mathematics umbrella modelciim.usf.edu/docs/nsf_step_2014_-_interdisciplinary...1. the quality of...

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

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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

• 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

https://docs.google.com/forms/d/1AMj7fbVrxtUfHlUhscxg5tWEr608plY6PZFSJrAVhKY/viewform

• 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

• 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

28

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


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


• 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

32


• 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

33


• 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


• 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


•

serving the community

• Support collaboration of students, mathematics advisors, and subject area advisors beyond educational lines

• Provide undergraduate research opportunities

36


– 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

http://ciim.usf.edu/




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

http://math.usf.edu/mug

http://ciim.usf.edu/ujmm

http://ciim.usf.edu/poster2012/

http://www.cas.usf.edu/research/form/ofest.aspx

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


AG



Fields

GFBiology and

Related Fields


External SAAs


• Coordinator for the

College of Engineering

(6 Departments)

• Leading engineering

advisor

ScottCampbell


AG



Fields

GFBiology and

Related Fields


External SAAs


• Coordinator for

Biology faculty

• Leading biology

advisor

GordonFox


AG



Fields

GFBiology and

Related Fields


External SAAs


• Coordinator for STEM

graduate advisors &

technical support

• Leading graduate

advisor

JonathanBurns


AG



Fields

GFBiology and

Related Fields


External SAAs



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




• 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



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

http://ciim.usf.edu/poster2012/

http://www.cas.usf.edu/research/form/ofest.aspx

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

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cti

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s

Semester

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Stu

de

nts

NSF Funded

0

25

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75

100

125

150

175

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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


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



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



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


http://math.usf.edu/mug/


http://scholarcommons.usf.edu/ujmm/

http://expertnet.org/index.cfm?fuseaction=centers.details&instituteID=5576

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