
The following are brief
descriptions of funded projects within the Center from 1990 - 2000. Several
of the projects were re-funded multiple times. More details can be found in
individual project proposals and in resulting materials.
The purpose of this project is to study several pilot programs
whose central feature is GIS/GPS technologies; to identify issues that appear
to have been critical for successful implementation of GIs/GPs in these new
programs; and to test these implementation issues in a different educational
setting.
Geographic Information Systems:
Testing Conditions for Classroom Implementation
R. Audet - P.I.
Differential
Equations: A Dynamical Systems Approach
P. Blanchard - P.I.
R. L. Devaney, M.I.
Freedman, and G. R. Hall -
Co.-P.I.'s
This project produced a large-scale revision of the
traditional sophomore-level ordinary differential equations course. The new
course emphasizes qualitative theory throughout with a distinct dynamical
systems orientation. The course provides a brief introduction to difference
equations as a prelude to discussions of differential equations. The computer
is used frequently to analyze solutions and to provide an earlier and more
detailed discussion of nonlinear systems.
See the ODES page.
This project aimed to promote a new style of differential equations instruction, one that emphasizes concepts and applications and one that involves faculty members from both the mathematics and engineering communities. The goal was to promote a style of differential equations instruction that better engages and serves students throughout their college and professional careers.
The goal of this planning grant project was to review energy-based
materials used in the precollege curriculum and analyze the methods and materials
that have been most effective. Its goal was to outline a way to develop materials
which are appropriate for middle and high school students who are at risk
of failing in mathematics and science. Modules were planned which focus on
topics of interest to students, particularly in their home environments. Energy
is the unifying theme, but content would be drawn from all areas of science.
Many of the concepts would be developed through hands-on and microcomputer-based
activities.
Project LITE is a two-year proof-of-concept
project involving materials development, course instruction, and student learning
assessment at Boston University. The project's goal is to develop a prototype
set of integrated educational materials--unique take-home laboratory experiments,
written guides, Web-based software, and lecture demonstrations--which aim
to clarify the nature of light, optics, color, and perception. The project's
major innovation is the development (and introduction into a range of university
courses) of a set of "homelabs"--experiments employing inexpensive original
devices and existing commercial and industrial optical materials. These inquiry-based,
quantitative laboratory experiences are being designed for use by students
in their dormitory rooms.
This project was a collaborative effort between Boston University
and several school districts in the Boston area. Its purpose was to train
high school mathematics teachers to incorporate new topics from dynamical
systems and fractal geometry into the secondary school mathematics curriculum
(grades 7-12). Teachers attended seminars during the summer and learned the
new knowledge base. They also used computers, software and related materials
to gain the practical experience needed to explore the new mathematical concepts
in their classrooms. It is anticipated that within five years the teachers
will have enough confidence with the new topics to incorporate them into the
mathematics curricula at their schools.
This project was a natural extension of Contemporary
Mathematics and Technology as a Driving Force for School Reform (see above).
Its goal was to develop teaching materials that will allow high school teachers
to introduce various concepts from dynamical systems theory and fractal geometry
into their curricula. Videotapes, software, HyperCard stacks, worksheets and
teacher guides were developed. These materials will help teachers to both
enhance their curricula and demonstrate to students the vitality of modern
mathematics.
See the LITE page.
Contemporary Mathematics and Technology
as a Driving Force for School Reform
R. L. Devaney - P.I.
J. Choate and C.
Findell - Co-P.I.'s
Chaos and Fractal Teaching
R. L. Devaney - P.I.
Contemporary Mathematics and the Internet
R. L. Devaney - P.I.
This project is developing six interactive
modules for high school mathematics classrooms that deal with aspects of the
geometry and algebra of chaos and fractals. Each module is a completely interactive
Java applet and is available free on a Boston University web server. The evaluation
includes a study of effective ways teachers use these materials in mathematics
classes. The Linear Web applet allows students to enter a particular linear
function and then view the associated graphical iteration and time series.
