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 MuseumsDescription/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 Foundation. Funding 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.
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.
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.
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
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.
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 Levine, Janet Bowers, Chris 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.
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
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).
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.
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
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.
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.
Philipp and Vicki
Jacobs, Studying Teachers' Evolving Perspectives
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.
Philipp and Judith
Sowder, Integrating Mathematics
and Pedagogy (IMAP), funded by the National Science
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.
Rasmussen, Differential Equations: Building a Theory
of Student Reasoning and Understanding, funded by the National Science
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
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
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.
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
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
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.
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.