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Algebraic thinking

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Variety of problems to promote algebraic thinking.

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Algebraic thinking

  1. 1. Strategies and Practices to Promote Algebraic Thinking Reva Narasimhan Associate Professor of Mathematics Kean University www.mymathspace.net
  2. 2. Algebraic Thinking • Many students struggle with developing generalizations for functional relationships • Bridge the gap between their concrete experiences in prior mathematics courses and the abstract symbolic work in later courses • Students need help to make sense of this increasing abstraction • By developing students’ facility in using multiple representations you give them a powerful tool for success in advanced mathematics. Reva Narasimhan www.mymathspace.net
  3. 3. M&M activity on decay 1. Count how many total M&M’s there are in your packet. This is the initial value. 2. Shake up M&M’s and drop the candies on a piece of paper. 3. Count how many have “m” on top 4. Record on paper. 5. Remove these candies and repeat Steps 2-4 until no candies with “m” on top appear 6. Record results in Excel spreadsheet and model the behavior. Reva Narasimhan www.mymathspace.net
  4. 4. Tiling the Border of a Pool Source: http://ccsstoolbox.agilemind.com/animations/functions_3.html Reva Narasimhan www.mymathspace.net
  5. 5. Minimizing Cost Consider the problem of designing the most costefficient cylindrical juice can that holds 20 cubic inches of soda. This problem requires students to bring together understanding of surface area and volume, and ability to use variables to represent geometric relationships Reva Narasimhan www.mymathspace.net Source: http://ccsstoolbox.agilemind.com/animations/functions_5.html
  6. 6. Technology and Algebraic Thinking A spreadsheet can be a powerful ally in facilitating algebraic thinking Reva Narasimhan www.mymathspace.net
  7. 7. Summary of Spreadsheets • A spreadsheet can be used to unify algebraic, tabular and graphical representations of an abstract concept. • Gives valuable insight which may not be gained by just pencil and paper work. • Shows students the power of technology to explore and make conjectures which would otherwise be very difficult or impossible. • Helping students build such insight is invaluable as they move on to other courses and their professions. Reva Narasimhan www.mymathspace.net
  8. 8. Algebraic Concepts and Connections What comes to your mind at the mention of algebra? Reva Narasimhan www.mymathspace.net
  9. 9. Reva Narasimhan www.mymathspace.net
  10. 10. Dynamic geometry – move it and see it Visual and tactile What does the algebra problem look like in GeoGebra? Reva Narasimhan www.mymathspace.net
  11. 11. Reva Narasimhan www.mymathspace.net
  12. 12. GeoGebra vs Graphing Calculator The ability to interact dynamically with a graph sets GeoGebra apart from many other graphing software and calculators Reva Narasimhan www.mymathspace.net
  13. 13. What is GeoGebra? • Free and open source software created Markus Hohenwarter of Austria www.geogebra.org • A multi-platform dynamic mathematics software that joins geometry, algebra, tables, graphing, statistics and calculus in one easy-to-use package. Reva Narasimhan www.mymathspace.net
  14. 14. What is GeoGebra? Graphics, algebra and tables are connected and fully dynamic Can easily create interactive learning materials as web pages Reva Narasimhan www.mymathspace.net
  15. 15. Solution of Equations • Relate algebraic representation to graphical representation • Recast an equation as an intersection of the graphs of two functions • Explore nature of solutions Reva Narasimhan www.mymathspace.net
  16. 16. Summary • Multistep applications hold student interest and get them to connect with the mathematics they are learning. • New algebraic skills that are introduced are now in some context. • Gives some rationale for why we define mathematical objects the way we do. Reva Narasimhan www.mymathspace.net
  17. 17. Contact Information • Web: http://www.mymathspace.net/presentations Reva Narasimhan www.mymathspace.net