The Nonlinear Web applet allows students to view the results of graphical
iteration of nonlinear functions. Target Practice helps students comprehend
the notion of graphical iteration in a "game" setting. The Orbit Diagram applet
brings together the concepts from the previous modules by painting various
orbit diagrams. The Mandelbrot and Julia Set applet assists with visualization
of complex iteration. A sixth applet, The Mandelbrot and Julia Set Explorer,
is a completely interactive primer dealing with the mathematics of these Mandelbrot
and Julia sets.
This project aims to: (1) design and implement an introduction
to quantum science for high school students and undergraduates in biology,
chemistry and physics through activities integrating computer modeling tools,
data resource base, and hands-on experiments; (2) do research on student response
to materials intended to introduce quantum science at a level appropriate
for interdisciplinary inquiry with hooks and paths between biology, chemistry
and physics; and (3) investigate the extent to which technologically rich
approaches to teaching interdisciplinary science can fundamentally change
high school and college instructional practices.
This project developed a three step sequential undergraduate
biology-chemistry experience to retain science majors and to inspire them
to enter research careers. Its integrated biological-chemical modular format
directly relates to and prepares science majors for modern research-oriented
upper division courses which parallel realistic career research experiences.
Materials developed are being disseminated through many organization including
the American Chemical Society.
Mathematics has been neglected at the preschool
and Kindergarten levels. New programs in this area are necessary first to
enable young children to pursue and enjoy their mathematical interests, and
second to prepare them for elementary school. In this project, mathematics
educators and psychologists will develop, evaluate and disseminate a mathematics
program - "Investigating the Big Ideas" - for 4- to 5- year-old children.
At the core will be a two year sequence of explorations and learning activities
aimed at extending and elaborating on preschoolers' informal mathematical
interests and abilities, and developing their understanding of core mathematical
concepts in an enjoyable and exciting way. The materials will be developed
and evaluated over a four year period, with an eye towards large-scale dissemination
in the near future, especially for low-income children.
Quantum Science Across Disciplines
(QSAD)
P. Garik - P.I.
G. Abegg - Co-P.I.
See the QSAD page.
Career Directions: Introductory
Biology-Chemistry
E. Godrick - P.I.
S. Hartman - Co-P.I.
Investigating the Big Ideas: A Mathematics
Program for Preschool Children
C. Greenes - P.I.
H. P. Ginsburg, and R. Balfanz - Co-P.I.'s.
Making the Connections: Undergraduate Algebra to School Mathematics
C. Greenes, P.I.
Boston University in
collaboration with the Education Development Center is developing materials
for a course, Connected Algebra, to prepare mathematics teachers. The materials
will make connections to the mathematics taught at the middle and secondary
school levels. The course will contain detailed information about the ideas,
including historical information and connections to school mathematics; mathematical
investigations that facilitate understanding and application of the key ideas
in mathematics and other content areas; and vignettes of lessons with middle
and high school students dealing with the key ideas. This "proof of concept"
project will result in sample modules on which full development of the materials
could be based.
This project aims to advance understanding
of how the brain generates intelligent behavior by examining our capacity
to think about sequences of events. The problem is being studied within the
project through an interdisciplinary approach. To directly probe brain mechanisms,
neurophysiological experiments are being performed on awake behaving animals.
Computer-based experiments with young children are being used to discover
how children learn sequential behaviors and to test how to optimize such learning.
Behavioral studies are being done on how human infants learn sequences. Cognitive
and neural modeling is being used to discover brain designs and mechanisms
to link the animal neuorphysiological data to the human cognitive data. Through
the analyses of how we learn and remember sequences of events, a foundation
will be built for studying the neural basis of high-level cognitive operations
such as planning and reasoning; for developing better educational software;
and for applying models towards the solution of outstanding technological
problems that require algorithms which emulate human intelligence.
