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32nd International Conference on Technology in Collegiate Mathematics

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VIRTUAL CONFERENCE

32nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE

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Project-Based Undergraduate Research Initiatives in Mathematics

32nd International Conference in Technology in Collegiate Mathematics 2020

• Dr. Bathi Kasturiarachi

Department of Mathematical Sciences Kent State University at Stark March 13, 2020

Project-Based Undergraduate Research Initiatives in Mathematics

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High-impact Educational Practices have shown to be beneficial for college students from many backgrounds.

• We want to teach mathematics in a way that allow students

connect it to themselves, their community, and their identity

• How can we empower the students and let them take

control of their learning and do it in a manner that minimizes injustice and inequality and promote intellectual excellence?

• Students can be who they are when they learn.

High-impact Educational Practices (HiEP)[9,14]

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Uri Triesman and Striving for Excellence[15]

• Replacing remediation with high expectations
• Excellence workshops (social, intellectual)
• Peer collaboration (social, communal)
• Faculty facilitators (high expectations, excellence)
• Academic Mastery Program[7] (Occidental College)
• Program for Excellence in Mathematics[6] (KSU)

Motivation for HiEP – First

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Cia Verschelden and Bandwidth Recovery[13] Angela Duckworth and Grit[2]

• Many scarcities in life-- money, health, respect, safety,

affirmation, belonging-- reduces “mental bandwidth”

• Bandwidth refers to cognitive and emotional resources needed to

deal with making good decisions, learning, caring for family, and having healthy relationships

• HiEP allows us to recover lost bandwidth and promote a growth

mind set

Motivation for HiEP – Second

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Brain’s regions are connected by some 100,000 miles of fibers called white matter—just enough to circle the Earth 4 times. Poverty, Racism, Social Marginalization depletes cognitive resources

Cognitive depletion and loss of bandwidth

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• Comparative simple changes make a big difference in what

we do as mathematics educators

• Result – construct new learning outcomes based on the

students’ interests and industrial needs Projects that count on Cooperative Leaning and promoting Undergraduate Research

“People Aren’t Dumb. The World Is Hard.” Richard Thaler, winner of Nobel Prize in Economics 2017

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Technology driven cooperative learning projects

• Student interest
• Mathematical background
• Brief (5-10 minute) learning activities in-class with a

cultural twist

• Technologically guided research projects during the

semester (both online and in-class)

Meaningful mathematical excursions that engage students

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• Yoda Ela (Giant Canal) in Sri Lanka is an 87 km long

single water canal constructed during King Dathusena’s reign in 459 AD

• It carrying excess water from Kala Wewa reservoir to

Thissa Wewa reservoir in the city of Anuradhapura.

• The Yoda Ela has a unique gradient.

10 centimeters per 1 kilometer!

A cultural example …

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A quick probability experiment …

TASK In a well shuffled deck of 26 cards labeled A-Z, what is the average number

• f cards you need to turn before the first vowel shows up?

SOLUTION There are 5 vowels. It divides the shuffled pack into six segments. 26/6 = 4.3 Add one more for correction. Average Number = 4.3+1 = 5.3, about 5 to 6 cards

T C … … …

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• Humans do mental accounting. How they

think about $.

• Money is fungible. No restrictions on its

use.

• “Save more tomorrow”

Daily Daily Weekly Monthly 20=1¢ 25=32¢ 210=1024¢ 215=32768¢ 21=2¢ 26=64¢ 211=2048¢ Bi-Monthly 22=4¢ 27=128¢ 212=4096¢ 216=65536¢ 23=8¢ 28=256¢ 213=8192¢ 217=131072¢ 24=16¢ 29=512¢ 214=16384¢ $2621.43

An Investment Example …

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• 1. Take a Breath [PROBABILITY THEORY]
• Julius Caesar died on 15 March 44 BC.

His famous dying words were “Et tu Brute”

• Take a minute and close your eyes and take a deep

breath

• What is the probability that the air you just breathed had

an atom from Julius Caesar’s dying breath?

• P(atom from Caesar’s breath) = 0.99

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• Quick activity on GCD and LCM for motivation.
• What is the period of

?

• 2. Making Waves [TRIGONOMETRY]
• 5
• 4
• 3
• 2
• 1

1 2 3 4 5

• 1.6
• 1.4
• 1.2
• 1.0
• 0.8
• 0.6
• 0.4
• 0.2

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

x y

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• A set of numbers

, … , are called “huddle numbers” if 𝟐

…

𝒐 = 𝟐 𝟑… 𝒐

• Example n=2:

𝑏 + 𝑏 = 𝑏𝑏 Solution: 𝑏 = 2, 𝑏 = 2.

