Geogebra

Website danpearcymaths.wordpress.com

Twitter @DanielPearcy

Pedagogy and Techniques

Starter

What’s 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

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

2×1

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, 𝑓 𝑥 =1

𝑥𝑛

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, 𝑓 𝑥 =1

𝑥𝑛

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

Appendix 5: Building Intrigue and Curiosity

1. Teacher: Shows the Ferris Wheel as they’re 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 don’t

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 people’s applets

using the Construction Protocol.

Where to find command terms?

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