March 5-7, 2014 Washington, D.C.
2014 Annual Grantees Meeting for NSF's
Science, Technology, Engineering, & Math
Talent Expansion Program (STEP)
Interdisciplinary Mathematics in STEM Education:
Undergraduate Retention and Research
Arcadii Grinshpan
Mathematics Umbrella Model
at the University of South Florida
* Updated to December 18, 2014
Challenges in college math education
• Most STEM professionals seem to agree that the overall quality of STEM education and research is closely connected with the quality of college level mathematics education: – over 89% of multidisciplinary STEM faculty and 97% of STEM students polled by our
team strongly support it.
• We believe that the difficulty in gearing students towards STEM disciplines while teaching math classes is a symbiosis of K12 legacy issues (under-preparedness to deal with routine math questions combined with underdeveloped creativity for deciphering real-life problems) and the wide spread abstractness of teaching mathematics at the college level.
• While taking pure math classes, many STEM students outside of mathematics lose interest in completing a STEM degree. For example, solutions to numerous industrial, business, and research problems require calculus methods; but when calculus is taught from a purely mathematical standpoint, many STEM students have difficulty understanding the subject, and the reason for studying it becomes elusive.
Mathematics Umbrella Model
• The University of South Florida's (USF) Mathematics Umbrella Group (MUG) bridges the gap between mathematics education and applications, while inspiring STEM students to attain the math skills essential for success in their respective disciplines. The MUG program is aimed at bringing creative, experiential learning into the curricula of undergraduate math courses through an optional project that can substitute for some course requirements. It forges a mutually beneficial partnership along educational lines between mathematics faculty and the non-mathematical community.
• Students embark on individualized business/science projects with mathematics application guided by both a mathematician and a subject area specialist. The projects are chosen from an area outside mathematics, often closely related to either the field of a student's study or a real-life problem within the Florida business community. This ensures that math content is relevant to the students' interests and aptitudes.
Project-option classes
• Standard knowledge assessment is administered throughout the semester. In-class tests covering the basic concepts are important. As a follow-up a student does a project or takes a comprehensive final exam.
• The project option is currently offered to students in Engineering and Life Sciences calculus classes and is designed to allow them to participate in doubly supervised, interdisciplinary (mathematics application) activities.
• As students are not obligated to participate in this option we call these classes the project-option ones.
• Each project must be guided by a subject area advisor and math advisor (usually a calculus instructor).
• The subject area may include any related STEM disciplines such as engineering, natural sciences, medicine, or other fields: economics, finance, etc. A subject area advisor may be a faculty (or PhD student) in these disciplines or a business professional.
Test 1 Test 2 Test 3
ComprehensiveFinal Exam
Project
All Course Curriculum
Project-only classes
• Some evening classes which are predominately occupied by working students are designated as project-only sections where students are encouraged to seek projects within their own work environments.
• The project-only model is suitable for these classes since most of the students attending are employed elsewhere, and they are often eager to incorporate their working environment within the course material.
Technology and students’ projects
• Online submission and evaluation
• Dissemination of the results
• Anti-plagiarism strategies
• Data analysis
Sinkhole Repair
While taking engineering calculus, C. Griffith was working for a sinkhole repair company which drills holes (some vertical, some askew) around the perimeter of a house, down to the bedrock, and fills them in with concrete. These repairs are common in Florida since it sits on a carbonate platform making the region highly susceptible to sinkholes.
The profitability of a sinkhole repair company is contingent on mixing the proper amount of concrete for each job (concrete should be poured continuously as it hardens if mixed and not used).
By calculating the modeled area between the surface of the ground and the bedrock, Griffith estimated the total amount of concrete needed for the repair pictured in Fig 1 to within 8% of what was actually needed. Griffith's work will appear in the upcoming issue of the UJMM.
Model of the holes drilled to stabilize a house atop a sinkhole. The surface is blue and the bedrock is brown.
Volume of Lake Behnke
For her life sciences calculus project, K. Deutsch contacted the director of USF’s botanical gardens to obtain a current bathymetric map of Lake Behnke, USF’s main stormwater drainage basin. Using contour integration, she found that the lake has changed from the linear area-to-depth relationship noted by the DPRM stormwatermanagement study conducted in 1998 to a quadratic area-to-depth relationship. This suggests that the topography of the lake has changed extensively over the past 14 years.
