Article
on the New York State Consortium of two and four-year schools
Prepared by
Jack Narayan
September 1999
with input from
Jack Winn, Constant Goutziers, Stuart Boersma,
Alan McCoy, Adam Stinchcombe, Patrick Halpin and Carol Freeman
During the past seven years,
mathematics and science faculty from the New York State Consortium (NYSC),
directed by Jack Narayan, John Winn and Co-directors from several up-state New
York campuses, have responded to the call of their professional organizations to
actively engage and involve their students in the process of learning.
Cooperative learning strategies have been introduced to increase
students’ achievement, create positive relations, and explore alternative
learning styles. SUNY Central
Administration and the individual colleges provided significant cost-share for
three NSF Undergraduate Faculty Enhancement Grants (UFE -- DUE9455113,
DUE9653446, and DUE9752736) and one NSF Course and Curriculum Development grant
(CCD -- DUE9455638). A UFE grant workshop was held in 1997 in Albany, New York,
and featured the project directors of seven NSF-funded national Mathematics
Across the Curriculum (MATC) projects that focus on promoting interdisciplinary
courses in Mathematics, Science and technology (MST).
We currently have formed a Seven College Collaboration for Integrating Inquiry-Based Learning, Mathematics Modeling and Technology into the Mathematics Curriculum (SCCIMT). With new NSF funding (DUE 9950803), the seven schools which represent a subset of the New York State Coalition (NYSC) of some 30 two-and four-year colleges, will adapt and adopt materials and educational practices developed by the principal investigators of the NSF Mathematics Across the Curriculum (MATC) projects as well as other publicly and privately supported Mathematics, Science, and Technology (MST) projects. The seven schools are SUNY Oswego, SUNY Farmingdale, SUNY Oneonta, SUNY Brockport, Adirondack Community College, St. John Fisher College, and Alfred University. Faculty and administrators at these institutions are committed to institutional-wide reform and are endorsing the programmatic changes outlined in this proposal.
Building upon the previous UFE and CCD grants, SCCIMT is now adequately
prepared to adapt and adopt materials and educational practices developed by the
MATC and other MST principal investigators.
In particular our consortium will work closely the Long Island Consortium
for Interconnected Learning (LICIL) and the University of Indiana Project
Mathematics Throughout the Curriculum Project.
John Winn (SUNY Farmingdale) and Alan Tucker (Stony Brook) play a key role
in maintaining the relationship the connection with LICIL. Two of our consortium
members Joseph Harkin and Alan McCoy from SUNY Brockport and John Winn (SUNY Farmingdale)
participated in the MATC Workshop
Friday, July 9 and Saturday, July
10, 1999 Indiana University, Bloomington, IN.
In May of 1999, our consortium, with support from NSF held a Faculty
Enhancement Workshop - Mathematical Modeling and Instructional Strategies at
SUNY Oswego. Twenty faculty from thirteen institutions learned about innovations in the context of mathematical modeling and inquiry-based learning.
The emphasis was on conceptual understanding, an exploitation of the connections
between mathematics and other quantitative disciplines, the examination of
realistic applications, open-ended problem solving, collaborative learning
techniques and use of technology. The workshop presenters included Sheldon
Gordon (Professor of Mathematics, SUNY Farmingdale), David Lomen
(Professor of Mathematics, University of Arizona), Daniel Maki (Professor
of Mathematics, Indiana University), and Dennis Sunal (Professor of Science
Education University of Alabama.)
Dr. Lomen discussed various ways to
help move a course away from a standard lecture format and towards an
environment more in tune with the ideals of an inquiry-based education.
Through the use of articles and headlines from newspapers, elementary
data analysis, the creation of mathematical models, intriguing classroom
activities, and overall course design, Dr. Lomen provided the participants with
many snippets of helpful information. Other
topics discussed included test design, methods of student assessment (including
the use of notebooks and written essays), and the importance he places on knowing
his students.
Dr. Maki gave a brief overview of Indiana University's Mathematics
Throughout the Curriculum project as well as an in depth description of a
mathematics course which relies on projects from industry to teach mathematics
and statistics to liberal arts majors.
As many of the participants had plans on implementing various aspects of
this course at their local institutions, Dr. Maki was extremely patient as he
answered many detailed questions from the audience.
