Introduction of Integral Calculus..

INTEGRAL CALCULUS

INTRODUCTION_BASICS

The word Calculus Latin word, meaning "Small Stone"

• The basic idea of Integral calculus is finding the area under a curve. 

• To find it exactly, we can divide the area into infinite rectangles of infinitely small width and sum their areas

• Calculus is great for working with infinite things! This idea is actually quite rich, and it's also tightly related to Differential calculus

                                                              

Number System..

NATURAL NUMBER: The natural (or counting) numbers are 1,2,3,4,5,$1,2,3,4,5,$ etc. There are infinitely many natural numbers. The set of natural numbers,$\left\{1,2,3,4,5,\mathrm{...}\right\}$, is sometimes written Nfor short.

WHOLE NUMBER: The whole numbers are the natural numbers together with 0.

INTEGER: The integers are the set of real numbers consisting of the natural numbers, their additive inverses and zero.

$\left\{\mathrm{...},-5,-4,-3,-2,-1,0,1,2,3,4,5,\mathrm{...}\right\}$

The set of integers is sometimes written J$J$ or Z for short.

RATIONAL NUMBERS: The rational numbers are those numbers which can be expressed as a ratio between two integers. Example, 1/2,1/3,1/4...

IRRATIONAL NUMBERS: An irrational number is a number that cannot be written as a ratio (or fraction).  In decimal form, it never ends or repeats. Example, 1.3333333333...

REAL NUMBERS: The real numbers is the set of numbers containing all of the rational numbers and all of the irrational numbers.  The real numbers are “all the numbers” on the number line.  There are infinitely many real numbers just as there are infinitely many numbers in each of the other sets of numbers.  But, it can be proved that the infinity of the real numbers is a bigger infinity. Denoted by R.

COMPLEX NUMBER: The complex numbers are the set {a+ib | 
$a$ and 
$b$ are real numbers}, where i is the imaginary unit. Example, minus value inside the square root.

−1−−−√

Lines and Angles

Pure maths, Applied maths

Course: EPC3_ICT

COURSE EPC 3: CRITICAL UNDERSTANDING OF INFORMATION AND COMMUNICATION TECHNOLOGY (ICT)

The aim of this course is to enhance the professional capacities of a student teacher in integrating Information and Communication Technologies (ICTs) with effective teaching and learning in a classroom.

Course objectives:

To enable the student-teachers:

 1. To teach effectively in a “technology enhanced classroom” (previously referred to as “smart classroom”).

 2. To achieve knowledge-comprehension, practice skills and presentation skills in ICT.

 How to prepare a student teacher for a technology enhanced classroom?

The teachers in Colleges of Education should train the student- teachers

1. To operate /use various ICT tools such as computer, laptop/Internet, Interactive whiteboard, Tablet PC, iPad, iPhone, Mobile phones, Digital cameras, Multimedia equipments (audio/video), Skype and video - conferencing.

2. To browse the Internet, using a computer /laptop, identify and use education related websites and video/audio resources in teaching- learning.

3. To prepare teaching material/learning resource materials: e-content, e-booklet for selected school subject areas and to create edu (cational) blogs for individual/ group students for strengthening sharing and learning.

4. To use a laptop /PC for preparing slides for PowerPoint presentations/ lectures and also download the video resources available on the internet and use them embedded with slide presentations.

 5. To teach a content /lesson using an Interactive whiteboard (by connecting a desktop computer to a whiteboard and project Google images onto it).

6. To use a visualizer/document camera (visual projector) to display and share an information to the whole class.

 7. To use a mobile device/a camera phone to take a series of snapshots of children’s actions events/ scenes/ activities and prepare a photo documentary or photo album with explanatory notes/ descriptions.

8. Prepare videos on different teaching styles of experienced teachers/ peers and keep them available for viewing as a stream on a computer. 

9. Organize a few video-conferencing classes (organize Skype-based video conferencing) inviting experts in school subjects and encourage the students to share the learning experiences through Whatsapp with their classmates and others. 