Deutsch also presented her poster at the 2012 STEP UP for Applied Calculus poster conference. She was recently named a 2014 Goldwater Scholar.
Bathymetric map of Lake Behnke.
Peak OilT. Luong, while taking a life sciences calculus class, estimated the remaining level of U.S. oil reserves. She modeled the crude oil production from 1859 to 2010 using the records published by the U.S. Energy Information Administration. Based on her model, she computed the “peak oil” by finding the derivative of the modeled crude oil production over time. By integrating the model from the present to the projected end of the oil production, she was able to estimate the remaining U.S. oil reserves.
Luong won a cash prize for her poster at the STEP UP for Applied Calculus: Undergraduate Student Poster Conference. Subsequently she received a DAAD (German Academic Exchange Service) RISE scholarship for an internship in Germany.
0
500
1000
1500
2000
2500
3000
3500
1856 1876 1896 1916 1936 1956 1976 1996 2016
Bar
rels
(Th
ou
san
ds)
Time (Years)
Calculated data
Production curve
Pallet Physics
Each night at Publix, delivery trucks arrive and need to be unloaded. Occasionally the pallet jacks break and the employees have to unload the trucks by hand. L. Woodbridge, a high school student taking engineering calculus, explored whether it was safe to unload a pallet from a supply truck by sliding it down a metal ramp. First she calculated the critical angle for which the palletwould overcome the friction of the wood on the metal and begin to slide. After calculating the pallet’s acceleration, velocity, and displacement, she concluded that it would not be safe to unload the truck in this manner.
Area of a Baseball Field
Motivated by his interest in baseball, J. Courchaine wanted to identify the costs of building a baseball field to Major League Baseball’s specifications. In particular, he considered the amount of clay need to cover the catcher’s box, pitcher’s mound, and infield, and the amount of fertilizer necessary to grow the grass for the infield diamond and outfield.
Most of a baseball field’s design follows basic geometric patterns (circles and squares), however the back wall of the outfield is an arc of an ellipse, i.e., center field is farther from home plate than the left and right outfields. Courchainedivided his model into smaller parts and used the inverse trigonometric integration techniques that he learned in engineering calculus to find the area of each of the subregions.
A baseball field with half the outfield highlighted in blue.
MOTIVATION
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• While taking pure math classes, many STEM students lose interest in completing a STEM degree
• Engineering students are required to take the calculus sequence and differential equations before ever starting their major courses
Current Challenge
Too many STEM students are neither motivated nor prepared to learn calculus as pure math content
Current Challenge
Motivated
Prepared
STEM Students
1. The quality of STEM education and research is closely connected with the quality of collegiate mathematics education.
2. The calculus sequence is a significant part of the collegiate mathematics education for STEM majors.
3. When calculus is taught as a pure mathematical content, most STEM students understand the subject and realize why they need to study it.
Take Quiz / View Results
True-False Quiz
24
• STEM students are judged on their ability to solve formal
math problems, but STEM disciplines rely on applying
mathematics
• Many math instructors are reluctant to adapt mathematical
methods to the professional interest of their students
– In fact all STEM students are required to learn math, but
mathematicians are not required to learn other STEM
disciplines in depth
Current Challenge
26
• The Calculus and Differential Equation sequence is the first
viable opportunity for STEM students to connect
mathematical tools with their professional interests and
community problems
– Solutions of numerous industrial, business, and research problems
require calculus methods
– Upper level calculus students are sufficiently mature and
motivated to collaborate with community professionals and
university faculty
Opportunity in Calculus
MATHEMATICS
UMBRELLA
MODEL
Aims & Scope
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The Mathematics Umbrella Model (MUM) was introduced
in 1999 by
• Arcadii Grinshpan
and developed jointly with
and others.
29
Mathematics Umbrella Model (MUM)
• Jonathan Burns, • Scott Campbell,
• Andrei Chugunov, • Gordon Fox,
• Marcus McWaters, • David Milligan,
To date, implementation of the MUM at USF has led to
• 1,909 interdisciplinary student projects involving
• 210 USF faculty members,
• 91 non-faculty professionals (USF), and
• 645 members of the surrounding professional
community.
