have not been met in general-education physical science curricula for use in large-enrollment (90+ student) courses: (1) the lack of inquiry-based curricula, (2) the lack of curricula that are coherent and focus on the fundamental content themes of physical science in an integrated way, and (3) unanswered calls for explicit instruction on the nature of science and learning. This curriculum is designed for general education settings, and for pre-service and in-service elementary school teachers.

Fred Goldberg and Sharon Bendall (PIs). Responsive Teaching in Science. (Original project name: Learning Progressions for Scientific Inquiry: A Model Implementation in the Context of Energy.)  Funded by: National Science Foundation Discovery Research K–12 Program. Funding period: 2008-2013.

This project focused on (1) devising learning progressions for students and teachers in scientific inquiry and its facilitation, with respect to energy, and (2) developing model materials and strategies for grades 4-6 curriculum and teacher professional development. One of the outcomes of this project is the Responsive Teaching in Science web site.

Rich LevineJanet BowersChris Rasmussen. Promising Course Redesign of Bottleneck Math/Stat Courses. Funded by CSU Chancellor’s Office. 2013-2014. Developing and assessing pedagogical innovations to improve student success and attainment of learning outcomes in three CSU recognized bottleneck, large enrollment courses: Pre-calculus, Calculus I, Elementary Statistics.  

Joanne Lobato, Coordinating Social and Individual Aspects of Generalizing Activity: A Multi-tiered ‘Focusing Phenomena’ Study, 2005-2008, funded by the National Science Foundation through the ROLE program, 2005-2009. 

The goal of this project is to account for: (a) the ways in which features of classroom environments influence what students attend to mathematically; (b) the particular mathematical focus that emerges in a classroom; and (c) how attention-focusing interactions are related to the ways in which students generalize or transfer their learning experiences. In order to pursue these theoretical goals, a series of empirical studies is being conducted in San Diego and in Madison, Wisconsin involving middle school and high school students learning about the topics of linear functions and quadratic functions. It is anticipated that this research will result in benefits for teachers and their students, by demonstrating how the durable concepts that students take away from instruction are influenced by many subtle and often unintentional aspects of teaching practices involving the nature of how certain mathematical properties come to be the object of focus when multiple sources of information compete for students’ attention. Project personnel include Joanne Lobato (PI, Associate Professor in the Department of Mathematics and Statistics), Amy B. Ellis (Co-PI, MSED Graduate and Assistant Professor in the Department of Curriculum and Instruction, University of Wisconsin at Madison), Ricardo Muñoz (Research Assistant), and Bohdan Rhodehamel (Research Assistant). 

Sandra P. Marshall, Cognitive Models of Decision Making in the Expeditionary Strike Group , funded by the Office of Naval Research.  

This research effort is designed to investigate the ways in which multiple decision makers with different backgrounds and training operate together in a common mission.  The context is the U.S. Navy’s new force deployment of the Expeditionary Strike Group (ESG). The overall objective of the project is to create a general schema model of decision making in the ESG.  This model will build on previous models of tactical decision making and problem solving as well as on existing models of group decision making.  Its unique contribution will be a common schema structure that applies to decision makers with varied backgrounds and areas of expertise.  As such, the model should be equally applicable to individual decision makers, teams of decision makers at comparable levels of command, and multi-echelon decision makers.  

Cheryl L. Mason (Co-PI), Dennis Sunal (PI) & Cynthia Sunal (Co-PI), University of Alabama; & Dean Zollman (Co-PI), Kansas State University, STEEP (Science Teacher Education and its Effect on Practice), funded by the National Science Foundation. 

This $2.1 million, 5-year project (2006-2011) focuses on critical needs in the undergraduate preparation and long-term professional development of K-6 teachers of science. The goal is to investigate the impact on these students of undergraduate, standards-based, reform undergraduate science courses developed by faculty in the NASA Opportunities for Visionary Academics (NOVA) professional development model. Thirty reform and 30 comparison undergraduate science courses from a national population of 101 diverse institutions, stratified by institutional type, will be selected and compared in a professional development impact design model. CRMSE’s Dr. Cheryl Mason and MSED first-year doctoral student, Corinne Lardy, will serve as the western region research team for STEEP, collecting data from study institutions within the Western United States, as well as helping to coordinate larger aspects of the project as a whole.

Ricardo Nemirovsky, SLC Catalyst: Research on Embodied Mathematical Cognition, Technology, and Learning. 

