Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics with GeoGebra- An innovationDr. P. K. ChaurasiaNational
Council of Educational Research and Training New Delhi INDIA
November 22, 2011
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
About the talkI will discuss briey on following
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
About the talkI will discuss briey on following A couple of
classroom scenario- regarding ICT integration
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
About the talkI will discuss briey on following A couple of
classroom scenario- regarding ICT integration Few quotes
towards-Potential of Technology for Mathematics Education
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
About the talkI will discuss briey on following A couple of
classroom scenario- regarding ICT integration Few quotes
towards-Potential of Technology for Mathematics Education The
Dynamic Mathematics Software GeoGebra
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
About the talkI will discuss briey on following A couple of
classroom scenario- regarding ICT integration Few quotes
towards-Potential of Technology for Mathematics Education The
Dynamic Mathematics Software GeoGebra here we will discuss
about-Brief background, Design of GeoGebra, Implementation of
e-learning Principles in GeoGebra, Creating Instructional Materials
and Teaching with GeoGebra
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
About the talkI will discuss briey on following A couple of
classroom scenario- regarding ICT integration Few quotes
towards-Potential of Technology for Mathematics Education The
Dynamic Mathematics Software GeoGebra here we will discuss
about-Brief background, Design of GeoGebra, Implementation of
e-learning Principles in GeoGebra, Creating Instructional Materials
and Teaching with GeoGebra Pedagogy emerged for the software
GeoGebra (A Summary of Pilot-study Research Outcomes)
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Classroom ScenarioIn a normal mathematics classroom,
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Classroom ScenarioIn a normal mathematics classroom, a teacher
bases her teaching on a textbook,during half of each lesson she
lectures (writing something on the blackboard etc.) and the rest of
the lesson students are allowed to work individually in their note
book, while she is available for answering questions.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Classroom ScenarioIn a normal mathematics classroom, a teacher
bases her teaching on a textbook,during half of each lesson she
lectures (writing something on the blackboard etc.) and the rest of
the lesson students are allowed to work individually in their note
book, while she is available for answering questions. Assignments
are given for home work.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Classroom ScenarioIn a normal mathematics classroom, a teacher
bases her teaching on a textbook,during half of each lesson she
lectures (writing something on the blackboard etc.) and the rest of
the lesson students are allowed to work individually in their note
book, while she is available for answering questions. Assignments
are given for home work. Students work through the book in the same
pace.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Classroom ScenarioIn a normal mathematics classroom, a teacher
bases her teaching on a textbook,during half of each lesson she
lectures (writing something on the blackboard etc.) and the rest of
the lesson students are allowed to work individually in their note
book, while she is available for answering questions. Assignments
are given for home work. Students work through the book in the same
pace. Some time teacher-made test, consisting of mixture of
open-ended and multiple choice items, by which the teacher rates in
order to monitor student progress.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Classroom ScenarioIn a normal mathematics classroom, a teacher
bases her teaching on a textbook,during half of each lesson she
lectures (writing something on the blackboard etc.) and the rest of
the lesson students are allowed to work individually in their note
book, while she is available for answering questions. Assignments
are given for home work. Students work through the book in the same
pace. Some time teacher-made test, consisting of mixture of
open-ended and multiple choice items, by which the teacher rates in
order to monitor student progress. At the end of the year the
learning of the textbook content be completed and students appear
in a summative test to demonstrate their knowledge of the
content.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Classroom ScenarioIn a normal mathematics classroom, a teacher
bases her teaching on a textbook,during half of each lesson she
lectures (writing something on the blackboard etc.) and the rest of
the lesson students are allowed to work individually in their note
book, while she is available for answering questions. Assignments
are given for home work. Students work through the book in the same
pace. Some time teacher-made test, consisting of mixture of
open-ended and multiple choice items, by which the teacher rates in
order to monitor student progress. At the end of the year the
learning of the textbook content be completed and students appear
in a summative test to demonstrate their knowledge of the content.
Now the question, how ICT use can inuence this classroom?Dr. P. K.
Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Few PossibilitiesThere could be few possibilities-
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Few PossibilitiesThere could be few possibilitiesIn a
substitution method
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Few PossibilitiesThere could be few possibilitiesIn a
substitution method teacher replaces some of the old technologies
with ICT. For instance: the teacher may use Power-Point for her
lectures. Or she may allow her student to send their homework via
e-mail to her. She even could present the tests electronically.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Few PossibilitiesThere could be few possibilitiesIn a
substitution method teacher replaces some of the old technologies
with ICT. For instance: the teacher may use Power-Point for her
lectures. Or she may allow her student to send their homework via
e-mail to her. She even could present the tests electronically.
Such ICT-scenario would not require much change and/or training.
This may be called a cosmetic change:old wine in new bottles.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Few PossibilitiesThere could be few possibilitiesIn a
substitution method teacher replaces some of the old technologies
with ICT. For instance: the teacher may use Power-Point for her
lectures. Or she may allow her student to send their homework via
e-mail to her. She even could present the tests electronically.
Such ICT-scenario would not require much change and/or training.
This may be called a cosmetic change:old wine in new bottles. There
is a need to have a paradigm shift in teaching-learning situations
through a transformational approach. But what is this
transformational approach?