• Example n=3:

𝑏 + 𝑏 + 𝑏 = 𝑏𝑏𝑏 Solution: 𝑏 = 1, 𝑏 = 2, 𝑏= 3

• 3. Huddle Numbers [NUMBER THEORY/TRIG]

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• A set of numbers

, … , are called “huddle

numbers” if

𝟐 … 𝒐 = 𝟐 𝟑… 𝒐

• General solution:
• For n = 2, 3, 4, 6, 24, 114, 174, 444 the above solution set is the

ONLY integer solution for all n < 1011

Huddle Numbers

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• A set of numbers

, … , are called “huddle numbers” if … = …

• /()

is a real number solution to the huddle equation.

What if we allow for real numbers and not just integers?

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What if we allow for real numbers and not just integers?

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Non integer huddle numbers

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• Suppose you are invited to play a game of chance. Each

game pegs you with a winning probability of p (p<0.5). Your opponent has a winning probability of 1-p (>0.5).

• You must play the game an even number of times. At the

end of 2n games, if you have more wins, you win a big prize.

• To play the game you have to put down a reasonable bet.
• On average, how many games should you play?
• 4. A not so intuitive Probability Game

[STATISTICS & PROBABILITY]

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• If your winning probability of p (p<0.5) is KNOWN, a

calculation gives:

A Probability Game

p # of games 0.1 0.25 and 2.25 (2) 0.3 1.5 and 3.5 (2) 0.4 4 and 6 (6) 0.49 49 and 51 (50)

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• Gauss-Bonnet theorem for compact surfaces
• 5. A donut and a coffee cup

[Differential Geometry]

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• Choose Ohio First scholarships (COF) for freshman in

STEMM fields

– [Ohio Department of Higher Education (ODHE) Grant 16.30]

• Undergraduate Research Assistant (URA) opportunities

– KSU’s Stark Campus sponsored

• Summer Undergraduate Research Experience (SURE)

– KSU’s Research and Sponsored Programs (RASP) sponsored

High impact practices …

32nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE

#ICTCM REFERENCES 1. Angelo, T., A., and Cross, K., P. (1993). Classroom Assessment Techniques: A Handbook for College Teachers. Jossey- Bass Publishers, San Francisco. 2. Duckworth, Angela. (2016). Grit: The Power of Passion and Perseverance. Scribner, New York, NY. 3. Gawende, Atul. (2010). The Checklist Manifesto: How to Get Things Right. Metropolitan Books, New York, NY. 4. Kahneman, Daniel, and Amos Tversky. (1973). “On the Psychology of Prediction.” Psychological Review 80, no. 4:237. 5. Kahneman, Daniel. (2011). Thinking Fast and Slow. Macmillan, New York, NY. 6. Kasturiarachi, A., Bathi. (2004). Counting on Cooperative Learning to Uncover the Richness in Undergraduate

• Mathematics. PRIMUS, Vol. XIV, No. 1, 55-78.

7. Kasturiarachi, A., Bathi. (1997). Promoting Excellence in Mathematics through Workshops Based on Collaborative

• Learning. PRIMUS, VII (2), 147-163.

8. Kolb, David A. (1976). The Learning Style Inventory: Technical Manual. McBev and Co. Boston, MA. 9. Kuh, G. D. (2008). High-impact educational practices: What they are, who has access to them, and why they matter. Washington, DC: Association of American Colleges and Universities. 10. Lang, James, M. (2016) Small Teaching: Everyday Lessons from the Science of Learning. Jossey-Bass. 11. Thaler, Richard, H. (2008). Nudge: Improving Decisions about Health, Wealth, and Happiness. Yale University Press, New Heaven, CT. 12. Thaler, Richard, H. (2015). Misbehaving: The Making of Behavioral Economics. W. W. Norton & Company, New York, NY. 13. Verschelden, Cia. (2017) Bandwidth Recovery: Helping students Reclaim Cognitive Resources Lost to Poverty, Racism, and Social Marginalization, Stylus, Sterling, VA. 14. The Mathematical Sciences in 2025. National Research Council, Washington, D.C., 2103. 15. Treisman, P., Uri. (1992). Studying Students Studying Calculus: A Look at the Lives of Minority Mathematics Students in College. College Mathematics Journal. 23 (5): 362-372. 16. Zhao, Chun-Mei; Kuh, George D. (2004). Adding Value: Learning Communities and Student Engagement. Research in Higher Education, v.45 n2 p115-138, Mar 2004.

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