Making Mathematics Interesting

Some tips and tricks to make mathematics interesting...

Introduce a topic by relating it with daily life, narrate a story,involve students.
Demonstrate some examples and leave rest for students to explore,call children to help you in solving the questions,they will feel important and involved.
Arrange one day in a week, when you are sitting and students are taking up the lessons ,turn wise. It instill confidence in students.
Give home work involving investigation,exploration, not just question solving from the text book.
Allow students to speak, express and write mathematics. This way they will learn to read ,speak and write correct mathematics.
Arrange some sessions of motivating them to read stories ,anecdotes about famous mathematicians and their contributions.
Show them mathematics. Provide them opportunities to visualise mathematics either by hands-on or by showing them readymade resources like Shiksha content CD/EFK content or something prepared by you.
Talk to them about the power of web resources. Tell them to utilise them effectively. Prepare some guidelines so that they do not waste time in surfing the internet.You may prepare a topic wise list of useful websites for them .
Give them sufficient knowledge of web tools/open source software ,like GeoGebra for learning geometry/algebra ,so that they can learn the subject in an interactive manner.
Arrange class competitions for exploring hidden talent in students. It may be a group activity like organising games/puzzles/vedic math demonstration/play etc by the students.
Appreciate work done by students. It is a source of motivation.

A small effort made by a teacher can change the life of many students

Using pictures

Pictures/photographs/diagrams/figures etc play an important role when we are teaching. The schemetic diagrams, flowcharts, mind maps helps a student in remembring outline of the topic.
We may utilise this strategy of teaching through them, in the following way.
Select a photograph.Show it to the students.
Ask them to observe it and note down the observations. This will help in improving the writing skills as well.
You may initiate a discussion on the same, according to the subject's need. .This will improve their verbal skills.
In the subject like mathematics pictures/figures may be used for relating the subject to daily life, deriving information etc.
Through inspiring pictures ,students may learn moral education lessons too.

You may draw animated figure/diagram related to your subject using UnFREEz . Part of an image may be taken using Irfan View. There are other ways also. It is all need based. You may draw the image yourself also and then click its photograph.
I have started with this technique with my students. They try to explain the hidden concepts in their own way, thereby enhancing creative ability, logical thinking and analytical ability. It has helped the students for retaining a concept because of visualisation.

Example Consider the following figure.

The students may observe many mathematical facts from it.

These are concentric circles .(Circles having same centre)

For inspirational picture lessons ,I have created a blog http://inspiringpictures.blogspot.com/

Irfan view..a freeware

Today, I am going to share with all of you, how I used Irfan view in my classroom teaching of mathematics. The students were to perform a mathematics activity in class IX. In place of dictating them the procedure in steps, I showed them a slide show of pictures showing the steps. The students were asked to observe the slide show . Then I had a discussion with them , regarding the steps which were shown to them through pictures. They were able to tell the mathematical concept hidden in the pictures. This way, induced brainstorming and resulted in a better learning. During the class the students were deeply engrossed in watching the show. After this, they did hands on activity with the required material.

Know more about this software...You may download this software from

http://www.irfanview.com/

Fascinating technique

If you want to multiply any number with 9, 99, 999, so on

Consider the following examples
Example 1
99 X 42 = 4158

Procedure
Step 1 Subtract 1 from 42, we get 41
Step 2 Now, Subtract 41 from 99, we get 58

Answer is 4158

Example 2
999x343=342657

Procedure
Step 1 343 – 1 = 342
Step 2 9-3 = 6, 9-4 = 5, 9-2 = 7

Answer is 342657

Audacity...for voice recording

In mathematics it is mandatory for the students to make a project. This time ,with one of the groups, of my class IX students, I decided to gave them a podcasting project . They were asked to prepare a discussion on utility of mathematics in surroundings and record the same using Audacity.Since the students were not familiar of the software, firstly I trained them on how to use it.Then they recorded an interview (kind of a discussion) .It was an enriching experience for me and the students as well.
The students find it quite interesting.
I would like to thank CII Shiksha for training the teachers on using such tools which are helping us for creating a difference in the classroom

Audacity is free, open source software for recording and editing sounds.

You may download it from

http://audacity.sourceforge.net/

Teaching fractions e way

Its a great pleasure sharing with you about a very interesting and useful content for the students of age group 5-12 years.