As a result of the extended question/answer session, participants learned
where to get ideas for projects and how to design a course around the projects. Dr. Maki gave many examples of projects that his students
successfully completed. Dr. Maki
also conducted an Excel workshop to allow the participants to work with some of
the actual data and forecasting techniques he uses in his course. Many of the participants were impressed with both the
simplicity and power of a spreadsheet that is widely available on many campuses.
Dr. Sunal helped enlighten the
participants to a potential major stumbling block in science and mathematics
education: the role of a student's "Prior Knowledge".
Through the use of anecdotal stories as well as videotaped student (and
faculty!) interviews, the participants came to see what a major role
Prior Knowledge plays in the classroom. Dr.
Sunal allowed the participants to feel the frustration and anxiety
most likely felt by many students by asking the audience to perform a few simple
drawing tasks using a mirror. Many
participants were equally humbled and enlightened by the experience.
Dr. Sunal emphasized that before students are ready to learn adequately
from a lecture, they first need to be made aware of their prior knowledge and be
able to articulate their misconceptions.
By focusing mainly on real
datasets, Dr. Gordon provided many examples of pre-calculus problems and
activities designed to capture the interest of the student.
Rather than providing students with a few basic examples and then asking
them to perform a series of (rote) tiresome calculations and manipulations, Dr.
Gordon recommended the use of more substantial problems.
These more complex problems should be, by their very nature, more
interesting to the students and provide the students with real-life examples and
motivation as well as practice with the necessary algebraic manipulation.
Dr. Gordon frequently emphasized the importance of having students being
able to recognize simple mathematical models (linear, exponential, logistic,
periodic) and many of his activities focused on attributing the (more) correct
model to a given dataset or phenomenon.
Progress
Report from the Seven Colleges
Alfred
Submitted by Stuart Boersma
As per our NSF proposal, Alfred University has been in the
process of developing Interdisciplinary Lively Application Projects (ILAPs).
Faculty from the Division of Mathematics have enlisted the help of
faculty from other disciplines to write short, in-depth, interdisciplinary
projects that can be used in Calculus and Statistics courses.
·
Stuart Boersma (Mathematics) and Michele Hluchy
(Environmental Studies) have completed a first draft of Graphing Directional Data. This
project introduces students to various methods used to describe, graph, and
analyze angular data. Students use
an aerial photograph of trees felled by the 1981 eruption of Mt. St. Helens to
gather data pertaining to the orientation of the felled trees.
This information can then be used to answer questions relating to the
initial direction of the blast and how the trajectory of the hot gases changed
as they encountered nearby topographic features.
·
Stuart Boersma (Mathematics) and Michele Hluchy
(Environmental Studies) have completed a first draft of Angle of Repose. Students
are asked to collect data and perform appropriate tests of significance to
determine if materials of varying physical characteristics have different angles
of repose. This becomes a matter of
safety if the unstable material is situated where its movement can affect people
or property.
·
Stuart Boersma (Mathematics) and Garrett McGowan (Chemistry)
are completing a first draft of See The
Light! Throughout this project,
the students are exposed to such physical concepts as absorbance of light,
transmittance of light, and Beer's Law. By
modeling the loss of intensity of light as it passes through some solution, the
students can then construct an appropriate Riemann Sum.
The resulting equation can then be interpreted as an integral equation
and solved, yielding the relationship between Absorbance and Concentration.
·
Addison Frey (Mathematics) and David Toot (Physics) are
completing a draft of Tides and Gravity.
Using Newton's Law of gravitational attraction, students investigate the
gravitational influence of the Sun, Moon, and Earth.
Some surprises await!
·
Addison Frey (Mathematics) and Jennifer Taylor (Ceramic
Engineering) are designing a spatially dependent heat flow problem.
SUNY
Oneonta
Submitted by Constant
Goutziers
The goal for Oneonta is the implementation of two national
NSF sponsored initiatives: (1) The Boston University Ordinary Differential
Equations project, by Robert L. Devaney, Paul Blanchard and Glen Hall, and (2)
The ATLAST project in Linear Algebra by Steven Leon.
For the academic year 1999/2000 the grant effort has three
participants (1) Constant J. Goutziers (principal investigator), (2) Frank C.
Kost and (3) David E. Manes.
