Download - Mathematics, Origami and GeoGebra Shi-Pui Kwan Lecturer The Hong Kong Institute of Education 1
Mathematics, Origami and GeoGebra
Shi-Pui Kwan
LecturerThe Hong Kong Institute of Education
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A model of teaching2
TPCK
TPCK
Content (Mathematical) KnowledgePedagogical KnowledgeTechnological Knowledge
hands-on manipulative virtual manipulative
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GeoGebra
Geometry + Algebra4
GeoGebraSpreadsheet5
GeoGebra3D6
Problem 1: Haga’s theorem
The lower left hand corner C is folded upward to toucha point F on DE.
If DF=1/n of DE, what fractionIs EN of DE?(n = 2, 3, ……, 9)
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Problem 2: mouhefanggai
A mouhefanggai is formed bycross sections which arecircumbscribing squares of thecircular cut sessions of a sphere.How does it look like?
Without knowing the volumeformula for the sphere, how todetermine the volume of themouhefanggai?
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origami simulation by GeoGebrasome construction techniques‘error free’ measurementsguided discovery through measuring, tabulating,
conjecturing and provingRecord to Spreadsheet select ‘value’ in
algebra view move slider ‘ denominator ’ to obtain data
observation: EF increases with DFcomputation of fractional valuesproblem extension
my teaching notes – Haga’s theorem9
my teaching notes – mouhefanggai
a solid formed from the circumscribing squares of the circular cut sections of a sphere
visualization of the mouhefanggaiquestions for discussionthe ancient Chinese way in determining its
volume1/8 mouhefanggai and its complementary part
inside the circumscribing cube(r3)introduction and visualization of Yangma (a
square pyramid)problem extension
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math proof outline: Haga’s theorem11
math proof outline: mouhefanggai (mhfg)
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ScreenCasts13
Learning in different styles
The cursor jumping from one spot to another during the process somehow distracts me so that I cannot concentrate on the picture
and cannot easily exert my own imagination.I prefer to stare at a static picture and think
about it,better yet, draw my own picture if that is
possible.- Prof. Siu M.K.
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Student’s drawings 15
GeoGebra
is a freewareis ‘error free’ (in compare with measurement)can generate lots of data (time saving)can help students in visualization (for spatial
sense development)is a useful tool in identifying the variants and the
invariants (particularly in learning geometry)is effective for problem extensionprovides insights in making conjectures
(inductive thinking)
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GeoGebra
files are more long lasting than origami modelsconstruction is itself a learning process (more
suitable for secondary students)is a new learning/teaching tool which provides
students/teachers with various modes of lesson delivery demonstration/illustration interaction/exploration project learning
……
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Thank You!18
Thanks to the teachers & students involved in the try-outs!
Thanks to the GeoGebra developers!
Thank You!