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
One Another Scenario of Classroom Processhere, teacher gives up
half of the time lecturing on the Mathematical concepts.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
One Another Scenario of Classroom Processhere, teacher gives up
half of the time lecturing on the Mathematical concepts. The
student are required -on the basis of a few questions- to work in
groups and produce further applications on dierent context, dierent
problems, write down in their own language, and make a presentation
in the end.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
One Another Scenario of Classroom Processhere, teacher gives up
half of the time lecturing on the Mathematical concepts. The
student are required -on the basis of a few questions- to work in
groups and produce further applications on dierent context, dierent
problems, write down in their own language, and make a presentation
in the end. Students use ICT environment whenever appropriate and
feasible. Once the group products are ready the students should
learn the content of each others work. They keep electronically
track of their planning and progress.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
One Another Scenario of Classroom Processhere, teacher gives up
half of the time lecturing on the Mathematical concepts. The
student are required -on the basis of a few questions- to work in
groups and produce further applications on dierent context, dierent
problems, write down in their own language, and make a presentation
in the end. Students use ICT environment whenever appropriate and
feasible. Once the group products are ready the students should
learn the content of each others work. They keep electronically
track of their planning and progress. The teacher provides guidance
and monitors progress, while the students also consult other
resources too.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
One Another Scenario of Classroom Processhere, teacher gives up
half of the time lecturing on the Mathematical concepts. The
student are required -on the basis of a few questions- to work in
groups and produce further applications on dierent context, dierent
problems, write down in their own language, and make a presentation
in the end. Students use ICT environment whenever appropriate and
feasible. Once the group products are ready the students should
learn the content of each others work. They keep electronically
track of their planning and progress. The teacher provides guidance
and monitors progress, while the students also consult other
resources too. This scenario would be called transformational,
because it radically changes the educational processes and probably
also the outcomes.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
One Another Scenario of Classroom Processhere, teacher gives up
half of the time lecturing on the Mathematical concepts. The
student are required -on the basis of a few questions- to work in
groups and produce further applications on dierent context, dierent
problems, write down in their own language, and make a presentation
in the end. Students use ICT environment whenever appropriate and
feasible. Once the group products are ready the students should
learn the content of each others work. They keep electronically
track of their planning and progress. The teacher provides guidance
and monitors progress, while the students also consult other
resources too. This scenario would be called transformational,
because it radically changes the educational processes and probably
also the outcomes. We will explore how GeoGebra help us a paradigm
shift towards this transformational approach.Dr. P. K.
Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Potential of Technology for Mathematics EducationUse of
computers- [Wikipedia, 2008c] mentions that - Nowadays, computers
are vital for business and economy and computer literacy is
considered a very important skill in our society. Its a very common
tool for communication, text processing, playing games etc.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Potential of Technology for Mathematics EducationUse of
computers- [Wikipedia, 2008c] mentions that - Nowadays, computers
are vital for business and economy and computer literacy is
considered a very important skill in our society. Its a very common
tool for communication, text processing, playing games etc.
[Wikipedia, 2008e] - Additionally, the development and rapid growth
of the Internet in combination with its increasing accessibility
for the public has opened up a whole new digital world - For
example- YouTube
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Potential of Technology for Mathematics EducationUse of
computers- [Wikipedia, 2008c] mentions that - Nowadays, computers
are vital for business and economy and computer literacy is
considered a very important skill in our society. Its a very common
tool for communication, text processing, playing games etc.
[Wikipedia, 2008e] - Additionally, the development and rapid growth
of the Internet in combination with its increasing accessibility
for the public has opened up a whole new digital world - For
example- YouTube Due to its increasing importance, several
educational organizations world-wide started to develop technology
related curriculum guidelines - For example, National Council of
Teachers of Mathematics (NCTM), declared Technology as one of their
six principles for school mathematics.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Potential of Technology for Mathematics EducationUse of
computers- [Wikipedia, 2008c] mentions that - Nowadays, computers
are vital for business and economy and computer literacy is
considered a very important skill in our society. Its a very common
tool for communication, text processing, playing games etc.
[Wikipedia, 2008e] - Additionally, the development and rapid growth
of the Internet in combination with its increasing accessibility
for the public has opened up a whole new digital world - For
example- YouTube Due to its increasing importance, several
educational organizations world-wide started to develop technology
related curriculum guidelines - For example, National Council of
Teachers of Mathematics (NCTM), declared Technology as one of their
six principles for school mathematics. [NCTM, 2000, p.11]
Technology is essential in teaching and learning mathematics; it
inuences the mathematics that is taught and enhances students
learning. Technology environments allow teachers to adapt their
instruction and teaching methods more eectively to their students
need.Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Potential of Technology cont....[Hollebrands, 2007, p.166] New
learning opportunities are provided in technological environments,
potentially engaging students of dierent mathematical skills and
levels of understanding with mathematical task and activities.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Potential of Technology cont....[Hollebrands, 2007, p.166] New
learning opportunities are provided in technological environments,
potentially engaging students of dierent mathematical skills and
levels of understanding with mathematical task and activities.
Additionally, the visualization of mathematical concepts and
exploring mathematics in multimedia environments can foster their
understanding in a new way.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Potential of Technology cont....[Hollebrands, 2007, p.166] New
learning opportunities are provided in technological environments,
potentially engaging students of dierent mathematical skills and
levels of understanding with mathematical task and activities.
