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Pedagogy and Techniques
Whats possible on Geogebra?
Why should you put time and effort into improving with Geogebra?
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.
1(a) Provide examples of Geogebra applets through
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
Pyramids and Prisms
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
Dialogic Teaching with Geogebra
More examples (all in Geogebra section of blog):
Deconstructing applets and learning
Is it fit for purpose?
Does it clearly show the concept/s?
Does it fit into a logical sequence of
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?
Do you need to be able to make expert level
Using Geogebra for Formative Assessment
3. Check Box
Outstanding tool for Dialogic Classroom Teaching.
Excellent Formative Assessment Tool of specific concepts.
What about purely student based tasks?
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
Join the Association of Teachers of Mathematics (ATM) for some lovely
geometry tasks by Dietmar Khan.
[Conjecture -> Confirm Conjecture -> Justification with Algebra]
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
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
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
Question: Find a model function for the
temperature of coffee over time.
View -> Spreadsheet
Copy and paste the data (without titles) into
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
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:
Interesting point about Geogebra Assessment. See the Pushback
section at the end of the post. @a_mcsquared
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
4. Teacher: End of the lesson Recreate the Ferris wheel
Appendix 6: How to Learn
John Golden: @mathhombre
Michael Borcherds: @mike_geogebra
How I started to learn:
How I continued to learn: Analysing other peoples applets
using the Construction Protocol.
Where to find command terms?