32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE ictcm.com | #ICTCM
32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM Project-Based Undergraduate Project-Based Undergraduate Research Initiatives in Mathematics Research Initiatives in Mathematics 32 nd International Conference in Technology in Collegiate Mathematics 2020 Dr. Bathi Kasturiarachi Department of Mathematical Sciences Kent State University at Stark March 13, 2020
32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM High-impact Educational Practices (HiEP) [9,14] 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.
32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM Motivation for HiEP – First 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)
32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM Motivation for HiEP – Second 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
32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM Cognitive depletion and loss of bandwidth 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
32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM 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 • 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
32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM Meaningful mathematical excursions that engage students 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)
32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM A cultural example … • 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!
32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM A quick probability experiment … TASK In a well shuffled deck of 26 cards labeled A-Z, what is the average number of 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
32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM An Investment Example … • Humans do mental accounting. How they think about $. • Money is fungible. No restrictions on its use. • “Save more tomorrow” Daily Daily Weekly Monthly 2 0 =1¢ 2 5 =32¢ 2 10 =1024¢ 2 15 =32768¢ 2 1 =2¢ 2 6 =64¢ 2 11 =2048¢ Bi-Monthly 2 2 =4¢ 2 7 =128¢ 2 12 =4096¢ 2 16 =65536¢ 2 3 =8¢ 2 8 =256¢ 2 13 =8192¢ 2 17 =131072¢ 2 4 =16¢ 2 9 =512¢ 2 14 =16384¢ $2621.43
32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM 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
32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM 2. Making Waves [TRIGONOMETRY] • Quick activity on GCD and LCM for motivation. What is the period of ? y 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 -5 -4 -3 -2 -1 1 2 3 4 5 -0.2 x -0.4 -0.6 -0.8 -1.0 -1.2 -1.4 -1.6
32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM 3. Huddle Numbers [NUMBER THEORY/TRIG] • A set of numbers � � , … , � are called “huddle numbers” if … 𝒐 = 𝟑 … 𝟐 𝟐 𝒐 Example n= 2: 𝑏 � + 𝑏 � = 𝑏 � 𝑏 � Solution: 𝑏 � = 2, 𝑏 � = 2. Example n= 3: 𝑏 � + 𝑏 � + 𝑏 � = 𝑏 � 𝑏 � 𝑏 � Solution: 𝑏 � = 1, 𝑏 � = 2, 𝑏 � = 3
32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM Huddle Numbers A set of numbers � � , … , � are called “huddle • numbers” if 𝟐 … 𝒐 = 𝟑 … 𝟐 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 < 10 11
32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM What if we allow for real numbers and not just integers? • A set of numbers , … , are called “huddle numbers” if … = … �/(���) � is a real number solution to the huddle equation.
32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM What if we allow for real numbers and not just integers?
32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM Non integer huddle numbers
32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM 4. A not so intuitive Probability Game [STATISTICS & PROBABILITY] • 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?
32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM A Probability Game • If your winning probability of p ( p<0.5) is KNOWN, a calculation gives: 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)
32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM 5. A donut and a coffee cup [Differential Geometry] • Gauss-Bonnet theorem for compact surfaces
32 nd International Conference on Technology in Collegiate Mathematics VIRTUAL CONFERENCE #ICTCM High impact practices … • 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
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