Teaching and learning about fractions is an integral part of mathematics. What if this topic is taught and learned in a different way i.e. e way. This topic is a part of EFK Content and it is explained so well that the students not only learnt the concept but also were talking about the presentation as well. The topic has been related to composing music using fractions. It is so interesting that while learning there is enjoyment and thrill involved. This way of teaching and learning has made mathematics learning very comfortable for the students of all types. There is incredible creativity involved. The link for the content is given on the Home page of CII Shiksha's e-portal www.eshikshaindia.in.

Magical 7 pieces

Tangram is a chinese puzzle, which has added a creative enhancement dimension to the learning of mathematics.

Mathematics is taught in the classroom ,having more focussed approach on textbook and the syllabus. A classroom learning scenario can be changed by adding more value to the learning of the subject through creative involvement of mathematics other than the textbooks. One such technique is using tangrams for teaching various mathematics concepts. I have explored tangrams and its utility in mathematics taeching.
Here I am sharing, how tangrams can be added to a classroom for teaching concepts like area of geometrical figures viz. square, right triangle, parallelogram etc.
I asked my students to make tangram pieces on a graph paper from the instructions given on the following link http://tangrams.ca/inner/makeset.htm

The students then calculated the area of each cut out shape by counting the complete squares and half squares method.

This way they learnt various properties of geometrical figures.

By paper folding tangram can be easily made. The instructions are explained on the following link http://mathforum.org/trscavo/tangrams/construct.html

Salute to my teachers

Tommorow is Teachers day 5th September.

India has been celebrating Teacher's Day on 5th of September since 1962. 5th of September is the birthday of Dr Sarvepalli Radhakhrishnan, a philosopher and a teacher par excellence. Some of his students and friends approached him and requested him to allow them to celebrate his birthday. In reply, Dr, Radhakrishnan said, "instead of celebrating my birthday separately, it would be my proud privilege if September 5th is observed as Teacher's day". The request showed Dr.Radhakrishnan's love for the teaching profession. All this lead to Teachers Day origin in India.

On the occasion of Teachers day I would like to express my gratitude to all my teachers from Kinder Garten to the Professional college for shaping my life and showing me the right path by providing their valuable guidance. I think, a teacher is like a candle which burns to spread light everywhere.

The mediocre teacher tells. The good teacher explains. The superior teacher demonstrates. The great teacher inspires. --William Arthur Ward

Exploring GeoGebra

Potential of GeoGebra is extraordinary!

I am using GeoGebra for teaching geometry to my students. In class IX, C.B.S.E. Syllabus the properties of circles are taught. I have realised that the students cram the theorems without actually understanding their meaning. At the time of examination they do not attempt the questions based on application of geometry. This year I tried this open source software for teaching the properties of circles . Due to the interactive interface of the software, the students can visualise the geometrical theorems by actually verifying them using the tools available.

For example , the theorem "angle subtended by an arc at the centre of a circle is twice the angle subtended by the same arc at any other point on the remaining part of the circle"

The students do the theoretical proof of this theorem and simply cram it.

I tried learning this theorem using GeoGebra with the students, and the outcome was incredible.

The software is very easy to use by the teacher as well as the students. It is freely available and can be easily downloadable.

The verification of other properties of circles can also be done in the same manner.

Sutra 1

This means "By one more than the previous one"
I am sharing one example where this sutra is applied.
Finding the square of a number ending with 5.
65^2
= [6 X (6+1)] 25 = 4225
For this number , the last digit is 5 and the 'previous' digit is 6. Hence, 'one more than the previous one', that is, 6+1=7.
The Sutra, in this context, gives the procedure 'to multiply the previous digit 6 by one more than itself, that is, by 7'. It becomes the L.H.S of the result, that is, 6 X 7 = 42. The R.H.S of the result 25.

85^2
= [8 X (8+1)] 25 = 7225
For this number , the last digit is 5 and the 'previous' digit is 8. Hence, 'one more than the previous one', that is, 8+1=9. The Sutra, in this context, gives the procedure 'to multiply the previous digit 8 by one more than itself, that is, by 9'. It becomes the L.H.S of the result, that is, 8 X 9 = 72. The R.H.S of the result 25.

Vedic Mathematics

Vedic Mathematics is the ancient system of Mathematics which was rediscovered from the Vedas between 1911 and 1918 by Sri Bharati Krisna Tirthaji (1884-1960). According to his research all of mathematics is based on sixteen Sutras or word-formulae.

Making a crossword

Solving crossword is a brainstorming activity. In teaching of mathematics,this strategy could be utilised effectively. But there is a scarcity of good crossword puzzles. Now, it is not a problem.By just a click of your mouse, you can make interesting and challenging crosswords for the students.

