geogebra pedagogy

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  • Geogebra

    Website danpearcymaths.wordpress.com

    Twitter @DanielPearcy

    Pedagogy and Techniques

  • Starter

    Whats possible on Geogebra?

    Why should you put time and effort into improving with Geogebra?

    Innovative Developers

    Large Community of support.

    To help students understand a concept better than they would be able to without it.

    To help you or a student solve a problem/provide more evidence for a conjecture [An extra tool alongside Calculator and Excel]

    To create diagrams or figures which you can use in worksheets or tests.

    www.tube.geogebra.org

    http://www.tube.geogebra.org/

  • Objectives

    1(a) Provide examples of Geogebra applets through

    discussing pedagogy.

    1(b) Develop the case for why Geogebra is a great tool

    for Dialogic teaching and confirming conjectures.

    2 Provide Technical tips on sliders, buttons, check

    boxes and basic commands.

    3(a) What makes a good learning experience?

    3(b) Do you need to be able to make great applets to

    get students using it effectively?

  • What is Dialogic Teaching?

    Collective : teachers and students address learning tasks together, whether as a group or as a class.

    Reciprocal : teachers and students listen to each other, share ideas and consider alternative viewpoints.

    Supportive : students articulate their ideas freely, without fear of embarrassment over 'wrong' answers, and they help each

    other to reach common understandings.

    Cumulative : teachers and students build on their own and each other's ideas and chain them into coherent lines of

    thinking and enquiry.

    Purposeful : teachers plan and steer classroom talk with specific educational goals in view.

  • Dialogic Teaching with Geogebra

    Using a Geogebra applet to provide extra evidence for a

    student or class conjecture.

    Example: How could you understand multiplying fractions

    with Geogebra?

    1

    1

  • Multiplying Fractions

    1

    21

    2=1

    4

    1

    4

    1

    4=

    1

    16

    1

    8

    1

    8= ?

  • Pyramids and Prisms

  • https://www.youtube.com/watch?v=4dYFe1gHidc

  • 1. Investigating the Connection between the Circumference

    and Diameter of a Circle

    2. Introducing Trigonometry

    3. Investigating the Discriminant of a Quadratic

    4. Understanding Standard Deviation

    5. Inverse relationship between Exponential and Logarithmic

    Graphs

    Dialogic Teaching with Geogebra

    More examples (all in Geogebra section of blog):

  • Deconstructing applets and learning

    experiences.

  • Is it fit for purpose?

    http://archive.geogebra.org/en/upload/files/english/lewws/regularpolygon3to20_int_extangles.html

  • Does it clearly show the concept/s?

  • Does it fit into a logical sequence of

    learning?

    1.Have you introduced the applet too early or too

    late in the learning sequence?

    2.Does the applet contain a natural progression of

    learning within it?

    Polygon applet

  • @Geogebrain

  • Do you need to be able to make expert level

    applets?

  • Using Geogebra for Formative Assessment

    1. Slider

    2. Button

    3. Check Box

    4. Lists

    5. RandomBetween[]

    6. RandomElement[]

    7. UpdateConstruction[]

  • Geogebra:

    Outstanding tool for Dialogic Classroom Teaching.

    Excellent Formative Assessment Tool of specific concepts.

    What about purely student based tasks?

  • Transformation Artwork

  • Collaborative Investigation

    Investigate the function, =1

    Record your observations and attempt to

    mathematically justify any observations made.

    Share your understanding with a partner.

    Investigate a different function with sliders.

    [Class Discussion first: Ideas from students as to what

    other similar functions they could investigate before

    they do]

  • Join the Association of Teachers of Mathematics (ATM) for some lovely

    geometry tasks by Dietmar Khan.