Additionally, the visualization of mathematical concepts and
exploring mathematics in multimedia environments can foster their
understanding in a new way. Thus, by integrating ICT based
educational tools into everyday teaching practices, teacher can
provide creative opportunities for supporting students
learning.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Potential of Technology cont....[Hollebrands, 2007, p.166] New
learning opportunities are provided in technological environments,
potentially engaging students of dierent mathematical skills and
levels of understanding with mathematical task and activities.
Additionally, the visualization of mathematical concepts and
exploring mathematics in multimedia environments can foster their
understanding in a new way. Thus, by integrating ICT based
educational tools into everyday teaching practices, teacher can
provide creative opportunities for supporting students learning. On
the one hand, gifted students can be supported more eectively than
ever by nurturing their individual interests and mathematical
skills.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Potential of Technology cont....[Hollebrands, 2007, p.166] New
learning opportunities are provided in technological environments,
potentially engaging students of dierent mathematical skills and
levels of understanding with mathematical task and activities.
Additionally, the visualization of mathematical concepts and
exploring mathematics in multimedia environments can foster their
understanding in a new way. Thus, by integrating ICT based
educational tools into everyday teaching practices, teacher can
provide creative opportunities for supporting students learning. On
the one hand, gifted students can be supported more eectively than
ever by nurturing their individual interests and mathematical
skills. On the other hand, slow learners can be provided with
activities that meet their special needs and help them to overcome
their individual diculties.Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
The Dynamic Mathematics Software GeoGebraWe will discuss about
user interface of the software and implementation of e-learning
principles in GeoGebra.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
The Dynamic Mathematics Software GeoGebraWe will discuss about
user interface of the software and implementation of e-learning
principles in GeoGebra. Since GeoGebra can be used to create
instructional materials, an overview of basic skills will be
discussed and types of instructional materials whose creation is
supported by GeoGebra will be discussed.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
The Dynamic Mathematics Software GeoGebraWe will discuss about
user interface of the software and implementation of e-learning
principles in GeoGebra. Since GeoGebra can be used to create
instructional materials, an overview of basic skills will be
discussed and types of instructional materials whose creation is
supported by GeoGebra will be discussed. Also ways of integrating
GeoGebra into everyday teaching will be discussed.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
GeoGebra- Brief backgroundGeoGebra, a brainchild of Prof. Markus
Hohenwarter, combines the ease of use of a dynamic geometry
software (DGS) with features of a computer algebra system (CAS) in
such a way that
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
GeoGebra- Brief backgroundGeoGebra, a brainchild of Prof. Markus
Hohenwarter, combines the ease of use of a dynamic geometry
software (DGS) with features of a computer algebra system (CAS) in
such a way that On the one hand, GeoGebra can be used to visualize
mathematical concepts as well as to create instructional
materials.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
GeoGebra- Brief backgroundGeoGebra, a brainchild of Prof. Markus
Hohenwarter, combines the ease of use of a dynamic geometry
software (DGS) with features of a computer algebra system (CAS) in
such a way that On the one hand, GeoGebra can be used to visualize
mathematical concepts as well as to create instructional materials.
On the other hand, GeoGebra has the potential to foster active and
student-centered learning by allowing for mathematical experiments,
interactive explorations, as well as discovery learning.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Design of GeoGebraGeoGebra oers two representations of every
object:
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Design of GeoGebraGeoGebra oers two representations of every
object: The numeric algebra component shows coordinates, an
explicit or implicit equation, or an equation in parametric form,
while the Geometric component displays the corresponding solutions
set. In GeoGebra both representations can be inuenced directly by
the users.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Design of GeoGebraGeoGebra oers two representations of every
object: The numeric algebra component shows coordinates, an
explicit or implicit equation, or an equation in parametric form,
while the Geometric component displays the corresponding solutions
set. In GeoGebra both representations can be inuenced directly by
the users. On the one hand, the geometric representation can be
modied by dragging it with the mouse, whereby the algebraic
representation is changed dynamically.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Design of GeoGebraGeoGebra oers two representations of every
object: The numeric algebra component shows coordinates, an
explicit or implicit equation, or an equation in parametric form,
while the Geometric component displays the corresponding solutions
set. In GeoGebra both representations can be inuenced directly by
the users. On the one hand, the geometric representation can be
modied by dragging it with the mouse, whereby the algebraic
representation is changed dynamically. On the other hand, the
algebraic representation can be changed using the keyboard causing
GeoGebra to automatically adjust the related geometric
representation.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Design of GeoGebraGeoGebra oers two representations of every
object: The numeric algebra component shows coordinates, an
explicit or implicit equation, or an equation in parametric form,
while the Geometric component displays the corresponding solutions
set. In GeoGebra both representations can be inuenced directly by
the users. On the one hand, the geometric representation can be
modied by dragging it with the mouse, whereby the algebraic
representation is changed dynamically. On the other hand, the
algebraic representation can be changed using the keyboard causing
GeoGebra to automatically adjust the related geometric
representation. Types of Triangle
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Design of GeoGebraGeoGebra oers two representations of every
object: The numeric algebra component shows coordinates, an
explicit or implicit equation, or an equation in parametric form,
while the Geometric component displays the corresponding solutions
set. In GeoGebra both representations can be inuenced directly by
the users. On the one hand, the geometric representation can be
modied by dragging it with the mouse, whereby the algebraic
representation is changed dynamically. On the other hand, the
algebraic representation can be changed using the keyboard causing
GeoGebra to automatically adjust the related geometric
representation. Types of Triangle There is a manual which explains
functions of each menu items of the software.Dr. P. K.
Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Implementation of e-learning Principles in GeoGebraThe design of
GeoGebras user interface provide solutions for eective learning by
considering the e-learning principles stated by Clark and Mayer
[2003].
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Implementation of e-learning Principles in GeoGebraThe design of
GeoGebras user interface provide solutions for eective learning by
considering the e-learning principles stated by Clark and Mayer
[2003]. Multimedia Principle: Use words and graphics rather than
words alone.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Implementation of e-learning Principles in GeoGebraThe design of
GeoGebras user interface provide solutions for eective learning by
considering the e-learning principles stated by Clark and Mayer
[2003]. Multimedia Principle: Use words and graphics rather than
words alone. At rst, the software oers two views of each object.
The algebraic representation corresponds to the textual component,
whereas the graphical representation adds the visual component
mentioned in this principle.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Implementation of e-learning Principles in GeoGebraThe design of
GeoGebras user interface provide solutions for eective learning by
considering the e-learning principles stated by Clark and Mayer
[2003]. Multimedia Principle: Use words and graphics rather than
words alone. At rst, the software oers two views of each object.
The algebraic representation corresponds to the textual component,
whereas the graphical representation adds the visual component
mentioned in this principle. Secondly, a dynamic construction
protocol can be opened and placed next to the graphics window. It
contains the name, denition, command, and algebraic expression for
each object used in the construction and provides a navigation bar
to go through the construction process step-by-step. The current
construction step is highlighted within the construction protocol
while the corresponding object appears in the graphics window of
GeoGebra.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Implementation of e-learning Principles in GeoGebra
cont...Contiguity Principle: Place corresponding words and graphics
near each other.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Implementation of e-learning Principles in GeoGebra
cont...Contiguity Principle: Place corresponding words and graphics
near each other. At rst, GeoGebra provides popup text that show the
denition of an object when the mouse is moved over one of its
representations. Additionally, popup text appears when the pointer
hovers over one of the toolbar icons, showing the name of the
corresponding tool.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Implementation of e-learning Principles in GeoGebra
cont...Contiguity Principle: Place corresponding words and graphics
near each other. At rst, GeoGebra provides popup text that show the
denition of an object when the mouse is moved over one of its
representations. Additionally, popup text appears when the pointer
hovers over one of the toolbar icons, showing the name of the
corresponding tool. Secondly, labels of objects can either consist
of the name, the algebraic value, or both the name and value of the
object. Since the label follows the movements of its object, the
graphical and algebraic representation of the object always stay
close to each other.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Implementation of e-learning Principles in GeoGebra
cont...Contiguity Principle: Place corresponding words and graphics
near each other. At rst, GeoGebra provides popup text that show the
denition of an object when the mouse is moved over one of its
representations. Additionally, popup text appears when the pointer
hovers over one of the toolbar icons, showing the name of the
corresponding tool. Secondly, labels of objects can either consist
of the name, the algebraic value, or both the name and value of the
object. Since the label follows the movements of its object, the
graphical and algebraic representation of the object always stay
close to each other. Thirdly, both representations of an object are
displayed in the same color, which can easily be modied by the user
to distinguish between objects of the same type. This makes it
easier to nd corresponding representations in the algebra window,
graphics window, as well as in the dynamic construction
protocol.Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Creating Instructional Materials with GeoGebraGeoGebra was
initially developed with the goal of letting students explore and
discover mathematical concepts on their own; it turned out to also
be a very useful and convenient tool for teacher creation of their
own instructional materials.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Creating Instructional Materials with GeoGebraGeoGebra was
initially developed with the goal of letting students explore and
discover mathematical concepts on their own; it turned out to also
be a very useful and convenient tool for teacher creation of their
own instructional materials. Basic Skills needed
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Creating Instructional Materials with GeoGebraGeoGebra was
initially developed with the goal of letting students explore and
discover mathematical concepts on their own; it turned out to also
be a very useful and convenient tool for teacher creation of their
own instructional materials. Basic Skills needed File Handling
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Creating Instructional Materials with GeoGebraGeoGebra was
initially developed with the goal of letting students explore and
discover mathematical concepts on their own; it turned out to also
be a very useful and convenient tool for teacher creation of their
own instructional materials. Basic Skills needed File Handling able
to create and name folder, need to know how to save les in dierent
programme, need to understand the extensions of the le names (e.g.