The core of this project was an intensive six-week practicum
designed to teach college faculty members the modern methods of recombinant
DNA and protein analysis. These procedures underlie much of current research
and development in biotechnology, an experimental field which has evolved
rapidly over the past 10-15 years. Since many college bioscience teachers
were trained in an earlier period, they have little or no immediate relevant
experience in this field. However, many of their students will need to use
the methods of biotechnology in their future careers. The project aimed to
bridge this gulf by providing college faculty with the expertise necessary
to introduce the "new biology" into their curricula. Recognizing that college
faculty must operate within financial and time constraints, the practicum
taught low-cost and time-efficient experimental methods appropriate to the
teaching setting.
This project harnesses the tremendous power of computer
technology as a resource for teaching specific topics in mathematics and science.
It focused on random processes in nature and their strong connection to concepts
in probability and fractal geometry. Computer simulations and visualizations
were used to aid the understanding and study of phenomena not visible to the
naked eye, such as the growth of snowflakes or the disordered geometric configurations
of polymer chains. In the process of doing hands-on experiments and computer
simulations, students learn abstract mathematical concepts in a context that
is both concrete and inherently motivating.
This project uses the advanced computer technology of powerful
work stations and supercomputers to zoom into the fascinating submicroscopic
world of water. Through advanced graphics and real-time simulations, students
are given a chance to learn about the properties of water at a molecular level.
A cycle of hands-on activities, games and experimentation is combined with
computer animation to allow students to discover concepts on their own. Guided
by a clear set of "cues" built into the computer display, students are prompted
to examine their own observations and to create for themselves important general
principles. In some classrooms, students are now able to access supercomputers
and their interactive programs from terminals via a high-speed network.
Neurophysiological, Computational
and Educational Studies of Sequence Learning and Cognitive Planning
S. Grossberg - P.I.
H. B. Eichenbaum, E. K. Miller, J.
A. Schickedanz, and E. S. Spelke - Co-P.I.'s
Undergraduate
Laboratory Instruction in Biotechnology
S. Hartman - P.I.
On Growth and Form: Learning Probability
Concepts by Doing Science (OGAF)
H.E. Stanley - P.I.
See the OGAF page.
Learning Science Through Guided
Discovery: Liquid Water and Molecular Networks (WAMNET)
H. E. Stanley - P.I.
See the WAMNET
page.
The primary goal of this
educational research project is to investigate how new materials developed
by two previous projects (see OGAF and WAMNET) affect the teaching and learning
of high school science. The materials, which combine hands-on activities with
visual, highly interactive computer simulations, support a new model of instruction
in which the high school science students are "apprentice researchers" and
the teachers guide them through their investigations. The project is studying
the impact of this approach on student concept development, motivation, understanding
of the scientific process, and attitudes toward science as a career, with
emphasis on female and minority students.
This project produced an interdisciplinary set of curriculum
modules, which introduced high school students to the role of microscopic
randomness in creating macroscopic patterns in nature. These curriculum materials
are based on incorporating hands-on activities, laboratory experiments, computer
simulations and data analysis software developed through previous research
and development projects (WAMNET and OGAF, discussed above). The projects
resulted in workbooks for use in biology, chemistry, earth science and physics
courses.
The aim of this project is to put into students hands the
computer tools to model and visualize many physical, chemical, biological
and other scientific phenomena at microscopic scales. The project is making
use of several new computer tools. One is JAVA, the platform independent language
which enables developers to build applications distributable over the World
Wide Web which run on any computer. The other is the application of "distributed
parallel processing" whereby each computer might be viewed as a piece of a
much larger computational fabric accessible to each student. Students will
make use of this capability to work with a "virtual" parallel computer.
Patterns in Nature (PINS) The focus of this project is to: (1) introduce high school
science teachers to the use of materials developed by the WAMNET and OGAF
projects; (2)prepare teachers for new roles as mentors in a cooperative learning
classroom environment in which students act a research workers, learning through
hands-on activities, laboratory experiments, and visual interactive computer
models of physical systems; (3) identify potential "master teachers" and work
with them to become resource agents for colleagues in their home regions;
and (4) prepare a teacher resource book and leader training kit for national
dissemination of this model.
