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Using dynamic geometry to bring the real world into the classroom

Using dynamic geometry to bring the real world into the classroom. Kaye Stacey University of Melbourne, Australia

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Using dynamic geometry to bring the real world into the classroom

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  1. Using dynamic geometry to bring the real world into the classroom Kaye Stacey University of Melbourne, Australia Pierce, R., & Stacey, K. (2011). Using dynamic geometry to bring the real world into the classroom. In L. Bu & R. Schoen (Eds.), Model-Centered Learning: Pathways to mathematical understanding using GeoGebra (pp. 41-55). Rotterdam: Sense Publishers.

  2. http://extranet.edfac.unimelb.edu.au/DSME/RITEMATHS • “Design research” in classrooms in 6 schools • Students aged 14 – 16 • Aim to assist students to see the links between abstract mathematics and real world situations. • Algebra and functions - many technologies • Dynamic geometry software was possibly the most successful of the technologies that were explored.

  3. Dynamic geometry offers opportunities to promote student engagement and deepen mathematical thinking by: •  bringing the real world into the mathematics classroom, adding interest, relevance and learning about applications • adding visualisation and animation • enabling multiple representations of concepts and mathematical objects • increasing pleasure (e.g. colour) for ‘halo’ effect

  4. Learning to graph

  5. Aspect ratio now familiar and interesting introduction to similarity Students drag corner– record of lengths, ratios, product, sum, difference Active discovery learning– with/without trace and grid Different dragging modalities (Arzarello et al 2000) - wandering dragging to explore, guided dragging to test theories etc Exploring similarity by dragging

  6. Max volume of open box:pre-calculus investigation

  7. Five modes of representation: • real world situation of paper boxes; • dynamic geometry simulation with corners of variable size removed; • numerical representation – tables of values of size of corner removed and volume; • graphical representations • plotted points from the table, • trace of dragged point from dragged simulation • graph of symbolic function; • symbolic representation – formula linking volume to size of corner removed. Research question – how many representations to use? – germane or extraneous cognitive load

  8. Classroom Observations • Generally prefer to use pre-constructed files • For students to manipulate in designed ways • Better constructed, robust, attractive • In class demonstration and discussion, teacher can provide sustained pressure for higher order thinking • “Decline to lower order thinking” for potentially higher order thinking tasks easy for lessons using technology • Too hard for most teachers to make good files – need to share good files and index them for easy selection

  9. Three uses illustrated • Similarity – explore regularity and variation in context of guided discovery • Function graphing – make links between symbolic rules and graphs • Maximum volume of open box – expansion of representations of algebra, with simulations and data capture

  10. Paper presented at the Geogebra ICME-12 Pre-conference Seoul, July 8, 2012 Thank you Kaye Stacey k.stacey@unimelb.edu.au http://extranet.edfac.unimelb.edu.au/DSME/RITEMATHS

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