30
Mathematics Umbrella Model (MUM)
1. Bring active experiential learning into the curricula of collegiate mathematics courses through individual interdisciplinary (mathematics application) projects
2. Forge a mutually beneficial partnership between mathematics faculty and the non-mathematical community along educational lines
3. Consider interdisciplinary projects as components of collegiate mathematics education
31
Mathematics Umbrella Model (MUM)
• Teach in a friendly environment with a focus on basic concepts and applications
• Encourage undergraduates to apply mathematics to their workplaces and fields of interest
•
interests through real-life problems and technology
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Mathematics Umbrella Model (MUM)
• Guide individual interdisciplinary projects with double supervision:
– a mathematics advisor
• most likely, calculus instructor
– a subject area advisor
• an expert in the project field who suggests the problem
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Mathematics Umbrella Model (MUM)
• Provide as much time for project development as possible during the semester
• Use individual project environments to educate students and test their understanding
• Comprehensive final exam can be omitted, provided that the basic concepts are tested by the in-class tests during the semester
34
Mathematics Umbrella Model (MUM)
• Help students to develop their critical thinking, writing, technological, and computational skills to reach their project objectives
• Provide as many office hours as possible for project discussions
• Use select projects for Course and Curriculum Improvement
35
Mathematics Umbrella Model (MUM)
•
serving the community
• Support collaboration of students, mathematics advisors, and subject area advisors beyond educational lines
• Provide undergraduate research opportunities
36
Mathematics Umbrella Model (MUM)
– Significantly increased
motivation and STEM retention
– Real-life problems in the field of
interest
– Better understanding and
retention of calculus
– Connecting with the professional
community
– Opportunities for research
Strengths
Students
Non-Math
Faculty
Math Faculty
Community
Professionals
CENTER FOR INDUSTRIAL
AND
INTERDISCIPLINARY MATHEMATICS
MUM Implementation
38
Center for Industrial and
Interdisciplinary Mathematics (CIIM)
• Home to the Mathematics Umbrella Group (MUG)
– Coordinators and Technical Support
• Publisher of the Undergraduate Journal of Mathematical Modeling: One + Two (UJMM)
• Organizer of student research conferences
– STEP Up for Applied Calculus: Undergraduate Research Student Poster Conference
– Oktoberfest: Research Symposium
Interdisciplinary Projects and Undergraduate Research
40
Center for Industrial and
Interdisciplinary Mathematics (CIIM)
Student
Online Publication
Subject Area Advisor
Math Advisor
Conference/Presentations
2
1
1
4
3
5
6
7
7
Coordinators and Advisors
AG
JBGraduate Assistants
SCEngineering and Related
Fields
GFBiology and
Related Fields
Independent Internal SAAs
External SAAs
Calculus Instructors
• Director of CIIM
• Coordinator of STEM and business
• Leading math advisor
ArcadiiGrinshpan
Coordinators and Advisors
AG
JBGraduate Assistants
SCEngineering and Related
Fields
GFBiology and
Related Fields
Independent Internal SAAs
External SAAs
Calculus Instructors
• Coordinator for the
College of Engineering
(6 Departments)
• Leading engineering
advisor
ScottCampbell
Coordinators and Advisors
AG
JBGraduate Assistants
SCEngineering and Related
Fields
GFBiology and
Related Fields
Independent Internal SAAs
External SAAs
Calculus Instructors