Boston University, in partnership with the Museum of Science,
Boston is designing and fabricating an exhibit entitled "The Dance of Chance
...Growing Order out of Randomness." The exhibit will integrate graphics,
artifacts, interactive electromechanical demonstration devices together with
state of the art interactive educational computer technology to demonstrate
how probability shapes nature. It is planned as a permanent addition to the
Museum's exhibition program, but is being designed to facilitate easy reproduction
for individual copies or for circulation as a traveling exhibit.
This project will create a new undergraduate interdisciplinary
course in which students explore the key role of randomness in biology, chemistry,
physics and earth science. The curriculum materials used will be adapted and
augmented from activities, experiments, simulations and data analysis software
already developed as individual modules for high school science classes. Existing
modules will be recast into a coherent one-semester course for liberal arts
undergraduates.
This project is a national scale-up of the project "Liquid
Water and Molecular Networks". A modular, multidisciplinary curriculum will
be produced, consisting of an integrated set of materials designed to allow
students to discover for themselves a molecular-scale view of a wide range
of materials from simple liquids and gases to complex proteins. A special
emphasis is placed on investigations of water, a material whose properties
play a critical role in living systems. All the materials will be integrated
into a textbook that will feature a CD-ROM containing complete computer programs,
supporting teaching materials, and laboratory exercises.
The Random Universe
H. E. Stanley - P.I.
See the Random
Universe page.
Teacher-Researcher Collaboration
in Scientific Modeling: The High School Science Virtual Machine Laboratory
H. E. Stanley - P.I.
R. Giles - Co-P.I.
See the The
Teacher Researcher Collaboration page.
H. E. Stanley - P.I.
G. Abegg - Co-P.I.
See the PINS page.
Dance of Chance
H. E. Stanley - P.I.
See the Dance of Chance
page.
The Role of Randomness in Science:
An Interdisciplinary Course for Nonscience Majors
H. E. Stanley, and E.
Taylor - P.I.'s
See the Role
of Randomness in Science page.
Bridging the Gap Between the Microscopic
and the Macroscopic: Student-Led Investigations in Multidisciplinary Science
H.E. Stanley - P.I.
See the Bridging
the Gap page.
Program in Mathematics for Young
Scientists (PROMYS)
G. Stevens - P.I.
D. Fried - Co-P.I.
PROMYS was an annual six-week
residential summer program for 60 high school students who were entering grades
10 through 12. PROMYS offered a lively mathematical environment in which students
could explore the creative world of mathematics. Students attended daily lectures
given by research mathematicians, but the heart of the program was the experience
they gained through their individual and collective efforts to solve an assortment
of unusually challenging problems in Number Theory. College-aged counselors
lived in the dormitories and provided a very effective network for beginning
students. More experienced participants studied advanced topics such as Abstract
Algebra, Dynamical Systems and Combinatorics.
See the PROMYS
page.
Exploration with
PROMYS: Program in Mathematics for Young Scientists
G. Stevens - P.I.
Boston University is conducting a 36-month
Teacher and Student Development through Research Experience project. Ten teacher/student
teams and twenty national students are being recruited each year. A total
of thirty local secondary teachers with 30 local secondary students and 60
national secondary students are divided into four person teams consisting
of one teacher/student pair from the same school and two national students.
These teams conduct six-week mathematics explorations in number theory in
a resident camp during the first year. In the following academic year the
teachers will participate in sixteen half-day workshops developing curricular
materials, as well as offer a research and problem-solving seminar at their
school. A website for student research, publication and communication is being
developed. Teachers and students can return for a second year of advanced
research.
Each year, this residential program placed 30 high school
students who had completed their junior year into research laboratories affiliated
with Boston University and other Boston area universities for six weeks during
the summer. Each student was paired with a research professor and worked in
a laboratory 30-40 hours a week. Students worked with their mentors performing
activities central to the research projects in the laboratories. By working
in the actual professional milieu of science, students learned the substance,
spirit and methodology of scientific research.
Research Internship Program in Science
and Engineering
G. Zimmerman - P.I.