.ggb for a GeoGebra le), need to be able to navigate within the
folder structure of their computers.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Creating Instructional Materials with GeoGebraBasic Skill needed
cont...Picture File Handling
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Creating Instructional Materials with GeoGebraBasic Skill needed
cont...Picture File Handling need to be able to identify image les
by means of le name extensions, should know how to resize and image
using appropriate software (e.g. Irfan View), should know how to nd
and download image les from the internet and be aware of copyright
issues.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Creating Instructional Materials with GeoGebraBasic Skill needed
cont...Picture File Handling need to be able to identify image les
by means of le name extensions, should know how to resize and image
using appropriate software (e.g. Irfan View), should know how to nd
and download image les from the internet and be aware of copyright
issues. Text Processing software
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Creating Instructional Materials with GeoGebraBasic Skill needed
cont...Picture File Handling need to be able to identify image les
by means of le name extensions, should know how to resize and image
using appropriate software (e.g. Irfan View), should know how to nd
and download image les from the internet and be aware of copyright
issues. Text Processing software need to be familiar with the basic
use of a text processing software etc.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Creating Instructional Materials with GeoGebraBasic Skill needed
cont...Picture File Handling need to be able to identify image les
by means of le name extensions, should know how to resize and image
using appropriate software (e.g. Irfan View), should know how to nd
and download image les from the internet and be aware of copyright
issues. Text Processing software need to be familiar with the basic
use of a text processing software etc. Accessibility and
Internet
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Creating Instructional Materials with GeoGebraBasic Skill needed
cont...Picture File Handling need to be able to identify image les
by means of le name extensions, should know how to resize and image
using appropriate software (e.g. Irfan View), should know how to nd
and download image les from the internet and be aware of copyright
issues. Text Processing software need to be familiar with the basic
use of a text processing software etc. Accessibility and Internet
need to know how to distribute les using CDs or USB drives and
uploading and downloading through internet etc.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Creating Instructional Materials with GeoGebracont...Static
Instructional Material
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Creating Instructional Materials with GeoGebracont...Static
Instructional Material Static instructional materials, such as
handouts, work-sheets, tests can be printout and literally handed
to the students:
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Creating Instructional Materials with GeoGebracont...Static
Instructional Material Static instructional materials, such as
handouts, work-sheets, tests can be printout and literally handed
to the students: By printing a GeoGebra Construction
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Creating Instructional Materials with GeoGebracont...Static
Instructional Material Static instructional materials, such as
handouts, work-sheets, tests can be printout and literally handed
to the students: By printing a GeoGebra Construction By printing
the construction protocol
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Creating Instructional Materials with GeoGebracont...Static
Instructional Material Static instructional materials, such as
handouts, work-sheets, tests can be printout and literally handed
to the students: By printing a GeoGebra Construction By printing
the construction protocol by exporting the drawing pad to the
clipboard
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Creating Instructional Materials with GeoGebracont...Static
Instructional Material Static instructional materials, such as
handouts, work-sheets, tests can be printout and literally handed
to the students: By printing a GeoGebra Construction By printing
the construction protocol by exporting the drawing pad to the
clipboard By exporting the drawing pad as a picture
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Creating Instructional Materials with GeoGebracont...Static
Instructional Material Static instructional materials, such as
handouts, work-sheets, tests can be printout and literally handed
to the students: By printing a GeoGebra Construction By printing
the construction protocol by exporting the drawing pad to the
clipboard By exporting the drawing pad as a picture An Example
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Creating Instructional Materials with GeoGebracont...Interactive
Instructional Materials
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Creating Instructional Materials with GeoGebracont...Interactive
Instructional Materials GeoGebra allows creation of web-based
interactive instructional materials,so called dynamic worksheets
which are also referred to as mathlets or virtual
manipulatives.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Creating Instructional Materials with GeoGebracont...Interactive
Instructional Materials GeoGebra allows creation of web-based
interactive instructional materials,so called dynamic worksheets
which are also referred to as mathlets or virtual manipulatives.
Students dont need to know any thing about the use of GeoGebra in
order to work with these materials.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Creating Instructional Materials with GeoGebracont...Interactive
Instructional Materials GeoGebra allows creation of web-based
interactive instructional materials,so called dynamic worksheets
which are also referred to as mathlets or virtual manipulatives.
Students dont need to know any thing about the use of GeoGebra in
order to work with these materials. Dynamic worksheets are web
pages that usually consist of a dynamic gure and corresponding
explanations, as well as questions and tasks for students.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Creating Instructional Materials with GeoGebracont...Interactive
Instructional Materials GeoGebra allows creation of web-based
interactive instructional materials,so called dynamic worksheets
which are also referred to as mathlets or virtual manipulatives.
Students dont need to know any thing about the use of GeoGebra in
order to work with these materials. Dynamic worksheets are web
pages that usually consist of a dynamic gure and corresponding
explanations, as well as questions and tasks for students. Theorem
of Thales; Pythagorus Theorem
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Creating Instructional Materials with GeoGebracont...Interactive
Instructional Materials GeoGebra allows creation of web-based
interactive instructional materials,so called dynamic worksheets
which are also referred to as mathlets or virtual manipulatives.
