P K Chaurasia: Dynamic Mathematics with GeoGebra: An Innovation

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


About the talkI will discuss briey on following A couple of classroom scenario- regarding ICT integration

Dr. P. K. Chaurasia


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


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


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


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


Classroom ScenarioIn a normal mathematics classroom,

Dr. P. K. Chaurasia


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


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


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


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


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


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


Few PossibilitiesThere could be few possibilities-

Dr. P. K. Chaurasia


Few PossibilitiesThere could be few possibilitiesIn a substitution method

Dr. P. K. Chaurasia


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


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


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


One Another Scenario of Classroom Processhere, teacher gives up half of the time lecturing on the Mathematical concepts.

Dr. P. K. Chaurasia


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


Design of GeoGebraGeoGebra oers two representations of every object:

Dr. P. K. Chaurasia


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


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


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


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


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


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


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


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


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


Implementation of e-learning Principles in GeoGebra cont...Contiguity Principle: Place corresponding words and graphics near each other.

Dr. P. K. Chaurasia


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


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


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


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


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


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


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


Creating Instructional Materials with GeoGebraBasic Skill needed cont...Picture File Handling

Dr. P. K. Chaurasia


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


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


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


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


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


Creating Instructional Materials with GeoGebracont...Static Instructional Material

Dr. P. K. Chaurasia


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


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


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


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


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


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


Creating Instructional Materials with GeoGebracont...Interactive Instructional Materials

Dr. P. K. Chaurasia


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


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


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


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


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


Creating Instructional Materials with GeoGebracont...Creating Interactive Exercise

Dr. P. K. Chaurasia


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


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


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


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


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


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


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


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


Practice Examples for Everyday TeachingFinding the sum of Interior Angles of a Polygon- Static Visualization

Dr. P. K. Chaurasia


Practice Examples for Everyday TeachingFinding the sum of Interior Angles of a Polygon- Static Visualization

Dr. P. K. Chaurasia


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


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


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


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


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


Practice Examples for Everyday TeachingDynamic Worksheets for Dynamic Visualizations, Representations and Experimentations

Dr. P. K. Chaurasia


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


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


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


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


Finding of Pilot studyOne of the point during the study was

Dr. P. K. Chaurasia


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


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


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


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


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


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


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


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


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


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


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


Learning through GeoGebra (Pedagogy)One striking thing about GeoGebra, which we had found, that instrumental learning is also frequently conceptual.

Dr. P. K. Chaurasia


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


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


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


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


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


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


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


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


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


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


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


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


Focusing attention when exploring cont....What if?

Dr. P. K. Chaurasia


Focusing attention when exploring cont....What if? What if . . .? questions provide a variation on the theme of looking for invariance.

Dr. P. K. Chaurasia


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


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


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


Focusing attention when exploring cont...Can I make happen?

Dr. P. K. Chaurasia


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


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


Thankyou for [email protected]

Dr. P. K. Chaurasia


Thankyou for [email protected]

Dr. P. K. Chaurasia


P K Chaurasia: Dynamic Mathematics with GeoGebra: An Innovation

Documents

Transcript of P K Chaurasia: Dynamic Mathematics with GeoGebra: An Innovation