Implementation schedule:
·
Constant Goutziers used part of the summer to prepare for
implementation of the ATLAST initiative in our first semester linear algebra
course MATH 323. At this moment the
effort is well on its way. The
textbook chosen is Linear Algebra by
Gilbert Strang, ISBN 0-9614088-5-5. Enrollment
in the course is 31 students. We have purchased a MATLAB classroom kit and students have
access to the software in a variety of PC computer labs on campus.
To allow for computer access during tests and quizzes the course meets
once a week in a computer lab. The
other class meetings are in a regular classroom with computer projection
facilities. Feedback from the
students is obtained through evaluation forms distributed approximately once
every five class meetings. Details
like the syllabus, homework assignments, MATLAB handouts and evaluation forms
can be found at Constant Goutziers’ web site http://www.oneonta.edu/~GoutziCJ/fall_1999/math323.html
.
·
David Manes used part of the summer to prepare for
implementation of the ATLAST initiative in our second semester linear algebra
course MATH 324, scheduled for the spring semester of 2000.
David Manes currently attends Constant Goutziers' MATH 323, which gives
allows him to become familiar with the new, technology enhanced, teaching
environment.
·
Frank Kost used part of the summer to prepare for
implementation of the Boston University ODE project in our differential
equations course MATH 277, scheduled for spring 2000. Frank Kost is an experienced symbolic algebra user, and he
intends to support our ODE efforts with Maple, for which our campus holds a
site-license.
SUNY College at Brockport
Submitted by Alan McCoy
Alan McCoy, Computational Science Program, Sandeep Singh, Business
Administration and Economics Joe Harkin, Mathematics are developing a
Computational Science, Business, and Technology (CBT) Program to provide
students with an opportunity to learn mathematics by solving problems in the
real world.
On July 9 and 10, Alan McCoy and Joe Harkin attended the MATC Workshop
(Mathematical Sciences and Their Applications Throughout the Curriculum) in
Bloomington, Indiana. They held discussions with Dan Maki, who has
successfully conducted a similar NSF program and whose materials they are
adapting for Brockport.
The first task was to solicit projects from local organizations. They sent
letters to 225 contacts local to the Rochester, NY area. We have had a
very positive response to these letters, including contacts from the George
Eastman House Museum and M&T Bank. They are currently meeting with the
interested parties to define the projects and select appropriate students.
They have also set up an initial Web page for the project, to be found at:
www.cps.brockport.edu/~cbt.html.
They plan to have students completely involved in the projects during the first
few weeks of the Fall 99 semester.
SUNY Farmingdale - Progress Report
Submitted by Jack Winn
SUNY Farmingdale has taken the initial step to
establish the Center of Applied Mathematics. We have formed an advisory
board, we contacted approximately 25 local businesses, and we are moving forward
on four projects. Dr. Irina Neymotin is working on a heat transfer problem
for Embassy Industries, Dr. Yajun Yang is working on an optimization problem
relevant to Avis Rent-A-Car, Dr. Carlos Marques is working on a traffic flow
problem for local government, and Dr. Lou Perone is working on a statistical
analysis problem for the College. Students will be brought into these
projects in the Spring 2000 semester. We will continue our search for
new projects as well. Below are listed projects by individual faculty.
Project: Optimization of
Baseboard Heaters for Embassy Industries, Inc.
Principal Investigator: Irina Neymotin
On Friday, August 27, 1999 an information meeting was held with two
representatives of Embassy Industries, Inc., 300 Smith St., Farmingdale, NY
11735: Anthony A. Campisi, Sales Manager, and Jamie R. Nella, Engineer. At the
meeting, which was also attended by Dr. Lev Neymotin of Brookhaven National
Laboratory we discussed possible approaches to developing a cooperative research
project between Embassy Industries and the SUNY Farmingdale.
The summary of the discussion and the proposed action plan follow.
The project involving SUNY students should consist of several phases:
1. The students will study technical materials (a publication in an industry
journal and Company's literature on their baseboards) provided by the Company. A
group of perhaps 3 to 4 students will have to be formed at that stage
2. A preliminary discussion will be held at the Company's offices to formulate
the problem and propose the approach of the investigation
3. The students will familiarize themselves with an Engineering Computational
Program, ALGOR suggested by the Company for sensitivity studies. This program
may not be ideal for the application at hand but it can be a starting point for
the next phase
4. The students will do their own search (perhaps using the Internet) for a
Computer based Engineering Program that would better suit their needs for
research
5. The selected program will be acquired by SUNY (possibly splitting its cost
with the Company - this issue was not discussed at our meeting; it can be
addressed at a later time)
6. Using the new program, the students will do the optimization study following
the approach developed in Item 2 (necessary modifications to the preliminary
approach can be made at this stage)
The Company provided us with a hardware sample of an element of the heat
exchanger used in their baseboard heaters. The model for the
optimization/sensitivity studies will be based on its geometry. It was suggested
that the results of optimization performed by the students will be considered
viable for implementation at the factory if Efficiency of the heat exchanger can
be increased by at least 10% while preserving the amount of aluminum required
for construction, or Optimization will allow saving of at least 10% of materials
while preserving the existing heat exchanger efficiency.