The goal of this SLC Catalyst activity is to bring together leading researchers in the fields of education, neuroscience, psychology, sociology, and mathematics to develop plans for a Science of Learning Center that pursues research on embodied mathematical cognition, technology, and learning. The Center will develop theory and empirical research that can encompass (a) the rapid emergence of new technologies and types of professional work that involve mathematical description and analysis, (b) the challenges of providing all students with equitable access to powerful forms of mathematical thinking, and (c) the need to prepare learners for the increasingly unpredictable demands of work and public life.

Susan Nickerson, Collaborating to Learn Mathematics and Improve Practice, funded by the Improving Teacher Quality State Grants Program ( California Postsecondary Education Commission).  

A primary goal of the project is to provide middle school teachers in low-performing urban schools with the opportunity to develop a profound understanding of mathematics and to couple this with support for developing stronger instructional practice. The project activities are grounded in the study of mathematics and provide opportunities for collaborative learning and reflection focused on instructional practice at the school site. The teachers' professional development experience is planned and tightly coordinated with the Secondary Site Mathematics Administrators. This project represents a significant effort at promoting coherence between university-based and school-based learning experiences. The first research study investigates the effectiveness of our professional development efforts. The second research study takes a perspective that the learning processes of teachers encompass more than explicit teaching events and that the practices of the teachers are situated within the communities of the schools and school district in which they work. The second study has a goal of understanding the projects' coherence, scalability, and sustainability. 

Walter Oechel and Donna Ross, GK–12: K–6 Science Corps Fellows for the San Diego PISCES Project, funded by the National Science Foundation. 

The PISCES Project is a district-based, community-supported elementary science improvement program for grades K through 6. For the first time in the participating school districts a collaboration model has been built through the consensus of all the partners (schools, universities and local corporations) to form science leadership teams across San Diego County and carry out the following enterprises: 1) Nurture systemic leadership for ongoing science education improvement in each school district. 2) Provide a high-quality, research-based professional development program in elementary science for district leadership teams and teachers and support its in-depth replication within each district. 3) Create a Science Corps in collaboration with higher education and industry to support schools and teachers in the use of exemplary science instructional materials and pedagogy. The project is the next step in an ongoing countywide initiative to exploit the full benefits of collaboration between schools and the region’s science-rich corporations, research centers, and universities. Eight district teams of teachers, administrators, and university and industry scientists have collaboratively developed a five year plan for curriculum, materials support, professional development, assessment, and administrative and community support.

Randy Philipp and Vicki Jacobs, Studying Teachers' Evolving Perspectives (STEP): A Cross-Sectional Snapshot of Teachers Engaged in Sustained Professional Development Focused on Children's Mathematical Thinking, funded by the National Science Foundation.  STEP Publications

In this 5-year (2005–2010) Teacher Professional Continuum project, the researchers seek to map a trajectory for the evolution of elementary school mathematics teachers engaged in sustained professional development related to children’s mathematical thinking. Four cohorts of 30 teachers each are differentiated on the basis of the length of their participation in such professional development: initial participants (in the beginning stage), advancing participants (completed 2–3 years), teacher leaders (completed at least 4 years and assumed leadership roles), and prospective teachers, a critical anchor for the initial participants’ evolutionary trajectory. Using a cross-sectional design to investigate teachers at distinct points along the trajectory, the researchers will design and employ beliefs surveys, noticing instruments to assess teacher interpretation of classroom interactions, observation protocols for professional development and classroom instruction, and content assessments to answer their research question: What are the similarities and differences among elementary school teachers at three points during sustained professional development in terms of their knowledge, beliefs, and practices? Additionally, a longitudinal analysis of six cases will provide important information about the changing needs of teachers while they evolve from initial participants to advancing participants. Secondary to the central research question is a formative assessment of the relevance and application of the research findings to providers of disparate models of professional development for both prospective and practicing teachers. 

Randy Philipp and Judith Sowder, Integrating Mathematics and Pedagogy (IMAP), funded by the National Science Foundation. 

This project is designed to integrate information about children’s thinking about mathematics into mathematics content courses for college students intending to become elementary school teachers. 159 prospective elementary school teachers engaged in one of several experiences to support their development as teachers of mathematics. Studies indicate that teachers who participated in the courses had more powerful growth in their mathematics content understanding and beliefs about teaching and learning mathematics than teachers who did not.

Chris Rasmussen, Differential Equations: Building a Theory of Student Reasoning and Understanding, funded by the National Science Foundation. 

