Writing Problems for Solution with Technology

1. Writing Problems for Solution with Technology Dr. Steve ArmstrongLeTourneau UniversityLongview, TX SteveArmstrong@letu.edu

2. Welcome to Texas

3. Words of Wisdom from Texas • Always drink upstream from the herd.

4. Words of Wisdom from Texas • The quickest way to double your money is to fold it over and put it back in your pocket.

5. Words of Wisdom from Texas • Never order chicken fried steak in a restaurant without a juke box.

6. Words of Wisdom from Texas • Never kick a cow chip on a hot day.

7. Words of Wisdom from Texas • Don't squat with your spurs on.

8. Writing Problems for Solution with Technology Dr. Steve ArmstrongLeTourneau UniversityLongview, TX SteveArmstrong@letu.edu

9. Necessity of Technology • Messy numbers • Functions that are difficult to graph • Varieties of regression • seek to find an appropriate modeling function • Multiple views of a problem • graphical • numerical • symbolic • textual

10. Motivation • Develop students' abilities to think mathematically • Need for good judgment about mathematical claims • advertisers • government • media • Problems should … • require thought and analysis • development ability to communicate results

11. Sources for Problems • World Almanac • population figures • finance figures • sports results • Amusement parks • physics • motion • business strategies

12. Jail Releases Upset Judges Sources for Problems • World Wide Web • science news • graphs • "off the wall" facts • Interesting quotes • Warning: take care lifting questions from existing text books

13. Writing the Questions • Begin with statements that grab the students' interest • "Recent evidence of skin cancer caused by excessive sun exposure has made us aware of the intensity of the sun. When might be the best/worst time of day to soak up sun?" • "A TV satellite dish service has hired you as a consultant to determine the best price for the initial fees for their dish and receiver." • "Consider a recent e-mail hoax about Bill Gates. People who participated in a pyramid e-mail experiment would be eligible for the prize of a trip to Disney World."

14. Writing the Questions • Two possible approaches: • Present total task in detail, students come up with all of solution • Lead students through derivation of intermediate formulas, functions, relationships • Occasionally state questions a bit loosely • Real life problems are rarely accurately and succinctly stated • Ask for preliminary guesses, reassessment

15. Can give clues as to the window required to graph a function Use a Variety of Viewpoints • Numeric • tables of values • dimensions • distances • profit, loss • View results of graphs • max, min, roots, intersections • combining functions (arithmetically, composition)

16. Use a Variety of Viewpoints • Symbolic representation • manipulated with technology • enables proofs • necessary for communication • Pictures, diagrams • for description of original problem • may be to scale or purposefully generic • may be required as part of solution

17. Describe Solutions • Written format • require full sentences • well formed paragraphs • labeled diagrams • Verbal presentations • use of visuals • encourage presentation technology • Post web pages

18. Problem Categories • Find real data • plot the data points • use regression for a modeling function • Given two functions graphed together, what questions can be asked?

19. Problem Categories Use Parametric Equations • Model objects moving on the graph as a function of time • straight line, spirals, circular • • time 0

20. Problem Categories Use parametric equations • Model two objects that must (not) meet • Measure distance between the moving objects

21. Levels of Problems • Usually we do not write our own homework questions • More likely to write test questions • write them to require technology • Also write project questions • for a one day exercise • for a long term • for groups or for individuals

22. Group Project Management • Best to assign the groups • randomize and manually alter as needed • Assign locations for group gathering • Assign one person to be the "scribe" who will record the official results • Provide a handout that precisely describes the task to be performed, problem to be solved

23. Project Grading • Instructor should • carefully read the handout • note specific answers asked for • assign values to be awarded • create a grading checklist • Inform students how grade is weighted in relation to total term grade • Award bonus points for … • extra elegance portions of the problem • early or first submission

24. A Project for this Workshop A problem for solution with technology concerning a rollercoaster.

25. Roller Coaster Questions • Which is the best seat? • see better in front seat • pull higher g's in back (100 feet from front) • Millennium Force facts • 310 foot high hill (300 foot drop) • first hill 80° angle • 92 mph max • track length 6595 feet • ride takes 2:45 • Facts about the Millennium Force

26. Roller Coaster Questions • What comparisons/contrasts can you make?

27. Roller Coaster Questions • The newest coasteris 420 feet high • Goes from 0 to 120 mph in 4 sec • More Facts

28. Your Task … • Write a problem that requires technology for its solution • Use whatever portion of the facts about the ride that you choose • Try to use/require all of symbolic, numeric, graphic, textual expressions • Lead students through solution steps • Final objective must be clearly stated • Suggest enrichment/elegance pursuits • Specify level: algebra, precalc, calculus

29. Teams • Gather in groups of 4 – 5 people • Person in group with first letter of family name closest to end of alphabet is the scribe • Write up your problem • Another group will use checklist to evaluate your submission

30. F.Y.I. • Technology used: • Ink Link pen, by Seico • This presentation available (PowerPoint and Web versions) at • web2\index.htm