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Teaching Mathematics with Technology. Chris Rakes. Why Technology in Math for Girls?. Discuss with partner Conclusions? What technology can be used to teach math?. Calculator Myths. If kids use calculators they won’t learn the “basics.” Calculators make students lazy

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Teaching Mathematics with Technology


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    Presentation Transcript
    why technology in math for girls
    Why Technology in Math for Girls?
    • Discuss with partner
    • Conclusions?
    • What technology can be used to teach math?
    calculator myths
    Calculator Myths
    • If kids use calculators they won’t learn the “basics.”
    • Calculators make students lazy
    • Students should learn the “real way” before using calculators
    • Students will become overly dependent on calculators
    the more things change
    The More Things Change…
    • Students today can’t prepare bark to calculate their problems. They depend upon their slates which are more expensive. What will they do when their slate is dropped and it breaks? They will be unable to write!

    Teachers Conference, 1703

    slide5

    Students today depend upon paper too much. They don’t know how to write on slate without chalk dust all over themselves. They can’t clean a slate properly. What will they do when they run out of paper?

    Principal’s Association, 1815

    slide6

    “Students today depend too much upon ink. They don’t know how to use a pen knife to sharpen a pencil. Pen and ink will never replace the pencil.”

    National Association of Teachers, 1907

    slide7

    “Students today depend upon store bought ink. They don’t know how to make their own. When they run out of ink they will be unable to write words or ciphers until their next trip to the settlement. This is a sad commentary on modern education.”

    The Rural American Teacher, 1929

    slide8

    “Students today depend upon these expensive fountain pens. They can no longer write with a straight pen and nib (not to mention sharpening their own quills). We parents must not allow them to wallow in such luxury to the detriment of learning how to cope in the real business world, which is not so extravagant.”

    PTA Gazette, 1941

    slide9

    “Ball point pens will be the ruin of education in our country. Students use these devices and then throw them away. The American virtues of thrift and frugality are being discarded. Business and banks will never allow such expensive luxuries.”

    Federal Teacher, 1950

    purpose of today s lesson
    Purpose of Today’s Lesson
    • Recognize the technology tools available to help you teach all students better
    • Develop ways to use technology to improve student conceptual understanding
    nctm 2000 principles
    NCTM (2000) Principles
    • Read Technology and Equity Position Statements
      • What can technology be used for?
      • When should it be used?
      • What technologies should be used?
      • What’s the role of the teacher when technology is used?
      • What can’t technology do?
    teaching procedurally
    Teaching Procedurally

    Consider the absolute value inequality:

    |5x + 4| < 5

    Write the equation twice without the abs. value sign. Second time, flip inequality and make RHS negative.

    5x + 4 < 5 5x + 4 > -5

    5x < 1 5x > -9

    x < 1/5 x > -9/5

    teaching conceptually
    Teaching Conceptually
    • What does absolute value mean?
    • How can we represent absolute value?
    • Explore meaning using GeoGebra
    what does research say about technology
    What does research say about technology?
    • Ellington, 2003: Compiled the results from 54 calculator studies.Conclusions: no difference in achievement from traditional lectures; improvement in attitudes
    • Ellington, 2006: Compiled the results from 42 graphing calculator studies. Conclusions: When GC’s used on test, GC students did better than traditional; When GC not used, no difference. Attitudes always improved with GC.
    • Rakes, Valentine, McGatha, & Ronau (2010): Compiled results from 82 algebra studies, including 7 technology based curriculum studies and 21 technology studies. Conclusions: Including or excluding technology does not impact student achievement – how strategies and tools are used makes the difference in how well students learn (e.g., conceptual vs. procedural focus)
    mathematical representations
    Mathematical Representations
    • Where is technology in this model?
    tpack
    TPACK
    • Shulman – Pedagogical Content Knowledge

    Pedagogical Knowledge

    Content Knowledge

    Technology Knowledge

    TPACK

    some technology tools available
    Some Technology Tools Available
    • Calculators
    • Probes
    • Graphing Calculators
    • Internet Applets (“Virtual Manipulatives”)
    • CD ROM Applets
    • Textbook CD ROMS
    • Commercial Mathematics Software
    • Microsoft Excel
    • Fathom; Minitab
    • Geometer’s Sketchpad; Geogebra; Wingeom
    • Online Games/Puzzles
    • Wiki Spaces; Blogs; Other Networking Sites
    • Microsoft PowerPoint
    • SmartBoards
    • Cell Phones
    slide22

    Want to vote over the web?

    http://www.polleverywhere.com/multiple_choice_polls/LTQ1MTgyNTk3NA/web

    results
    Results

    Don’t forget: You can copy-paste this slide into other presentations, and move or resize the poll.

    exploring technology
    Exploring Technology
    • Station 1: Motion Detector CBR Probe
      • NCTM Algebra Standard: Patterns, Relations, Functions
    • Station 2: Online Virtual Manipulative
      • NCTM Algebra Standard: Represent, Analyze Situations with Symbols; Math Modeling to Understand Relationships
    • Station 3: Microsoft Excel
      • NCTM Data/Probability Standard: Probability
    • Station 4: Calculator
      • NCTM Number Operations Standard: Meaning, Relationships; Number Computation: Fluency, Estimation
    • Station 5: Geometer’s Sketchpad
      • NCTM Geometry Standard: 2D Shape Characteristics
    wrap up
    Wrap Up
    • Think, Pair, Share:
      • What is the most important/surprising idea we learned today? Why?
      • Get with a partner and discuss.
    slide26

    Don’t forget: You can copy-paste this slide into other presentations, and move or resize the poll.

    technology resources
    Technology Resources
    • http://polleverywhere.com
    • Math Tools: http://www.mathforum.org/mathtools
    • National Library of Virtual Manipulatives: http://nlvm.usu.edu
    • NCTM Illuminations: http://illuminations.nctm.org
    • Chris’ Applet Page: http://applets.yolasite.com
    • Online Search Engines
    references
    References

    Ellington, A. J. (2003). A meta-analysis of the effects of calculators on students’ achievement and attitude levels in precollege mathematics classes. Journal for Research in Mathematics Education, 34, 433-463.

    Ellington, A. J. (2006). The effects of non-CAS graphing calculators on student achievement and attitude levels in mathematics: A meta-analysis. International Journal of Instructional Media, 106, 16-26.

    Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students' learning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 371-404). Reston, VA: National Council of Teachers of Mathematics.

    Niess, M. L., Ronau, R. N., Shafer, K. G., Driskell, S. O., Harper S. R., Johnston, C., Browning, C., Ozgun-Koca, S. A., & Kersaint, G. (2009). Mathematics teacher TPACK standards and development model. Contemporary Issues in Technology and Teacher Education [Online Serial], 9(1). Retrieved from http://www.citejournal.org/vol9/iss1/mathematics/article1.cfm

    Rakes, C. R. (2010). Misconceptions in rational numbers, algebra, geometry, and probability. Unpublished doctoral dissertation, University of Louisville.

    Shulman, L. S. (1986). Those who understand: A conception of teacher knowledge. American Educator, 10, 9-15.

    Skemp, R. R. (1976/2006). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20-26. Reprinted in Mathematics Teaching in the Middle School, 12, 88-95.