The purpose of this project is to enlarge our understanding of how emerging analyses of student thinking, technology, context problems, and symbol use can be profitably coordinated to promote student learning of advanced, undergraduate mathematics, using differential equations as a specific case. The project will illustrate how theory-driven work at the elementary and secondary level can inform, guide, and sustain the learning and teaching of university mathematics in technology-rich classrooms. The particular perspective that guides this research is a version of social constructivism termed the “emergent perspective.” The project also draws on the theory of Realistic Mathematics Education, developed over the past two decades at the Freudenthal Institute. The research methodology employed in this project falls under the heading of “design research.” Design research highlights the dialectical relationship between research and practice, centering on the learning-teaching process with particular attention to the mental activities of students. Three one-semester-long classroom teaching experiments and individual student interviews will be conducted over a period of five years. Data sources will include videorecordings of all classroom sessions, videorecordings of student interviews, copies of student work, and records of project meetings. Data analysis will follow the constant comparative method adapted for longitudinal classroom videorecordings and multiple data sources. The integrated education plan focuses on the creation of a shareable, local instructional theory underpinning a sequence of instructional activities designed to promote students’ mathematical development in differential equations.

Chris Rasmussen, Investigating Issues of the Individual and the Collective along a Continuum between Informal and Formal Reasoning, funding by the National Science Foundation. Students often find the transition from taking calculus courses to more rigorous, proof-based mathematics courses particularly challenging.  The focus of this project is to use the instructional design heuristics of Realistic Mathematics Education (RME) as a tool for creating courses that help students bridge this transition.

Marcy Towns, Chris Rasmussen, John Thompson, and Warren Christensen, Collaborative Research: A Conference to Promote the Integration of Research on Undergraduate Mathematics, Physics, and Chemistry Education, funded by the National Science Foundation.

The literature indicates in large measure that synergies and partnerships between research in undergraduate mathematics education (RUME), physics education research (PER), and chemical education research (CER) have not emerged as a feature of the landscape in those fields. While this finding might be expected because such nascent fields of inquiry need to establish themselves, such compartmentalization is, in the long term, unproductive for the national improvement of the teaching and learning of STEM disciplines. A goal of this project is to transform the compartmentalized way in which mathematics and science education research is conducted and reported by bringing together leading researchers in undergraduate mathematics, physics, and chemistry education for two four-day intensive conferences. In addition to sharing methodologies, projects, and findings, these conferences will create collaborative research programs and build capacity for such integrative work by involving a significant number of graduate students in mathematics and science education.


Donna Ross. Bahia: Secondary Students Teaching Teachers. Funded by: Improving Teacher Quality State Grants Program (California Postsecondary Education Commission). 

The BAHIA program uses an intensive educational experience, including 5 weeks at a field station in Bahia de Los Angeles, to teach marine science content to high school English Learners. The Hoover High School students spend 17 weeks together, with support from scientists, museum educators, graduate students and the primary investigators. Close mentorships are forged, building on the academic strengths of 11th graders and the Spanish language skills of 9th graders. BAHIA provides an intense science experience in a novel and scientifically rich environment. 

After thorough preparation, the students, with support from scientists and educators, lead professional development for science in-service and pre-service teachers. BAHIA recognizes and values the community's existing cultural and linguistic strengths and strives to improve attitudes about students' abilities, equity in science, and environmental stewardship while imparting science content knowledge.

 

Rafaela M. Santa Cruz, No Child Left Behind, funded by the California Department of Education thorugh the UC Regents. 

NCLB funding supports professional development activities designed to meet the following goals: 

Goal I. In collaboration with the schools and districts, SDMP will provide technical assistance to teachers that enable them to meet licensing and certification requirements to become highly qualified pursuant to California policy and federal law (ESEA, 2001). 

Goal II. In collaboration with the schools and districts, SDMP will provide technical assistance to teachers that support the development of the academic content knowledge and content-specific pedagogical skills required to teach in accord with California Academic Content Standards and promote student achievement consistent with such standards. 

Goal III. In collaboration with the schools and districts, SDMP will provide technical assistance to teachers to develop the knowledge and skills needed to ensure that English Learners (EL) have full access to the core curricula and demonstrate satisfactory (or better) academic literacy skills - reading and writing - in the core content areas. 

Goal IV. In collaboration with the schools and districts, SDMP will provide technical assistance to administrators and teachers that support LEAs in meeting or exceeding Annual Yearly Progress (AYP) and Academic Performance Indicator (API) goals.