Students dont need to know any thing about the use of GeoGebra in
order to work with these materials. Dynamic worksheets are web
pages that usually consist of a dynamic gure and corresponding
explanations, as well as questions and tasks for students. Theorem
of Thales; Pythagorus Theorem Thus, dynamic worksheets can support
guided discovery learning and encourage self- dependent learning as
well as mathematical inquiries.Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Creating Instructional Materials with GeoGebracont...Creating
Interactive Exercise
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Creating Instructional Materials with GeoGebracont...Creating
Interactive Exercise GeoGebra oers a Java Script interface for the
interactive applets of dynamic worksheets.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Creating Instructional Materials with GeoGebracont...Creating
Interactive Exercise GeoGebra oers a Java Script interface for the
interactive applets of dynamic worksheets. It makes possible to
create interactive exercise that check the students answer to a
problem and give feedback.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Creating Instructional Materials with GeoGebracont...Creating
Interactive Exercise GeoGebra oers a Java Script interface for the
interactive applets of dynamic worksheets. It makes possible to
create interactive exercise that check the students answer to a
problem and give feedback. Mixed Number problem-sheet; Fractions of
Quantities
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Creating Instructional Materials with GeoGebracont...Creating
Interactive Exercise GeoGebra oers a Java Script interface for the
interactive applets of dynamic worksheets. It makes possible to
create interactive exercise that check the students answer to a
problem and give feedback. Mixed Number problem-sheet; Fractions of
Quantities At present we are working for a model Dynamic
Mathematics in a Dynamic Learning Environment- Integrating GeoGebra
in Moodle
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Teaching Mathematics with GeoGebraSince GeoGebra combines the
ease of use as well as the construction features , it opens up a
wide range of application possibilities for teaching
mathematics
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Teaching Mathematics with GeoGebraSince GeoGebra combines the
ease of use as well as the construction features , it opens up a
wide range of application possibilities for teaching mathematics
GeoGebra as a Presentation Tool- Static Visualizations; Dynamic
Visualizations
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Teaching Mathematics with GeoGebraSince GeoGebra combines the
ease of use as well as the construction features , it opens up a
wide range of application possibilities for teaching mathematics
GeoGebra as a Presentation Tool- Static Visualizations; Dynamic
Visualizations GeoGebra as a Static Visualizations- To create
sketches and constructions for presentations, handouts or
quizzes.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Teaching Mathematics with GeoGebraSince GeoGebra combines the
ease of use as well as the construction features , it opens up a
wide range of application possibilities for teaching mathematics
GeoGebra as a Presentation Tool- Static Visualizations; Dynamic
Visualizations GeoGebra as a Static Visualizations- To create
sketches and constructions for presentations, handouts or quizzes.
GeoGebra as a Dynamic Visualizations- The dynamic worksheets can be
used for presentation and dynamic visualization of Mathematical
concepts.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Practice Examples for Everyday TeachingFinding the sum of
Interior Angles of a Polygon- Static Visualization
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Practice Examples for Everyday TeachingFinding the sum of
Interior Angles of a Polygon- Static Visualization
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Practice Examples cont...This type of traditional worksheets
that guides students towards nding a formula can be created using
GeoGebra and can be integrated into a traditional teaching
situation in dierent ways:
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Practice Examples cont...This type of traditional worksheets
that guides students towards nding a formula can be created using
GeoGebra and can be integrated into a traditional teaching
situation in dierent ways: Teacher centered approach: Students work
along with teacher while every step of the process should be
discussed and explained.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Practice Examples cont...This type of traditional worksheets
that guides students towards nding a formula can be created using
GeoGebra and can be integrated into a traditional teaching
situation in dierent ways: Teacher centered approach: Students work
along with teacher while every step of the process should be
discussed and explained. Student centered approach: Students work
either alone or in pairs and try to gure out the formula on their
own.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Practice Examples cont...This type of traditional worksheets
that guides students towards nding a formula can be created using
GeoGebra and can be integrated into a traditional teaching
situation in dierent ways: Teacher centered approach: Students work
along with teacher while every step of the process should be
discussed and explained. Student centered approach: Students work
either alone or in pairs and try to gure out the formula on their
own. Mixed approach: After a short introduction and discussion
students could be encouraged to work either alone or in pairs.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Practice Examples cont...This type of traditional worksheets
that guides students towards nding a formula can be created using
GeoGebra and can be integrated into a traditional teaching
situation in dierent ways: Teacher centered approach: Students work
along with teacher while every step of the process should be
discussed and explained. Student centered approach: Students work
either alone or in pairs and try to gure out the formula on their
own. Mixed approach: After a short introduction and discussion
students could be encouraged to work either alone or in pairs.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Practice Examples for Everyday TeachingDynamic Worksheets for
Dynamic Visualizations, Representations and Experimentations
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Practice Examples for Everyday TeachingDynamic Worksheets for
Dynamic Visualizations, Representations and Experimentations For
understanding linear equations following dynamic worksheets can be
used
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Practice Examples for Everyday TeachingDynamic Worksheets for
Dynamic Visualizations, Representations and Experimentations For
understanding linear equations following dynamic worksheets can be
used Understanding Linear Equations
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Practice Examples for Everyday TeachingDynamic Worksheets for
Dynamic Visualizations, Representations and Experimentations For
understanding linear equations following dynamic worksheets can be
used Understanding Linear Equations Thus, transformational scenario
can be presented using GeoGebra, which provides opportunity for
Student Activity, Multiple Representations with Experimental and
Guided Discovery Learning.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Practice Examples for Everyday TeachingDynamic Worksheets for
Dynamic Visualizations, Representations and Experimentations For
