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Writing Problems for Solution with Technology

This document discusses innovative approaches to using technology in writing problems and finding solutions. Dr. Steve Armstrong from LeTourneau University emphasizes the importance of developing students’ mathematical thinking through diverse problem-solving techniques that incorporate graphical, numerical, symbolic, and textual analyses. The content includes motivational insights, sources for real-world problems, and guidelines for writing engaging questions. It also covers the presentation of solutions and the effective use of technology to enhance learning and communication among students.

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Writing Problems for Solution with Technology

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  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. New Attraction

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

  10. 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

  11. 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

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

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

  14. 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."

  15. 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

  16. 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)

  17. 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

  18. Presenting Solutions What expectations would you want for written reports? • Written format • State the problem • Describe the solution • Give all formulas used • Use full sentences, well formed paragraphs • Diagrams with labels • Screen shots from calculator

  19. Presenting Solutions • Verbal presentations • Use of visuals • Encourage presentation technology • All members of group participate • Speak plainly, avoid "verbal commas" • Give points for "dressing up" What elements should be included in verbal presentations?

  20. Presenting Solutions Describe recommendations you would give for a sequence of web pages. • Post web pages • Consistent backgrounds, fonts • Logical sequence of ideas • Easily used links • Links to other relevant pages • Diagrams, screen shots from calculator

  21. Problem Categories http://lib.stat.cmu.edu/DASL/DataArchive.html • Find real data • plot the data points • use regression for a modeling function • Given two functions graphed together, what questions can be asked?

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

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

  24. 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

  25. 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

  26. 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

  27. A Project for this Workshop A problem for solution with technology concerning a roller coaster.

  28. 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

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

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

  31. 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

  32. 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

  33. F.Y.I. • Technology used: • Ink Link pen, by Seico • This presentation available (PowerPoint and Web versions) at • www.letu.edu/people/SteveArmstrong/NCTM/Web2

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