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Using Regression Analysis to Develop Algebraic Understanding

Learn to create learning experiences developing algebraic reasoning, pattern identification, and data modeling with functions. Discover algebra outside the classroom using data sources like GRE scores and patent data. Examples include Titanic box office gross and Olympic swimming winning times. This session includes practical tips on regression analysis, trend lines, and interpreting regression equations. Participants will explore strategies to engage students in meaningful algebraic tasks.

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Using Regression Analysis to Develop Algebraic Understanding

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  1. Using Regression Analysis to Develop Algebraic Understanding KCTM Fall 2009 Conference Roland O’Daniel

  2. Standards for the Presentation Participants will understand how to create learning experiences that: • Make connections and develop a framework for algebraic reasoning • Identify and describe patterns in data using functions that approximate the data. • Flexibly move between multiple representations of functions to model mathematical ideas, solve problems, and communicate understandings.

  3. Where do you see algebra outside of your classroom?

  4. When looking for a data source, what are you looking for?

  5. GRE Score Concentrations in 28 Fields of PhD Study

  6. Cost/month in US $ Electricity Gas

  7. U.S. Origin Patent Data

  8. Height of teachers in school Height in cms Height in inches

  9. Finding a Source of Data • Gather your own! • Measure/CBR/Go Motion • Swivel • http://www.swivel.com/graphs • The Numbers • http://www.the-numbers.com/charts/thisweek.php • ZIPskinny • http://zipskinny.com/

  10. Example 1

  11. Determining a Relationship • Choose the tool you wish to use • TI graphing calculator • Excel spreadsheet • Create a representation of the data set • What are the kinds of questions that we can ask students regarding the representation of data?

  12. Titanic W.B.O. Gross 12/97- 3/98

  13. Titanic Weekend Box Office Gross December ‘97 thru March ‘98 What questions do you have about the graphs? What information, is necessary for the graphs to be more understandable?

  14. Researching a Data Set: Titanic WBO Gross 12/97-3/98 Why do these points behave differently? 1/16/98 2/13/98 12/19/97

  15. Creating a Regression Analysis • Identify regression equation • Display trend line and data set • Interpolate/Extrapolate • Trace function • Point of intersection • What questions can we ask?

  16. What did we find? How can we use it?

  17. Kinds of Tasks/Questions to Ask • Describe what the values in the regression equation mean in terms of this problem. • What does ( , ) mean in terms of this data? • What would happen to the model if the data were changed by ….? • Compare trend lines…

  18. Titanic Data w/ Trend Line

  19. Patent Data with Trend Line

  20. Example 2

  21. What’s the problem here? How can you handle this kind of problem? y= -3,107,000 x + 16,063,000 r2 = 0.9442

  22. y = 19,160,000∙0.646x

  23. Another Example of a System Olympic Men 400 Meter Free Style Swimming Winning Times Since 1924 y1 = -1.3x + 305 y2 = -0.31x + 248 What kind of questions could your students ask about this system?

  24. What algebra do you see in this graph?

  25. Questions? Next Steps?

  26. Photo Acknowledgements

  27. Number of Patents Granted in US by Origin Full Data Set from Swivel.com

  28. Notes

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