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Making Sense of Algebra with Realistic Mathematics Education

Making Sense of Algebra with Realistic Mathematics Education. Mieke Abels Freudenthal Institute Utrecht University, Netherlands Michael Matassa and Raymond Johnson Freudenthal Institute US University of Colorado Boulder. Expectations?.

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Making Sense of Algebra with Realistic Mathematics Education

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  1. Making Sense of Algebra with Realistic Mathematics Education MiekeAbels Freudenthal Institute Utrecht University, Netherlands Michael Matassa and Raymond Johnson Freudenthal Institute US University of Colorado Boulder

  2. Expectations? • How can RME help teachers and students to understand and meet the common core goals of Algebra? • How can students develop strategies for solving systems-of-equations? • What can I do with my 6th (7th, 8th) grade students? • How may a learning trajectory for (systems of) equations look like? • Sources?

  3. Tug-of-war How would a sixth grade student solve this problem? Source: Comparing Quantities (MIC)

  4. Substitute and compare This side wins

  5. Substitute and compare This side wins

  6. Substitute and compare This side wins

  7. ICEBERG METAPHOR FORMAL L=30y+320 L=35y+295 INFORMAL

  8. Three frogs How would a sixth grade student solve this problem? Visualizations? Source: MiTC

  9. Sunny 1 jump = 7 steps

  10. Cal 1 jump = 8 steps

  11. Leg 13 5 2 jump = 18 steps 1 jump = 9 steps

  12. Balance scales How can this problem be solved using informal strategies?

  13. 1 Compare the student work. What are the differences, what is the same? What concepts are developed?

  14. 2

  15. ICEBERG METAPHOR FORMAL L=30y+320 L=35y+295 PRE-FORMAL MODELS INFORMAL

  16. Generate new equations $ 6.80

  17. Generate new equations $ 1.00

  18. Combination chart $7.80 2 3 1 1 $3.40 X 2 Find the difference 2 2 $6.80 0 $1.00 1

  19. A Learning trajectory FORMAL y = 2x +5 2y = 4x − 3 8 + 4x = 10 − 2x 3j − 2 = 2j + 2 FLOATING CAPACITY L=4j +5 L=2j+15 Substitute and compare Balance strategy Compare jumps and steps Generate new equations Notebook strategy Sets of Equations Equations

  20. MIC (Mathematics in Context) http://mathincontext.eb.com Units: Comparing Quantities Graphing Equations • MiTC (Mathematics in the City) http://mitcccny.org http://www.contextsforlearning.com Unit: The California Frog-Jumping Contest: Algebra • DME (Digital Mathematics Environment) http://dme.colorado.edu/dwo/colorado.html, or http://www.fi.uu.nl/dwo/en (login as guest) Math Secondary Education> Algebra> Lesson-Systems of equations More information: http://www.fisme.uu.nl/wisweb/en • RME conference in Boulder. 4th International RME Conference, 2013 sept 27-29, University of Colorado, Boulder See for more information: www.fius.org • Utrecht Summer School on Mathematics and Science Education August 19 - 30, 2013 in Utrecht, the Netherlands. http://www.utrechtsummerschool.nl/index.php?type=courses&code=H7 http://www.utrechtsummerschool.nl

  21. MiekeAbels • M.J.Abels@uu.nl Michael Matassa • michael.matassa@colorado.edu Raymond Johnson • raymond.johnson@colorado.edu • mathed.net, @MathEdnet • google.com/+RaymondJohnson

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