understanding linear equations following dynamic worksheets can be
used Understanding Linear Equations Thus, transformational scenario
can be presented using GeoGebra, which provides opportunity for
Student Activity, Multiple Representations with Experimental and
Guided Discovery Learning. GeoGebra 3D- 5.0 beta version
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Finding of Pilot studyOne of the point during the study was
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Finding of Pilot studyOne of the point during the study was To
emerge pedagogy for GeoGebra integration with emphasis on process
involved in teaching and learning of Mathematics.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Towards Pedagogical enhancementIf GeoGebra is to be successfully
incorporated into any lesson then there are some fundamental issues
that need to be tackled at a very early stage. The subsequent
success of the lesson depends upon that.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Towards Pedagogical enhancementIf GeoGebra is to be successfully
incorporated into any lesson then there are some fundamental issues
that need to be tackled at a very early stage. The subsequent
success of the lesson depends upon that. Planning the GeoGebra
based lesson
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Towards Pedagogical enhancementIf GeoGebra is to be successfully
incorporated into any lesson then there are some fundamental issues
that need to be tackled at a very early stage. The subsequent
success of the lesson depends upon that. Planning the GeoGebra
based lesson the key features that one would expect in a plan for a
mathematics lesson:
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Towards Pedagogical enhancementIf GeoGebra is to be successfully
incorporated into any lesson then there are some fundamental issues
that need to be tackled at a very early stage. The subsequent
success of the lesson depends upon that. Planning the GeoGebra
based lesson the key features that one would expect in a plan for a
mathematics lesson: Selecting an appropriate topic, Key learning
objectives, The content of the lesson, Details of any prior
learning, Teaching methodology to be used, Key teaching points, The
foci for assessment, Cross-curricular links, Follow-up work,
Resources
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Learning through GeoGebra (Pedagogy)There are two dierent but
related kinds of learning involved in using GeoGebra, which is
called instrumental and conceptual.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Learning through GeoGebra (Pedagogy)There are two dierent but
related kinds of learning involved in using GeoGebra, which is
called instrumental and conceptual. Instrumental learning is about
how to do things in GeoGebra: how to create points or lines or
circles, how to operate with menu items (like rotate or construct
perpendicular bisector), etc..
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Learning through GeoGebra (Pedagogy)There are two dierent but
related kinds of learning involved in using GeoGebra, which is
called instrumental and conceptual. Instrumental learning is about
how to do things in GeoGebra: how to create points or lines or
circles, how to operate with menu items (like rotate or construct
perpendicular bisector), etc.. It reects the decisions made by the
GeoGebra designer.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Learning through GeoGebra (Pedagogy)There are two dierent but
related kinds of learning involved in using GeoGebra, which is
called instrumental and conceptual. Instrumental learning is about
how to do things in GeoGebra: how to create points or lines or
circles, how to operate with menu items (like rotate or construct
perpendicular bisector), etc.. It reects the decisions made by the
GeoGebra designer. In order to be an eective user of GeoGebra, For
example, users may need to nd and use the tool to construct a
mid-point.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Learning through GeoGebra (Pedagogy)There are two dierent but
related kinds of learning involved in using GeoGebra, which is
called instrumental and conceptual. Instrumental learning is about
how to do things in GeoGebra: how to create points or lines or
circles, how to operate with menu items (like rotate or construct
perpendicular bisector), etc.. It reects the decisions made by the
GeoGebra designer. In order to be an eective user of GeoGebra, For
example, users may need to nd and use the tool to construct a
mid-point. Such learning is not intrinsically mathematical and can
be developed in a context in which users are not deliberately
extending their mathematical understanding.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Learning through GeoGebra (Pedagogy)There are two dierent but
related kinds of learning involved in using GeoGebra, which is
called instrumental and conceptual. Instrumental learning is about
how to do things in GeoGebra: how to create points or lines or
circles, how to operate with menu items (like rotate or construct
perpendicular bisector), etc.. It reects the decisions made by the
GeoGebra designer. In order to be an eective user of GeoGebra, For
example, users may need to nd and use the tool to construct a
mid-point. Such learning is not intrinsically mathematical and can
be developed in a context in which users are not deliberately
extending their mathematical understanding. Tasks that develop
instrumental understanding may involve the creation of images or
the use of features such as reection or animation.Dr. P. K.
Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Learning through GeoGebra (Pedagogy)One striking thing about
GeoGebra, which we had found, that instrumental learning is also
frequently conceptual.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Learning through GeoGebra (Pedagogy)One striking thing about
GeoGebra, which we had found, that instrumental learning is also
frequently conceptual. Mathematical language of the interface both
provides and seeds the preferred vocabulary for subsequent
mathematical discussion.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Learning through GeoGebra (Pedagogy)One striking thing about
GeoGebra, which we had found, that instrumental learning is also
frequently conceptual. Mathematical language of the interface both
provides and seeds the preferred vocabulary for subsequent
mathematical discussion. An understanding of some or many of these
terms is gained in GeoGebra and the words act as both labels for
that experience as well as the commands to make that action
occur.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Learning through GeoGebra (Pedagogy)One striking thing about
GeoGebra, which we had found, that instrumental learning is also
frequently conceptual. Mathematical language of the interface both
provides and seeds the preferred vocabulary for subsequent
mathematical discussion. An understanding of some or many of these
terms is gained in GeoGebra and the words act as both labels for
that experience as well as the commands to make that action occur.
Conceptual learning develops gradually, through deepening
experience with both geometry and GeoGebra.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Learning through GeoGebra (Pedagogy)One striking thing about
GeoGebra, which we had found, that instrumental learning is also
frequently conceptual. Mathematical language of the interface both
provides and seeds the preferred vocabulary for subsequent
mathematical discussion. An understanding of some or many of these
terms is gained in GeoGebra and the words act as both labels for
that experience as well as the commands to make that action occur.
