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Writing Problems for Solution with Technology

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World Wide Web. science news. graphs 'off the wall' facts. Interesting quotes ... e-mail experiment would be eligible for the prize of a trip to Disney World. ... – PowerPoint PPT presentation

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Title: Writing Problems for Solution with Technology


1
Writing Problems for Solution with Technology
Dr. Steve Armstrong LeTourneau University Longview
, TX
SteveArmstrong_at_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 Armstrong LeTourneau University Longview
, TX
SteveArmstrong_at_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
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
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 245
  • Facts about the Millennium Force

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

27
Roller Coaster Questions
  • The newest coaster is 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
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