1 / 25

First International GeoGebra Conference July 14, 2009 Dr. Pamela J. Buffington

First International GeoGebra Conference July 14, 2009 Dr. Pamela J. Buffington . Formative Assessment Assessment Principle: Assessment should support the learning of important mathematics and furnish useful information to both instructors and learners. (NCTM, 2000, p 22).

vondra
Download Presentation

First International GeoGebra Conference July 14, 2009 Dr. Pamela J. Buffington

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. First International GeoGebra Conference July 14, 2009 Dr. Pamela J. Buffington

  2. Formative Assessment Assessment Principle: Assessment should support the learning of important mathematics and furnish useful information to both instructors and learners. (NCTM, 2000, p 22) Interactive Technology Technology Principle: Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances learning. (NCTM, 2000, p 24) The Power of Convergence Formative assessment can provide critical information about existing conceptions / misconceptions Technology can provide accurate, interactive, visual images of mathematical concepts and ideas Instructors can provide a targeted instructional intervention for learners’ specific needs and remediate potential barriers to learning

  3. Students come to the classroom with preconceptions about how the world works. If their initial understanding is not engaged, they may fail to grasp the new concepts and information that are taught, or they may learn them for purposes of a test but revert to their preconceptions outside the classroom -How People Learn, National Research Council

  4. Foundational Resources Diagnostic Assessment Using Probes Targeted Interventions Using Interactive Technologies

  5. Diagnostic Prompts: Example Errors • Overgeneralizations: • Applying incorrect rules such as “two negatives always make a positive” • Conceptual Misunderstandings • Viewing the equals sign as “place answer here” • Common Errors (Procedural) • Incorrect Decimal Placement when multiplying

  6. Research Base Example #1 • Direct translation of the words into an algebraic equation without understanding the relationship described. • Using variables to represent words

  7. Example #2 – In GeoGebra

  8. Research Base Example #2: • Failure to see the difference in the x and y scales applying an “up one over one” rule to misinterpret a rate of change of one. • Although the visual aspect of graphs makes them a powerful medium for generating meaning, it is also the source of many of the incorrect responses

  9. Foundational Resources Diagnostic Assessment Using Probes Targeted Interventions Using Interactive Technologies

  10. Riding the Ferris Wheel 100 m height 0 m Loading dock time The distance from the loading dock at the bottom of the Ferris wheel to the very top is 100 meters. You are in a seat on the Ferris wheel at the 3:00 position and are being asked to graph the height of your seat as you move around the ride. The Ferris wheel is moving in a counterclockwise rotation.

  11. Resources • Research Brief around a Given Topic • Diagnostic Probe to Elicit Understanding and Misunderstandings • Instructional Materials: • Applet • Supporting Resources • Overview • Student Exploration

  12. Research Example: Rational Numbers • Research has verified that learners continue to use properties they learned from operating with whole numbers even though many whole number properties do not apply to rational numbers. (Adding It Up, NRC ) • Examples: • Reason that 1/8 is larger than 1/7 because 8 is larger than 7. • May believe that 3/4 equals 4/5 because in both fractions the difference between the numerator and denominator is 1.

  13. Diagnostic Probe: Comparing Rational Numbers

  14. Applet Example: Comparing Rational Numbers - Many virtual manipulatives include dynamic numerals that change as the representation on the screen changes. This direct and immediate connection to numeric representation is impossible with physical models. -VandeWalle

  15. Applet Example: Comparing Rational Numbers Learning Tools List # 5b Comparing Rational Numbers (Fractions) - 2

  16. Applet Example: Comparing Rational Numbers • Explore the Applet • - What specific questions would you ask? What specific examples should be explored?

  17. Research Example: Equivalent Expressions • In general, if students engage extensively in symbolic manipulation before they develop a solid conceptual foundation for their work, they will be unable to do more than mechanical manipulation. The foundation for meaningful work with symbolic notation should be laid over a long time. (PSSM) • Examples: • Some students simply ignore bracketing symbols such as parentheses , as in 4(n+5) = 4n+5 (Algebraic Thinking) • Some students make errors writing totals and products They wrote h10 , meaning h plus 10 or x4 meaning “x times 4” (Algebraic Thinking)

  18. Diagnostic Probe: Equivalent Expressions

  19. Applet Example: Equivalent Expressions Learning Tools List # 12 Equivalent Expressions – Distributive Property (2)

  20. Applet Example: Equivalent Expressions • Explore the Applet • How would you use this applet? • Which checkboxes would you turn on first? Explain why.Would you show all three expressions at once? Why or why not? • What examples would you use? • What questions would you ask students?

  21. Supporting Resources: Equivalent Expressions • Resources • Applet Overview • Student Explorations

  22. Diagnostic Probe: Equivalent Expressions

  23. Associated Applet: Equivalent Expressions Learning Tools List # 6 Equivalent Expressions – Difference of Squares 1

  24. Real Life Explorations: Comparing DVD Plans Interactive Mathematics Tools for Assessment & Instruction # 10 DVD Rental Plans Problem

  25. Interactive Resources • Accessible online at http://maine.edc.org/ • For Additional Information Contact: • Pam Buffington pbuffington@edc.org

More Related