Conceptual learning develops gradually, through deepening
experience with both geometry and GeoGebra. During the pilot study
we found the need to separate out exploratory versus expressive
approaches to using GeoGebra.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Learning through GeoGebra (Pedagogy)One striking thing about
GeoGebra, which we had found, that instrumental learning is also
frequently conceptual. Mathematical language of the interface both
provides and seeds the preferred vocabulary for subsequent
mathematical discussion. An understanding of some or many of these
terms is gained in GeoGebra and the words act as both labels for
that experience as well as the commands to make that action occur.
Conceptual learning develops gradually, through deepening
experience with both geometry and GeoGebra. During the pilot study
we found the need to separate out exploratory versus expressive
approaches to using GeoGebra. One place where this distinction
arises in relation to GeoGebra is with the question of oering users
preconstructed les to explore, rather than having them construct
gures of their own at start.Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Focusing attention when exploring (For Tutorials)Whether
constructing from a blank screen (expressing) or exploring a
preconstructed le (exploring), students will benet from having some
fundamental questions to ask themselves as they investigate.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Focusing attention when exploring (For Tutorials)Whether
constructing from a blank screen (expressing) or exploring a
preconstructed le (exploring), students will benet from having some
fundamental questions to ask themselves as they investigate. Some
fundamental questions need to address while working on applets,
both with and without preconstructed les.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Focusing attention when exploring (For Tutorials)Whether
constructing from a blank screen (expressing) or exploring a
preconstructed le (exploring), students will benet from having some
fundamental questions to ask themselves as they investigate. Some
fundamental questions need to address while working on applets,
both with and without preconstructed les. It might be involved in
helping students deal meaningfully with these questions.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Focusing attention when exploring (For Tutorials)Whether
constructing from a blank screen (expressing) or exploring a
preconstructed le (exploring), students will benet from having some
fundamental questions to ask themselves as they investigate. Some
fundamental questions need to address while working on applets,
both with and without preconstructed les. It might be involved in
helping students deal meaningfully with these questions. Whats
happening?
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Focusing attention when exploring (For Tutorials)Whether
constructing from a blank screen (expressing) or exploring a
preconstructed le (exploring), students will benet from having some
fundamental questions to ask themselves as they investigate. Some
fundamental questions need to address while working on applets,
both with and without preconstructed les. It might be involved in
helping students deal meaningfully with these questions. Whats
happening? This is the fundamental question that all students must
ask when confronted with an applet.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Focusing attention when exploring (For Tutorials)Whether
constructing from a blank screen (expressing) or exploring a
preconstructed le (exploring), students will benet from having some
fundamental questions to ask themselves as they investigate. Some
fundamental questions need to address while working on applets,
both with and without preconstructed les. It might be involved in
helping students deal meaningfully with these questions. Whats
happening? This is the fundamental question that all students must
ask when confronted with an applet. One way of beginning to make
sense of whats happening is to start with the question of What
stays the same and what changes?
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Focusing attention when exploring (For Tutorials)Whether
constructing from a blank screen (expressing) or exploring a
preconstructed le (exploring), students will benet from having some
fundamental questions to ask themselves as they investigate. Some
fundamental questions need to address while working on applets,
both with and without preconstructed les. It might be involved in
helping students deal meaningfully with these questions. Whats
happening? This is the fundamental question that all students must
ask when confronted with an applet. One way of beginning to make
sense of whats happening is to start with the question of What
stays the same and what changes? This question focuses attention on
the hunt for invariance, a fundamental issue in mathematical
thinking.Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Focusing attention when exploring cont....What if?
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Focusing attention when exploring cont....What if? What if . .
.? questions provide a variation on the theme of looking for
invariance.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Focusing attention when exploring cont....What if? What if . .
.? questions provide a variation on the theme of looking for
invariance. The process is now one of asking if I change this, what
else changes? and, by implication, what stays the same?.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Focusing attention when exploring cont....What if? What if . .
.? questions provide a variation on the theme of looking for
invariance. The process is now one of asking if I change this, what
else changes? and, by implication, what stays the same?. What if .
. .? questions are particularly important in whole-class discussion
around a single screen.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Focusing attention when exploring cont....What if? What if . .
.? questions provide a variation on the theme of looking for
invariance. The process is now one of asking if I change this, what
else changes? and, by implication, what stays the same?. What if .
. .? questions are particularly important in whole-class discussion
around a single screen. At every stage, students can be asked to
predict what will happen if the teacher changes something.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Focusing attention when exploring cont...Can I make happen?
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Focusing attention when exploring cont...Can I make happen? The
question might be quite simple can I create a triangle of a certain
area? or it might involve complex problem-solving. The answer to
the question may turn out to be no, but the process of exploration
still may well be valuable.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Focusing attention when exploring cont...Can I make happen? The
question might be quite simple can I create a triangle of a certain
area? or it might involve complex problem-solving. The answer to
the question may turn out to be no, but the process of exploration
still may well be valuable. For example, an attempt to create a
triangle with two right angles may lead to an understanding of why
this is not possible.
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Thankyou for [email protected]
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w
Thankyou for [email protected]
Dr. P. K. Chaurasia
Northern Region Conference (NIME-NRC) New Delhi Dynamic
Mathematics w