1. Writing Problems for Solution with Technology Dr. Steve Armstrong LeTourneau University Longview, TX SteveArmstrong@letu.edu

2. Necessity of Technology Messy numbers Functions that are difficult ____________ Varieties of regression –seek to find an appropriate _____________ Multiple views of a problem –

3. Motivation Develop students' abilities to think ________________________ Need for good judgment about mathematical claims –advertisers –government –media Problems should … –require _____________________________ –development ability to _____________ results

4. Sources for Problems World Almanac –population figures –finance figures –sports results Amusement parks – World Wide Web –science news –graphs –"off the wall" facts –NCTM Mathematics Teacher Media Clips Interesting quotes Warning:

5. Writing the Questions Begin with statements that __________________________ Two possible approaches: –Present total task in detail, ______________________________ –Lead students through derivation of intermediate formulas, functions, relationships Occasionally state questions _____________ –Real life problems are rarely accurately and succinctly stated Ask for _________________________________

6. Use a Variety of Viewpoints Numeric –tables of values –dimensions –distances –profit, loss View results of graphs – – Can give clues as to the ______________ to graph a function

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

8. Presenting Solutions Written format –

9. Presenting Solutions Verbal presentations – – – – – –

10. Presenting Solutions Post web pages – – – – – –

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

12. Problem Categories Use Parametric Equations Model objects moving on the graph as a function of time –straight line, spirals, circular Model two objects that ______________ Measure ______________________ between the moving objects

13. Levels of Problems Usually we do not write our own homework questions More likely to write test questions –write them to technology Also write project questions –for a ______________ exercise –for a long term –for _____________ or for individuals

14. Group Project Management Best to assign the groups –____________ and manually alter as needed Assign locations for group gathering Assign one person to be the "_________" who will record the official results Provide a handout that _________________________________ to be performed, problem to be solved

15. Project Grading Instructor should –carefully read the handout –note specific _______________ asked for –assign values to be awarded –create a _________________________ Inform students how grade is weighted in relation to total term grade Award _________________ for … –extra elegance portions of the problem –early or first submission

16. A Project for this Workshop 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

17. 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

18. This Presentation Can be found at www.letu.edu/people/SteveArmstrong/NCTM/Web2 www.letu.edu/people/SteveArmstrong/NCTM/Web2 Both PowerPoint and.html versions F.Y.I. The technology used in the presentation was the Ink Link Pen by Seiko