During the period from August 28 to September 28 three junior students expressed
interest in the project. All of these students have successfully completed a few
course projects in such sophomore courses as Calculus III and Differential
Equations. The background of these students, however, is not sufficient for them
to comprehend the original technical materials provided by the company.
Therefore, it is necessary to present those materials in a form accessible to
the students: work on this task is currently underway.
DIRECTOR: Carlos Marques
Vehicular Traffic Flow Problems
Objective:
The purpose of this study is to identify and develop quantitative problems
arising from vehicular traffic flow whose solutions are accessible to
undergraduate mathematics, computer science and engineering majors. These
problems will be used as topics for research by the students in Farmingdale's
Math 400 - Problem Solving. This set of problems on traffic flow will
enhance the curriculum by serving as a demonstration of the practical use of
mathematics in a real-world application directly relevant to a problem facing
the Long Island community. An example of the type of the research that we will
contemplate is that of the queue length at a traffic light and how it interferes
with the traffic
at neighboring lights. This is an interdisciplinary project bringing together
mathematics (statistics, differential equations, graph theory etc.),
engineering, computer modeling and actual field traffic surveys.
Local and Global Benefits:
Besides the immediate educational benefits to be harvested by the students at
Farmingdale, it is hoped that some of these students will further continue the
study of traffic flow problems as an undergraduate project concretely relating
to the traffic problems facing Long Island.
Methodology:
1. Acquire expertise in mathematics relevant for the study of traffic patterns,
e.g. dynamical systems.
2. Develop traffic flow problems and exercises.
3. Develop computer and mathematical models of relevant traffic conditions.
4. Identify various points on local roads where students will collect traffic
data for statistical analysis.
5. Prepare materials in order to help students present written and oral reports
of their results. This entails not only helping with the mathematical
content of the presentations but also the teaching of software used to typeset
scientific documents (TEX) as well as software used to perform advanced
mathematical computations.
DIRECTOR: Lou Perone
Subject: Statistics Project - Statistics and
the Campus Community
The goal of this project is to provide a real world learning experience
for students enrolled in a noncalculus introductory statistics course.
During the Fall 1999 semester students in one section of Math 110 Statistics
will work on a project using real world data.
Students will be grouped into teams of four or five students and will be
assigned to work with volunteer mentors from various campus offices. The
Dean of Academic Services and the Office of Institutional Research haveagreed to
provide opportunities for these students. The students will meet with
their mentors to define their projects. It is not intended that the
students be required to use sophisticated statistical techniques but theywill be
expected to keep records of their activity, provide progress reports and present
the results of their project. It is hoped this experience will provide
them with a better understanding of how statistics is used in practice.
Data Processing and Forecasting --
Business Computer Application Approach
Yajun Yang
This project is designed to teach mathematics and statistics using the
real-world data from a car rental company. Predicting the correct rental
demand is vital to the company's daily operation. The project requires students
to build a rental demand forecasting model using either time series models
(moving averages, exponential smoothing) or regression
models. Before students can establish the forecasting model, they need to
have a good understanding of the data. They have to analyze the data by
examining the means, variations, trends, seasonalities, and other statistics.
The project will use business computer software to process the data and forecast
the car rental demand. The students will learn the basic theories and
techniques of data processing and forecasting. They are also expected to present
and interpret their results.
