21 st Century Teaching Leads to 21 st Century Learning Grant: Virginia’s Mathematics Capstone Course

1. 21st Century Teaching Leads to 21st Century Learning Grant:Virginia’s Mathematics Capstone Course October 9, 2013 GRCTM Conference Diane Leighty mthmtcs@verizon.net

2. Ensuring that Every Virginia Student Becomes STEM College and Career Ready Increasing the Rigor in Virginia’s Mathematics Classrooms

3. Increased Rigor • Increasing rigor does not mean making the math harder; it does mean having students engage in doing mathematics and thinking harder about the mathematics. • (Vickie Inge)

4. Four Ways to Integrate…. Critical Thinking for Students: The student will • Problem solve; • Ask questions that require critical analysis; • Evaluate sources; and • Be actively involved in decision making. The teacher will act as a “coach” rather than a “director”!

5. “Governor's Commission on Higher Education Reform, Innovation and Investment” Executive Order No. 9 (2010) (revised July 9, 2010) • Attracting and preparing young people for the STEM (science, technology, engineering, and math) areas and other disciplines (e.g., healthcare and advanced manufacturing) where skill shortages now exist and/or unmet demand is anticipated. http://www.governor.virginia.gov/Issues/ExecutiveOrders/2010/EO-9.cfm

6. Mathematics Capstone CourseVA Course Code 3136 • A senior level course • Offered to students who are college intending or students who need a boost in readiness levers for work force or further career training • Applies and extends what students learned in previous courses • Aligns with the Mathematics College and Career-Readiness Performance Expectations (MPE) • Prerequisites: Include earning at least two verified credits in mathematics, and satisfactory completion of either Algebra, Functions, and Data Analysis (AFDA) or Algebra II. • Does NOT count as a verified credit toward the Advanced Diploma.

7. Goal: Moving Instruction to the Next Level UVA SCPS Office of Mathematics Outreach

8. Challenges • New way of teaching • New way of creating learning experiences • Limited knowledge of how to translate real world situations into mathematics lessons for high school students

9. Where do we start? • Use Team Building Activities – how to share the workload; how to communicate ideas! • Start Small! • Build to problem based learning • Tasks – Explore open problems • Projects – Research introduced • Problems – Totally Student Driven!

10. Task • Engage – Introduce the problem – something to spark interest • Explore – Helpful resources to get students started. • One or two foundational activities (somewhat teacher directed/guided) • Explain – Main task • What questions does the problem raise? • What are the expectations for “solving” the problem? • What will students be assessed/graded on? Rubrics/Checklists • Elaborate – Students working in groups to develop a workable solution (or partial solution) to the problem. • Evaluate – Provide rubrics for any written work, presentation, product produced by the group. Also peer and self-evaluations.

11. Where to find materials…. • UVA Capstone Project • https://sites.google.com/site/mathematicscapstonecourseunits/ • http://www.exeter.edu/documents/math1all.pdf • http://www.exeter.edu/documents/math2all.pdf

12. EXPLORE Activity • After rolling off the end of a ramp, a ball follows a curved trajectory to the floor. To test a theory that says the trajectory can be described by an equation y= h – ax2, Sasha makes some measurements. The end of the ramp is 128 cm above the floor, and the ball lands 80 cm downrange (see figure below). In order to catch the ball in mid-flight with a cup that is 78 cm above the floor, where should Sasha place the cup?

13. Main Task – Elaborate & Evaluate • Using a driver on the 7th tee, you hit an excellent shot, right down the middle of the level fairway. The ball follows the parabolic path described by the quadratic function h = 0.5f−0.002f 2. This relates the height h of the ball above the ground to the ball’s progress f down the fairway. Distances are measured in yards.

14. If you got a hole in one, how far is the hole from the tee? • At what distance down the fairwaydoes the ball reach the highest point of its arc? What is the maximum height attained by the ball? • Now on the 8th tee which is on a plateau 10 yards above the level fairway, using the same driver creating the same trajectory, you hit another fine shot. Again, you get a hole in one. How far is the hole from the tee?

15. “Project” Unit • Engage – Introduce the problem – something to spark interest • Explore – Helpful resources to get students started. • One to three foundational activities (somewhat teacher directed/guided) • Explain – Main project • What questions does the problem raise? • What needs to be researched in order to develop a solution? • What are the expectations for “solving” the problem? • What will students be assessed/graded on? Rubrics/Checklists • Elaborate – Students working in groups to research and develop a workable solution (or partial solution) to the problem. • Evaluate – Provide rubrics for any written work, presentation, product produced by the group. Also peer and self-evaluations.

16. Projects • Longer, more open situations. Allow for more student choices, flexibility, varied solutions.

17. Sample Unit – Stealing From the Sun • Main Project: Your school superintendent wants to know if using solar energy will help meet budget requirements. Your class has been requested to research, analyze, and recommend whether or not to invest in solar panels as an energy source for your school.

18. Is This The Best? Project • What is the “best” restaurant? • What is the “best” cell phone or cell phone plan? • What is the “best” car? Decision Matrices and Data Analysis

19. Creating a Problem-based Unit • Engage – Introduce the problem • Explore – Helpful resources to help students get started. • Explain • What questions does the problem raise? • What are the expectations for “solving” the problem? • What will students be assessed/graded on? Rubrics/Checklists • Elaborate – Students working in groups using research to develop a workable solution (or partial solution) to the problem. • Evaluate – Provide rubrics for any written work, presentation, product produced by the group. Also peer and self-evaluations.

20. Problem • Culminating “Unit” – end of course • Of local, state, national, international interest • Clearly Interdisciplinary

21. Algebra •  A local man wins a large amount of money in the lottery and asks for advice on how to invest his winnings wisely. (Students explore the concept of investing and learn investment terms. They contact local tax advisors, investment advisors and financial institutions to understand how the financial industry works.)

22. Guided Problem: Two-Scoop Ice Cream Cone • How many different combinations of ice-cream flavors are possible on a double cone for • Two flavors? • Three flavors? • 4, 5 or 6 flavors? • n flavors?

23. More open-ended problems… • Towers of Hanoi • Escalator • VIP Dilemma

24. NCTM Article • “Open-Ended Questions and the Process Standards” • Mathematics Teacher, October 2013