• Coordinator for
Biology faculty
• Leading biology
advisor
GordonFox
Coordinators and Advisors
AG
JBGraduate Assistants
SCEngineering and Related
Fields
GFBiology and
Related Fields
Independent Internal SAAs
External SAAs
Calculus Instructors
• Coordinator for STEM
graduate advisors &
technical support
• Leading graduate
advisor
JonathanBurns
Coordinators and Advisors
AG
JBGraduate Assistants
SCEngineering and Related
Fields
GFBiology and
Related Fields
Independent Internal SAAs
External SAAs
Calculus Instructors
Coordinators and Advisors
Math Advisors: Weekly office hours and extra time at the end of the semester
Subject Area Coordinators: Project recommendations may be obtained during the first 3 months
Subject Area Advisors: No restrictions
Research Assistants: Additional help provided by a group of STEM PhD Students (during the final 4 weeks of the semester)
Instructional Guidelines Provided for:
1. Subject Area Advisors
• Suggestions
• Grading Rubrics
2. Instructors
3. Students
• Technical Writing Tips
• Deadlines & Submission Rules
MUM Guidelines
Project Submission Period:
• After last test to the end of the semester (10-12 days)
• For example, Fall 2014: 12/04/14 - 12/15/14
Online Submission & Evaluation
Undergraduate Journal of Mathematical
Modeling: One + Two (UJMM)
• Advisors recommend high quality projects for online publication (http://ciim.usf.edu/ujmm)
• Editorial board selects projects based on:
– Quality
– Diversity of subject areas
– Usefulness
• Employs STEM PhD students to assist the selected students edit their projects before final publication
ISSN: 2326-3652
Undergraduate Journal of Mathematical
Modeling: One + Two (UJMM)
• Editorial Board
– Arcadii Grinshpan, Editor
– Scott Campbell, Engineering Editor
– Gordon Fox, Biology Editor
– Jonathan Burns, Managing Editor
– Egor Dolzhenko, Associate Editor
– David Milligan, Associate Editor
– Rebel Cummings-Sauls, Production Editor
ISSN: 2326-3652
Undergraduate Journal of Mathematical
Modeling: One + Two (UJMM)
Graduate Content Editors:
– Helen Barclay
– Andrew Burruss
– Joy D'Andrea
– Elliot Findley
– Matthew Fleeman
– Daria Karpenko
– Michelle Krause
– Vindya Kumari
– Aaron Landerville
– Stephen Lappano
– Chamila Siyambalapitiya
– Joseph Van Name
Undergraduate Research Conferences
STEP Up for Applied Calculus:
Undergraduate ResearchStudent Poster Conferencesat the University of South Florida
September 29, 2012April 5, 2014
Oktoberfest:
Research Symposiumat the University of South Florida
October 26, 2012
PROJECT DATA SUMMARY
53
Upper Level Engineering Calculus (ECII&III),
Life Sciences Calculus (LSCII), and
Pure Calculus Courses (CII&III)
Spring 2000 Fall 2014:
Total 144 sections (6,633 students)
Applied Calculus Project or Comprehensive Final Exam,provided that the basic concepts are covered by the in–class tests.
Project Option Sections
Project Sections by Subject
84
43
15
2
Engineering Calculus
Life Sciences Calculus
Calculus (Pure)
Business Calculus
All Project Option Sections: 144
Number of Project Option Sections
05
1015
S0
0F
00
S0
1F
01
S0
2F
02
S0
3F
03
S0
4F
04
S0
5F
05
S0
6F
06
S0
7F
07
S0
8F
08
S0
9F
09
S1
0F
10
S1
1F
11
S1
2F
12
S1
3F
13
S1
4F
14
Se
cti
on
s
Semester
0
100
200
300
400
500
600
Stu
de
nts
NSF Funded
0
25
50
75
100
125
150
175
S0
0F
00
S0
1F
01
S0
2F
02
S0
3F
03
S0
4F
04
S0
5F
05
S0
6F
06
S0
7F
07
S0
8F
08
S0
9F
09
S1
0F
10
S1
1F
11
S1
2F
12
S1
3F
13
S1
4F
14
Pro
jec
ts S
ub
mit
ted
Semester NSF Funded
Number of Projects by Semester
Projects by Subject
1114, 58%
188, 10%
395, 21%
212, 11%Engineering
Medicine
Natural Sciences
Other
All Submitted Projects: 1,909