St. JOHN FISHER COLLEGE
Submitted by Carol Freeman
John Fisher College is developing six new courses for pre-service K – 6 teachers integrating mathematics, science and technology. During fall 1999, MSTE 211: Mathematical Explorations in the Real Number System, and MSTE 214: Heat and Motion in Chemical Systems are being taught. MSTE 211 is being revised using problem-based learning (PBL) and inquiry-based learning as the student-centered teaching strategies used to teach the content and MSTE 214 is being developed and taught for the first time using these teaching strategies. Dr. Leslie Schwartz, Chemistry, and Dr. Gerald Wildenberg, Mathematics, are team teaching MSTE 214. MSTE 214 will investigate two major physical phenomena that involve motion and change: heat and chemical systems. The rate of change mathematical concept is developed in MSTE 213 and then further developed in MSTE 214. All courses are being designed so that the mathematical and scientific concepts in the New York State MST Learning Standards are fully implemented and so that all pre-service teachers have a certain level of conceptual expertise. Dr. Carol Freeman and Dr. Kris Green, MST faculty, are revising and developing MSTE 211.
In spring 2000, MSTE 211 will be
revised and taught again and MSTE 310, Dynamics of the Physical World, and MSTE
320, Geometric Perspectives with Technology, will be offered for the first time.
Dr. Kris Green is developing MSTE 310 and Dr. Carol Freeman and Dr. Allen
Emerson, Mathematics, are developing MSTE 320.
MSTE 213, Mathematical Explorations in the Sciences will be revised and
offered for the second time, taught by Dr. Carol Freeman and Dr. Allen Emerson. Each of these courses will utilize problem-based learning and
inquiry-based teaching strategies.
MSTE 320 will provide students with
the opportunity to explore, investigate, make conjectures, and verify various
synthetic, coordinate, and transformational geometry ideas by using technology
to discover geometric ideas by creating multiple examples and experiments,
making observations about the emerging patterns and drawing inferences that lead
to more general mathematical statements. The
course will resemble a hands-on, inquiry-based science laboratory more closely
than it will a traditional geometry classroom.
The development of MST 310 is currently in its second stage.
Stage one focused on identifying the key concepts of physics needed by
middle school teachers. This is a
broad range of content and will help to further develop student knowledge of
both physical processes and mathematical tools.
Stage two involves the development of inquiry and problem based learning
activities for the students. Such
activities will provide introduction to and exploration of the course content.
MSTE 330, Biological Systems, will
be developed during spring 2000 and offered for the first time fall 2000.
SUNY Osweg
Submitted by Patrick Halpin
The main focus of the Oswego project is the infusion of
modeling throughout the mathematics curriculum. In the first year our goal
is to incorporate modeling in the first two calculus courses. During the
second year we will concentrate our efforts on statistics and differential
equations. Eventually modeling will become a common theme in most, if not all,
of our program.
In the first calculus course much of the effort will be expended on gathering
data and fitting the data with mathematical models through regressions using
Texas Instruments calculators. Each instructor of this calculus course is
using a set of labs, which are used weekly by the students during an extended
period. The data gathering devices are the CBR (Ranger) and the CBL
(Calculator Based Laboratory). The labs are designed for students to work on in small groups with possible assistance from
the instructor. For example, in one lab the mathematical relationship
between Centigrade and Fahrenheit temperature is first found by regressing some
data from a newspaper, then by the usual approach of considering the boiling and
freezing points of water at sea level. This early linear model is used to
begin exploring the notion of rate of change. A later lab explores ball drop data through a quadratic regression
and leads the student to the notion of instantaneous rate of change. Still
another lab uses the Ranger to have the student attempt to match certain given
distance-time and velocity-time graphs. Further student assistance is
being supplied through the Newton Club, an optional once a week evening hands on
help session.
The second calculus course is expected to continue this modeling theme.
Implementation will begin during the spring semester. For example,
students will explore the Fundamental Theorem of Calculus through the use of the
Ranger device. The students will create a velocity-time graph. The data,
stored in lists, will be used to approximate the signed area with one of the
numerical methods that they have learned. This value will be compared to
the actual displacement, which is also retrieved from list data. Another
lab will use a force probe with the CBL to discover Hookes Law for a simple
spring. This result will be used in the calculation of the work performed
in stretching the string. The value obtained will be compared to the area
beneath the force-time graph, again approximated by a numerical method.
Other labs will explore topics in Ordinary Differential Equations, which use
exponential and logistic growth models.
Adam is working on a module that will cover applications of trig functions to employment cycles in a resort economy, and is considering a clarity of water module. Water clarity is measured on a logarithmic scale.
Planned Consortium Activities for 99,00
The SCCIMT will hold its fall meeting in Oswego New York on
October 1,2 to share experiences and plan activities for the Spring Semester.