EclipseCrossword is an easy, fun way to create crossword puzzles. And the program is completely free.
This freeware is easy to use.
You simply enter a list of words, along with clues to go with each. Then, EclipseCrossword gets to work turning those words into a crossword puzzle.
EclipseCrossword comes with a tutorial that will have you creating crossword puzzles in no time. The simple interface makes the program easy to use, and there are many options and features that will help you get your crossword puzzles just the way you want them.
Once your crossword puzzles are completed, you can share them with others in a variety of ways. You can print them out. Or you can post them online in either in printable form, or as interactive crossword puzzles. A JavaScript or Java applet allows visitors to your website can solve online.
Create and print out crosswords or save them into either a web page, Microsoft word or text file. ...Try it

http://www.greeneclipsesoftware.com/eclipsecrossword/download.html

A sample Crossword created

Across

2. has famous theorem for a right triangle
4. meaning measuring earth

Down

1. a branch of mathematics
3. tool for solving a mathematics problem
5. father of geometry

Solution

Fibonacci Sequence...Part II

Fibonacci Sequence in nature
The Fibonacci sequence has intrigued mathematicians for centuries. It is noticed that these numbers appear in many different patterns in nature, often creating the beauty we admire.
I have collected the following pictures from various resources to show them to my students. They are asked to look for Fibonacci numbers in pictures of objects from nature. They are asked to look for specific numbers that appear in the sequence, not for the entire sequence.
Normally, I divide students into groups of three or four and distribute the Activity Sheet containing pictures: Finding Fibonacci Numbers in Nature.

Count the number of dots on each flower.

Fibonacci Sequence...Part I

It was first observed by the Italian mathematician Leonardo Fibonacci in 1202. He was investigating how fast rabbits could breed under ideal circumstances. He made the following assumptions:
Begin with one male and one female rabbit. Rabbits can mate at the age of one month, so by the end of the second month, each female can produce another pair of rabbits.
The rabbits never die.
The female produces one male and one female every month.
He calculated how many pairs of rabbits would be produced in one year.

Motivate the students to develop the sequence themselves. Remind them that they have to count only the pairs of rabbits and not individual rabbits.

Give them some hint

You begin with one pair of rabbits ,write 1.
At the end of the first month, there is still only one pair ,again write 1.
At the end of the second month, the female has produced a second pair, so there are 2 pairs, write 2.
At the end of the third month, the original female has produced another pair, so now there are 3 pairs.so write 3.
At the end of the fourth month, the original female has produced yet another pair, and the female born two months earlier has produced her first pair, making a total of 5 pairs ,write 5.

Write the pattern that has emerged : 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and 233...

Observe what rule is being followed to get from one number to the next.

Understand that to get the next number in the sequence, you have to add the previous two numbers.

Kirigami

Kirigami is an art which is a combination of origami i.e. paper folding, and paper cutting. In Japan, the word kirigami had been in use for a long time because "kiru” means to cut, and “gami” means paper.
Making Paper snowflakes is an example of Kirigami. The students can explore incredible hidden symmetry patterns and write on mathematical interpretations. This way they would not only start loving mathematics but surely ask for more mathematics. Click on the following link and visualize the beauty of mathematical patterns generated. The students can explore many patterns and create them using a paper and a pair of scissors.

Interactive Kirigami tool
http://members.aol.com/kevinsw/kweb/kirigami.html

On the following link the instructions for making a Kirigami Flower are given .
http://www.origami-resource-center.com/kirigami-flower.html

Origami

Origami is an art of paper folding. This technique can be utilised in teaching various mathematical concepts.It is known that when we fold a paper, a crease is formed. On that crease a line segment of desired length can be drawn. And by folding that paper again, in such a way that the extreme points of the line segment concides,one can get the mid point of the line segment.Because this technique is based on "working with hands" domain, so the learning of a concept is maximum .The students can visualise the theoritical geometrical concepts taught in the classroom .
Nearly everyone has made paper airplanes or tried origami when we were children. Take these memories further when you download dozens of 3D-Papercraft projects for free.

http://cp.c-ij.com/english/3D-papercraft/

Brain teasers/ videos

We teachers all the time are discussing problems given in the text books and the students also get use to accept this as a regular feature. When there is an inter school mathematics competition or general Olympiads, we expect good results from the students. On the real side we actually are not training the young achievers to solve the non routine problems. In the process a stereotype approach of doing /solving math problems gets registered permanently into the young minds. I personally feel that if we would spend some time on taking up variety of problems in the classroom, it will surely help the students to tackle the non routine problems asked in various competitive examinations.
One way could be taking up simple brain teasers. It is an excellent way to improve the critical thinking, develop on logical thinking and problem solving skills of the students.
Recently, I visited http://www.teachertube.com/ and found various videos on math teasers. It is really a pool of useful resources. You can reach there by the following URL http://www.teachertube.com/groups_home.php?urlkey=BrainTeasers.

