Mentoring Students on Independent Research Projects

1. Mentoring Students on Independent Research Projects Joe Large Marmion Academy MTA Spring Diner, 4/10/13

2. Dedicated to Bob Huntoon

3. Why Independent Research? • Development of Critical-Thinking Skills • Problem-Solving • Authentic Assessment • College and Career Readiness • Common Core

4. History of the Marmion Program • 6th Year of the Program • 1 or 2 Semester Course – Senior Elective (Honors) • Pre-requisites: • 1. Student has demonstrated strong academic performance • 2. Student must apply for Honors placement • 3. Student has demonstrated ability to be an independent learner • 4. Student must participate in preliminary interviews • 5. Final approval by Assistant Headmaster/Director of Student Services and Department Chairperson

5. Marmion Program (cont.) • Students develop, with the assistance and guidance of instructors, an independent research project to include a written and oral report which is submitted to the appropriate department. This is considered an elite level of learning with formal presentation of results to faculty board, family and other members of the general public. Students may choose to do a one semester or full year project within any discipline. • Sample Topics • Bioluminescence • Assessment of Contemporary English Literature • Molecular Dynamics Simulation • Global Impact of the Cold War • Applications of Artificial Intelligence

6. Phases of the Research Process • 1) Develop the research question • 2) Formulate the hypothesis • 3) Find background information • 4) Create a methodology for exploring the topic • 5) Experiment/Simulate the research question • 6) Gather data • 7) Draw conclusions

7. Case Study: Nuclear Medicine • Research Question: • How do we use advanced statistics to accelerate the decision-making process on nuclear contamination? • Hypothesis: • Using the Poisson Distribution, we should be able to accurately forecast whether a sample will exceed the contamination level

8. Case Study: Nuclear Medicine • Background information: • Nuclear decay of radioactive isotopes • Use of isotopes in the field of nuclear medicine • Government safety regulations for contamination • Advanced statistics – Poisson Distribution • Computer programming – MATLAB • Methodology: • Simulate the decay of a radioactive isotope using MATLAB, and use this to test our hypothesis

9. Case Study: Nuclear Medicine • Research Project Summary • http://prezi.com/yjoaq4il-kkn/statistics-in-nuclear-medicine/ • http://prezi.com/bddnvjktivx7/statistics/ • Simulation Results • Student Reflection Interview • http://youtu.be/jvVOmHS0afE

10. Case Study: Nuclear Medicine • Building connections outside the classroom and communicating with professionals in the field • FermiLab, Dr. Erik Ramberg • Laboratory Technologies, Mr. Scott Oesterlin

11. Common Issues • What should we research? • Where do we begin? • What if I don’t know the answers? • Time management? • Structure?

12. Jacklyn (Jacki) Naughton • Science teacher and research advisor for 30+ years. • Developed and taught a STEM Inquiry and Research class at Niles North High School in Skokie, IL. • Has served on both the regional and state Illinois Junior Academy of Science boards for over 15 years. • Currently employed at IMSA as an Online Education Specialist.

13. PROJECT TITLE Determining Integers Expressible as the Sum of Two Squares and in the Form x^2+Dy^2 Purpose: To determine whether a given positive integer n can be expressed as a sum of two integer squares and, more generally, in the for x^2+Dy^2, where x and y are integers, and D is a given positive integer. Procedure: Determine which integer primes are expressible as a sum of two squares. Using numerical examples and the property of unique prime factorization in the integers, conjecture and prove a criterion determining which positive integers are expressible as a sum of two squares. Repeat by determining which integer primes are expressible in the form x^2+Dy^2 for some integers x and y, given a positive integer D. Use this information to find a criterion to determine which positive integers are expressible in the form x^2+Dy^2. Conclusion: Given a positive integer n, n is expressible as the sum of two integer squares if and only if every prime factor of n that is congruent to 3 modulo 4 is raised to an even power in the prime factorization of n. Also, there exists integers x and y such that n = x^2+Dy^2 if and only if every prime factor p of n such that -D is not a quadratic residue modulo p, p is raised to an even power in the prime factorization of n.

14. Math projects • Modeling the Efficacy of a Chemotherapy Drug with a Differential Equation for Drug Resistance • Modeling the Movement of a Crowd Through an Exit Using NetLogo • Using a Network Model to Analyze the Efficacy of Targeted Vaccinations • Route Planning for Municipal Transportation with Shared Car Rides • The Association Between Student-Teacher Ratio and High School Graduation Rate • A Markov Analysis of Wins Above Replacement • Efficient Evasion on a 2D Surface • Synthesizing Flute Waveforms using Fourier Series • Determining the More Efficient Algorithm: A Comparison between the Nearest Neighbor Algorithm and the 2-Opt Algorithm • The Circle Algorithm: A Novel Heuristic for the Traveling Salesman Problem • Investigating the Spread of Tuberculosis within an Airplane using a Network Model • Modeling the Growth in the Population of Illinois Using Differential Equations • Statistical Analysis of Shootout Goals in Hockey Using Defense Independent Goalie Rating • Turbulence and Splash Analysis of a Rip Entry in Competitive Diving

15. Thoughts from a math-modeling teacher "I think it is important for teachers to realize that they can not individually help every student on all aspects of their projects. If students don't have mentors, then the students need to be very good independent workers. Both teachers and students need to be comfortable not ‘knowing the answer’. This is a course about getting things figured out; that can be very unnerving for math students who are used to looking up the right answer in the back of the book, and it can also be unsettling for teachers if they think that they need to know it all. We don't, so don't be afraid to find mentors or seek help from other experts in the school."

16. Student Research Facilitation Course Benefits • Learn about models and tools for implementing student research in your school or district • Advance your local planning efforts to facilitate student research opportunities • Share best practices for in-school, after-school and summer program models from experienced area teachers and STEM leaders

17. Student Research Facilitation Course Specifics • Duration: 11 weeks • Format: Hybrid - 3 contact meetings with remaining sessions done independently, online • Meeting locations: Northwestern University in Evanston or Illinois Mathematics and Science Academy (IMSA) in Aurora or virtual meeting • Program is free; 45 CPDU credits available • Teachers are encouraged to come in teams

18. Visit the OSEP website to enroll osep.northwestern.edu Under projects and programs, look for STEM Student Research

20. RISE: Research Inquiry Skills and Experimentation Course Benefits • Learn the skills necessary to conduct independent research and report your findings • Choose a topic of your own interest • Collaborate with other high school students involved in independent research • Connect with a research expert in your field of inquiry as an e-mentor • Conduct authentic research • Present your research findings at various regional/state venues

21. RISE: Research Inquiry Skills and Experimentation Course Specifics • RISE is an online, non-credit bearing course offered by the Illinois Mathematics and Science Academy • Access to a computer with Internet capabilities is necessary • Duration: Two semesters • For registration information contact Jacki Naughton @ jacnau@imsa.edu

22. Discussion Questions? Comments? Thoughts?