10.To create educational blogs (edublogs) for individual/group students for sharing and learning articles/ class notes/ assignments and participating in active blogging community.

 Tasks and Assignments:

 1. Write a report based on your preparation of e-content and presentation of it to the class with different ICT tools.

2. Write a report on the organization of video-conferencing with an educational expert

EXERCISE 01: ICT TOOLS

ICT tools: ICT stands for Information and Communications Technologies Computer, Laptop/Internet, Interactive whiteboard, Tablet PC, iPad, iPhone, Mobile phones, Digital cameras, Multimedia equipments (audio/video), Skype and video - conferencing are comes under ICT tools to imparting knowledge to the students in a smart and attractive way.

COMPUTER: It stands for Common Operating Machine Particularly Used for Trade Education and Research. It place a major role in the society nowadays. Each and every department it consider to be as an important and valuable tool. For Education, Computer can be used in education field to improve teaching and learning process. Computer is used in colleges to provide the methods of teaching in different ways. It is used to educate students effectively. Many computer-based educational programs are available for learning purpose.

LAPTOP / INTERNET: 

• Fostering online collaboration with other students
• Providing curriculum support and additional information to students
• Promoting better organization: Laptops help students keep track of their assignments and utilize an online school calendar
• Allowing students to receive and view assignments online and submit their work via e-mail rather than being required to print them
• Improving the review process: Teachers may edit student papers and return them digitally to provide more detailed feedback
• Improving students’ computer skills

INTERACTIVE WHITEBOARD: 

Interactive whiteboards (also known as smart boards) can be described as instructional tools which allow for computer images to be accurately displayed a board with the help of a digital projector.

The elements on the board can then be manipulated by the instructor using a mouse, stylus, pen or his finger and this is done directly done on the screen.

It allows items to be clicked, dragged, copied and even the handwriting of notes is possible. 

The board is usually mounted onto a wall or even to a floor stand. It can be used in work places as well as in classrooms of different levels of learning.

The education system has experienced tremendous changes in the past few years as the traditional heavy textbooks are being replaced by convenient eBooks while notebooks are replaced by devices such as interactive whiteboards, Tablets and iPads etc.,

Tablet PC: Advantages of using TABLET PC in class room environment are as follows:

• Easy to Use
• Direct communication
• Live knowledge base
• Personal approach
• More cost effective than text books
• Faster visualization and quicker reporting
• Improving computer skills boosting creativity
• Hassle-free assessment
• Paperless homework
• Learning Stimulation

 iPad and iPhone:

     There’s a reason both teachers and students love iPad. It enables endless opportunities to create hands-on, customizable learning experiences. Reach more students with apps and books geared to any level or subject. Develop your own interactive materials with iBooks Author. Organize and deliver your lessons with iTunes U. Discover a world of possibilities with iPad.

MOBILE PHONES: 

• Use of audio recording features.
• Live polling tool
• Creating of Videos
• Chart and online discussion forums
• Use of QR codes

Note: Usages of mobile phones in class room environment are allowed only when the permission provided by the management of educational institution and the teachers.

DIGITAL CAMERAS: 

1. Take photos or videos of field trips.
2. Take photos or videos illustrating vocabulary words.
3. Take photos or videos of plant growth
4. Take photos or videos of community
5. Use photos for seating charts.
6. Take photos to illustrate stories or poems
7. Take photos or videos for illustrating emotions
8. Take photos or videos of classroom pet
9. Take photos to prompt creative writing
10. Take photos of learning centers for a choice chart
11. Take photos or videos of bulletin boards or classroom ideas from other teachers
12. Tape a student's photo on their desk nametag so that other students and substitutes learn names.
13. Use photos for attendance chart
14. Use photos for graphing
15. Use photos for story about the child
16. Take photos or videos in Physical Education to record events and skills
17. Use photos or videos for concept illustration for curriculum areas
18. Use photos to create classroom awards. Act of Kindness, Caught being good, Great reader
19. Take a photo of an object zoomed in. Have students guess what it is.
20. Document vandalism with photos or videos

MULTIMEDIA EQUIPMENTS (AUDIO AND VIDEO):

One of the techniques to improving the students’ meets the academic needs and helps them developing English language skills is providing multimedia during the process of teaching and learning in the classroom.