    [Conjecture -> Confirm Conjecture -> Justification with Algebra]

    Tasks Online

  • Appendix 1: Developing a Geogebra Curriculum

    Investigate the area of a triangle G6

    Scale Diagram of the School G6

    Investigate diameter and circumference of a circle [Sliders] G7

    Make a set of parallel lines and investigate connections G7

    Investigating Straight Line Graphs [Sliders] G7

    Investigating Properties of Quadrilaterals G7

    Understanding Tessellations G7

    Discovering Pythagoras Theorem G8

    Transformation Artwork Grade 8

    Developing an understanding of transformations [Sliders] - G8

    Expanding Double Brackets using CAS view G8

    Interior and Exterior Angles of Polygons G8/9

    Investigating the roots of a quadratic [Sliders] G9

    Understanding the parameters of a quadratic [Sliders] G9

    Making a Picture using knowledge of Functions G10

    Investigating the Modulus Function and Trigonometric Functions (half class vs half class) then each

    present on their findings G10

    Investigating different models for data sets G10

    Making an animated Ferris Wheel using Unit Circle Trig [Sliders] G10

  • Word of Caution

    Tinkering with the tools to get comfortable with

    them often takes three times longer than you plan

    for in lower year groups.

  • When developing a Geogebra

    applet for any form of use

    1. Is there a better way to display the concept?

    2. Does it fit into a meaningful sequence of

    learning?

    3. Is it efficient in clearly displaying a concept?

    4. Would it be more effective as teacher

    demonstration or student exploration?

    5. Are students concentrating on technical aspects

    of Geogebra or the actual concept at hand?

    6. Have you generated opportunities for further

    investigation/exploration?

  • Appendix 2: The CAS View

    View (in top toolbar) -> CAS

    Hover your mouse of different tools to find out what they do.

    How could you use this as a teaching tool either within Dialogic

    teaching, student discovery or student checking?

    Could you have a laptop set up in your classroom for students to use as

    a tool like they would do a calculator?

  • Appendix 3: The Spreadsheet View

    Time

    (minutes)

    Temperature

    (oC)

    0 77.5

    2.5 70

    5 64

    7.5 59

    10 55

    12.5 50.5

    15 48

    17.5 45

    20 42.5

    22.5 40

    25 38

    27.5 36.5

    30 35

    32.5 33.5

    35 32

    37.5 31

    40 30

    42.5 29

    45 28.5

    Question: Find a model function for the

    temperature of coffee over time.

    View -> Spreadsheet

    Copy and paste the data (without titles) into

    the spreadsheet.

    Select all the data in the spreadsheet

    Make a list of points from the data (called list1)

    Start typing in the bottom input bar: Fit

    Select one to use e.g. FitLine[list1]

    Which one is the best fit? E.g FitExp[list1]

    Will there be times when you have to create

    sliders to fit a function rather than the Fit

    command?

  • Appendix 4a: Assessment with Geogebra

    Something I tried with Grade 10:

    Investigate the function, =1

    Record your observations and attempt to mathematically justify

    any observations made.

    See more ideas: @tombutton, @SparksMaths:

    http://tube.geogebra.org/material/show/id/1367455

    Interesting point about Geogebra Assessment. See the Pushback

    section at the end of the post. @a_mcsquared

    http://audrey-mcsquared.blogspot.ca/2013/11/more-student-

    created-geogebras-and-some.html

    http://tube.geogebra.org/material/show/id/1367455http://audrey-mcsquared.blogspot.ca/2013/11/more-student-created-geogebras-and-some.html

  • Appendix 5: Building Intrigue and Curiosity

    1. Teacher: Shows the Ferris Wheel as theyre coming in.

    2. Students: Drawn to look at it curiosity about how it was made.

    3. Teacher: Sorry, I was just messing around with some maths you dont

    know yet

    4. Teacher: End of the lesson Recreate the Ferris wheel

    See Video:

    https://vimeo.com/142053723

  • Appendix 6: How to Learn

    John Golden: @mathhombre

    http://mathhombre.blogspot.ch/p/geogebra.html

    Michael Borcherds: @mike_geogebra

    How I started to learn:

    http://mathandmultimedia.com/geogebra/

    How I continued to learn: Analysing other peoples applets

    using the Construction Protocol.

    Where to find command terms?

    https://wiki.geogebra.org/en/Commands

    http://mathhombre.blogspot.ch/p/geogebra.htmlhttp://mathandmultimedia.com/geogebra/https://wiki.geogebra.org/en/Commands

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