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Teaching Mathematics with Technology

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  1. Teaching Mathematics with Technology

    Chris Rakes
  2. Why Technology in Math for Girls? Discuss with partner Conclusions? What technology can be used to teach math?
  3. 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
  4. 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
  5. 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
  6. “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
  7. “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
  8. “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
  9. “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
  10. “Students today depend too much on hand-held calculators” Anonymous, 1985
  11. Can You Predict What Tomorrow’s Argument will be?
  12. 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
  13. How Students Learn Mathematics (Rakes, 2010)
  14. 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?
  15. 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
  16. Teaching Conceptually What does absolute value mean? How can we represent absolute value? Explore meaning using GeoGebra
  17. 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)
  18. Mathematical Representations Where is technology in this model?
  19. TPACK Shulman – Pedagogical Content Knowledge Pedagogical Knowledge Content Knowledge Technology Knowledge TPACK
  20. 5 Stages of TPACK Growth
  21. 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
  22. Want to vote over the web? http://www.polleverywhere.com/multiple_choice_polls/LTQ1MTgyNTk3NA/web
  23. Results Don’t forget: You can copy-paste this slide into other presentations, and move or resize the poll.
  24. 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
  25. Wrap Up Think, Pair, Share: What is the most important/surprising idea we learned today? Why? Get with a partner and discuss.
  26. Don’t forget: You can copy-paste this slide into other presentations, and move or resize the poll.
  27. 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
  28. 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.