Multimedia classroom provide the students chances for interacting with diverse texts that give them a solid background in the tasks and content of mainstream college courses.

The writing shows that there are some advantages in teaching English using multimedia as a technique in teaching process in the classroom.

Through the media the teacher could give more opportunity to students to express their opinions and enjoy during the course

The highly presence and motivation also bring positive aspects to students so that they can improve their skills.

SKYPE / VIDEO CONFERENCING: 

• Connects different schools for colloboration
• Lets students learn with no out
• Enables to record lessons for review
• Empowers to chart with experts face to face
• Makes out of class learning easier
• Helps connect teachers to parents closely
• Lets students experiences virtual school trips
• Reduces the cost for education

The above are the essential tools (ICT) to enhance the professional capacities of a student teacher in integrating Information and Communication Technologies (ICTs) with effective teaching and learning in a classroom.

EXERCISE 02

To browse the Internet, using a computer /laptop, identify and use education related websites and video/audio resources in teaching- learning

INTERNET:

It can improve the quality of education in many ways. It opens doorways to a wealth of information, knowledge and educational resources, increasing opportunities for learning in and beyond the classroom. Teachers use online materials to prepare lessons, and students to extend their range of learning

USING A COMPUTER / LAPTOP:

• Fostering online collaboration with other students.
• Providing curriculum support and additional information to students.
• Promoting better organization: Laptops help students keep track of their assignments and utilize an online school calendar.

Education related websites and video/audio resources in teaching- learning:

It purely based on the aim to participate students as an active listeners. The following are the some of the websites related to education:-
1- Teacher Tube
2- YouTube for Schools
3- YouTube for Teachers
4- YouTube Education
5- Discovery Education

EXERCISE 03

To prepare teaching material/learning resource materials: e-content, e-booklet for selected school subject areas and to create edu (cational) blogs for individual/ group students for strengthening sharing and learning.

E-Book: The ability to carry many books, references, and resources electronically allows users to make better use of the information, with just-in-time educational advantages. The eBook system allows users to have volumes of information either at their desktop or within their pocket.

E-Content: Content includes facts, ideas, principles, evidence, and descriptions of processes or procedures. A great deal of time is spent on discussing what content should be included in the curriculum, what needs to be covered in a course or a program, what content sources such as text-books students should access, and so on

USES:
1. Universal Access. With e-books, students have access to every book title at all times.
2. Guided Reading Across the Curriculum. Teachers can choose nonfiction titles that are related to science, math, and social studies lessons and use that content to teach key reading skills in small groups
3. Informational Texts. There is a much greater emphasis on students reading nonfiction content than ever before 4. Student Choice. E-book series offer flexibility in the classroom.  For example, in the Britannica Guides Series, there are 10 different titles, all set up in the same structure.

5. Search by MARC Records. E-books provide free linked MARC records, enabling search, discovery, and access to collections from your library catalog.
6. In-class Teaching Tools. E-books are great to explore with the whole class.
9. Student-Tailored Options. Teachers can select e-books by GRL, Lexile level, and grade level to find books on the same subject at multiple reading levels
10. They’re Great for Everyone. E-books are environmentally friendly, they are more affordable than paper-based books, and they take some of the weight off… literally! Books are so heavy!

EXERCISE 04

To use a laptop /PC for preparing slides for PowerPoint presentations/ lectures and also download the video resources available on the internet and use them embedded with slide presentations.

