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Algebraic thinking

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Variety of problems to promote algebraic thinking.

Publicado en: Tecnología, Educación
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Algebraic thinking

  1. 1. Strategies and Practices to Promote Algebraic Thinking Reva Narasimhan Associate Professor of Mathematics Kean University
  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
  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
  4. 4. Tiling the Border of a Pool Source: Reva Narasimhan
  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 Source:
  6. 6. Technology and Algebraic Thinking A spreadsheet can be a powerful ally in facilitating algebraic thinking Reva Narasimhan
  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
  8. 8. Algebraic Concepts and Connections What comes to your mind at the mention of algebra? Reva Narasimhan
  9. 9. Reva Narasimhan
  10. 10. Dynamic geometry – move it and see it Visual and tactile What does the algebra problem look like in GeoGebra? Reva Narasimhan
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  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
  13. 13. What is GeoGebra? • Free and open source software created Markus Hohenwarter of Austria • A multi-platform dynamic mathematics software that joins geometry, algebra, tables, graphing, statistics and calculus in one easy-to-use package. Reva Narasimhan
  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
  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
  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
  17. 17. Contact Information • Web: Reva Narasimhan