Math Advisors by Affiliation
24
11
Calculus Instructors
Consultants
All Math Advisors: 35
Subject Area Advisors by Affiliation
645
122
64
46 54
External Advisors
Non-Engineering Faculty (USF)
Engineering Faculty (USF)
Non-Faculty Professionals (USF)
PhD Students (USF)
All Subject Area Advisors: 931
Top Advisors (Fall 2008-Fall 2014)
Name # of Projects Name # of Projects Name # of Projects
Arcadii Grinshpan * 740 Noureddine Elmehraz * 42 Jing Wang 9
Scott Campbell * 559 Gerald Hefley 37 Rosy Flora 8
Brian Curtin 144 Leslaw Skrzypek 30 Susan Hartranft 8
Jonathan Burns * 101 Kanakadurga Nallamshetty 26 Paris Wiley 8
Masahiko Saito 89 Razvan Teodorescu 25 Stanley Kranc 7
Thomas Bieske 73 David Kephart 24 Zhimin Shi 7
Mayur Palankar * 65 Ihor Luhach 19 Don Dekker 6
Fernando Burgos 53 Karim Nohra 16 Elliot Findley * 6
Andrei Chugunov 53 Vindya Pathirana Arachchilage * 13 Pamela Hallock-Muller 6
Scott Rimbey 50 Egor Dolzhenko * 9 Alison Meyers 6
Gordon Fox * 47 Laurie Walker 9 Richard Stark 6
* NSF Funded
Top Advisors (Fall 2008-Fall 2014)
Name # of Projects Name # of Projects Name # of Projects
Michael Stokes 6 Andrew Hoff 3 Haithem Al-Masroori 2
Autar Kaw 5 Henry Jeanty 3 Clayton Beardsley * 2
James Olliff 5 Thomas Juster 3 Glen Besterfield 2
Heidi Capozza 4 Mile Krajcevski 3 Kirpal Bisht 2
Robert Criss 4 Stephen Lappano * 3 Liana Boop 2
Daniel Simkins 4 William Lee 3 Jianfeng Cai 2
Charles Connor 3 Thomas Lynn 3 Robert Cory 2
Joy D`Andrea * 3 David Milligan 3 Ann Davis 2
Joni Downs 3 Matthew Pasek 3 Eva Fernandez 2
Mohamed Elhamdadi 3 Rajan Sen 3 Neranga Fernando 2
Lori Green 3 Philip van Beynen 3 Katrina Fortier 2
* NSF Funded
Top Advisors (Fall 2008-Fall 2014)
Name # of Projects Name # of Projects Name # of Projects
Robert Frisina 2 Sean McAveety 2 Dmytro Savchuk 2
Douglas Gobeille 2 Thomas McKinley 2 Rudy Schlaf 2
Christopher Heath 2 Connie Mizak 2 Chamila Siyambalapitiya * 2
David Hilsabeck 2 Lauren Morganti 2 Ralph Tindell 2
Paul Jermyn 2 Robert Muller 2 Ryan Toomey 2
Kenneth John Cabana 2 Christopher Osovitz 2 Robert Tufts 2
Sherwin Kouchekian 2 D.J. Pollock 2 Alex Volinsky 2
Ashok Kumar 2 Brendan Power 2 Jeffery West 2
Linda Leon 2 Kingsley Reeves 2 Ken Zambito 2
Craig Lusk 2 Martha Robinson 2
* NSF Funded
References and Presentations
References:
• Arcadii Z. Grinshpan, ``The Mathematics Umbrella: Modeling and Education : Mathematics in Service to the Community: Concepts and Models for Service-Learning in the Mathematical Sciences, Ed. Ch. Hadlock. The Mathematical Association of America, MAA Notes 66, Washington DC, 2005, 59-68.
• Sergei Abramovich and Arcadii Z. Grinshpan, mathematics tonon-mathematics majors through applications : Problems, Resources, and Issues in Mathematics Undergraduate Studies 18:5 (2008): 411-428.
• Sergei Abramovich and Arcadii Z. Grinshpan, K-12 and university mathematics: building the staircase from the top : Open Mathematical Education Notes 2 (2012): 1-21.
• Conference presentations:
• Sergei Abramovich and Arcadii Z. Grinshpan, applications to non-mathematics majors across disciplines: an apprenticeship approach." International Congress on Mathematical Education, Copenhagen, Denmark, 2004.
• Sergei Abramovich and Arcadii Z. Grinshpan, STEM education by bridging K-12 and university mathematicsThe New York State STEM Education Collaborative, Syracuse University, 2012.
• ectMAA Meeting, Ruskin, Florida, 2013.
Web Links
• CIIM: http://ciim.usf.edu
• MUG: http://math.usf.edu/mug
• UJMM: http://ciim.usf.edu/ujmmhttp://scholarcommons.usf.edu/ujmm/
• ExpertNet:
http://expertnet.org/index.cfm?fuseaction=centers.details&instituteID=5576