Slide show presentations:

Potential benefits of using presentation graphics include:

• Increasing visual impact
• Improving audience focus
• Providing annotations and highlights
• Analyzing and synthesizing complexities
• Enriching curriculum with inter disciplinary
• Increasing spontaneity and interactivity
• Increasing wonder

Video Resources:

The benefits for teachers using videos in the classroom

• Videos are easier to be accepted by students. ...
• Immerse students in the prodcution. ...
• Stimulate activities. ...
• Video brings more information. ...
• Engage learners. ...
• Integrate the outside world into classroom. ...
• More than words can tell. ...
• Easier to understand.

EXERCISE 05

To teach a content /lesson using an Interactive whiteboard (by connecting a desktop computer to a whiteboard and project Google images onto it)

INTERACTIVE WHITEBOARD: An interactive smart board, also known as an electronic whiteboard, is a classroom tool that allows images from a computer screen to be displayed onto a classroom board using a digital projector. The teacher or a student can “interact” with the images directly on the screen using a tool or even a finger.

 1. Presenting Additional Content on the Whiteboard

2. Highlight Important Information from the Lesson

3. Engage Students in Group Problem Solving

4. Answer Student Questions

EXERCISE 06

To use a visualizer/document camera (visual projector) to display and share an information to the whole class.

Document cameras, also known as visual presenters, visualisers (in the United Kingdom), digital overheads are real-time image capture devices for displaying an object to a large audience. ... Different types of document camera/visualizer allow great flexibility in terms of placement of objects.

Graphing Tool

Highlighting Tool

Test Review Tool

Display Tool

Discussion Tool

EXERCISE 07

To use a mobile device/a camera phone to take a series of snapshots of children’s actions events/ scenes/ activities and prepare a photo documentary or photo album with explanatory notes/ descriptions

Students can identify their mistakes and rectify themselves

Self updating

Focus on the development

Key to commit new projects with several new ideas with the reference of the previous one

Good remembrance and future reference..

EXERCISE 08

Prepare videos on different teaching styles of experienced teachers/ peers and keep them available for viewing as a stream on a computer.

a. Different observers may focus on the same video as the basis of a shared analysis. This increases inter-rater reliability, and if the required level of reliability is not achieved initially, further training of observers may be conducted to increase the reliability.

b. The use of multiple cameras may allow different aspects of the classroom to be captured simultaneously, and synchronization and the use of a mixer will enable the different aspects to be related to each other.

c. Since the videos are permanent records of classroom activities, multiple analyses may be performed. The videos may be analyzed repeatedly, at any time and in any place.

d. The videos may be paused, rewound, fast-forwarded, etc., for further analysis.

EXERCISE 09

Organize a few video-conferencing classes (organize Skype-based video conferencing) inviting experts in school subjects and encourage the students to share the learning experiences through Whatsapp with their classmates and others.

1. Tell your audience exactly what they’ll get at the conference. Identify the key theme, key offerings and, importantly, the benefits they get from attending.
2. Clearly convey in your conference invitation when and where the conference is and how to register.
3. If possible, include a clickable action button to take them right to the registration page.
4. Script your message so your conference invitation covers all the right points concisely. We recently wrote about the pros and cons of scripting. This is a great opportunity for scripting because the conference invitation is a short and sweet message.
5. Choose a good spokesperson, someone the attendees will recognize and who can speak clearly and authentically.

EXERCISE 10

To create educational blogs (edublogs) for individual/group students for sharing and learning articles/ class notes/ assignments and participating in active blogging community.

• Blogging Exercises Student Creativity. One of the best benefits that come as a result of blogging is that it allows people to express and hone their creativity
• Regular Writing Sharpens the Brain's Performance
• Promote Expression of Self
• Blogging Boosts Confidence
• Improve Communication Skills
• Earn Income and Take away..

Exercise 09: Video conferencing given by PROFESSOR THIYAGU SURIYA, Dept. of Education, Central university of Kerala. The following are the pictures taken during the video conferencing..