Fear of solving word problems

Fear of solving word problems.
There is a fear of solving a word problem in mathematics among the students .About 80% of the students try to avoid it during the examination. Once I had a survey in my class and I asked the students to solve two word problems from the chapter mensuration in class X.
30% students do not even read the problems.
35% do not understand what is being asked in the question?
15% tried to form correct equations but failed.
20% attempted the questions correctly.

There is no way…to skip word problems. But yes we can make solving word problems interesting for students. It is a challenge for a teacher to add a creative element to a dullest and boring work. The first effort made by a teacher could be to inculcate in students an attitude of doing/learning all kinds of problems which are essential for them. The second and the most important aspect is visualizing a problem. If the students visualize a concept, it helps them to learn/grasp the concept quickly. We can use the resources available on the web for making them visualise the concept.

Story telling

Story telling is a strategy which could help math teachers to bind students close to mathematics.There are various true tales/anecdotes of mathematicians which could add a long lasting impact on students to explore mathematics deeply. In my free periods as well as in class teacher period or in House meetings I am using this strategy of story telling.
Here I am sharing some incidents about a famous Mathematician Gauss.
Gauss was a child prodigy (a teenager who acclaimed success at a young age), of whom there are many anecdotes pertaining to his astounding precocity while a mere toddler, and made his first ground-breaking mathematical discoveries while still a teenager.
At the age of three he corrected, in his head, an error his father had made on paper while calculating finances.
Once in primary school his teacher, J.G. Büttner tried to occupy pupils by making them add up the integers from 1 to 100. The young Gauss produced the correct answer within seconds by a flash of mathematical insight, to the astonishment of his teacher,J.G.Buttner.
He added the integers from 1 to 100 in the following manner
S=1+2+3+4+-------------100
S=100+99+98+------------1

2S = 101+101+101+-------------101 (100 times)
S= 10100/2 = 5050.

Gauss had realized that pairwise addition of terms from opposite ends of the list yielded identical intermediate sums: 1 + 100 = 101, 2 + 99 = 101, 3 + 98 = 101, and so on.

If you are sharing some real stories of mathematicians in your classrooms ,Please do share.

eways Probability

In class X C.B.S.E. Mathematics syllabus, the concept of Probability is introduced for the first time to the students. The students more or less cram the idea and do the questions using the formula. But when they actually experiment on probability they ask the questions like I tossed the coin two times and both the times head appeared so the probability of getting a head is 1 instead of 1/2.

I think this way they will not correctly learn the actual probabilty concepts. To make them understand the actual meaning and interpretation of probability,in my classroom teaching of probabilty I have used the probability Applets given on the web for generating the readings.

E.g. if a coin is tossed 100 times then how many times a head appeared and how many times a tail appeared.Then I ask my students to compare the results with the results which they have learned.

And if we increase the number of throws to 200, 300 or more then the students can actually learn the correct interpretation of probability.

I have designed various probability problems. I am sharing some of them.

Throw a pair of die 200 times .Note down the readings. Calculate the probability of the following

getting sum more than 8 on both the dies.

getting a multiple of 3 on first die .

getting prime number on both the dies.

getting an even sum

I have used the following links for generating the readings.

Dice Applets
http://www.math.csusb.edu/faculty/stanton/m262/intro_prob_models/intro_prob_models.html
http://people.hofstra.edu/Stefan_Waner/tutorialsf2/dicesim.html
http://www.joma.org/images/upload_library/4/psol/DiceExperiment.html

http://leepoint.net/notes-java/examples/graphics/rolldice/rolldice.html

Coin applet
http://www.wiley.com/college/mat/gilbert139343/java/java04_s.html
http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/bookapplets/chapter1/CoinTosses/CoinTosses.html

eways coordinates

Here I am sharing, how I have used the cam studio software in my math teaching. I have prepared a lesson plan on the chapter plotting coordinates of points on a graph paper. This topic is introduced for the first time in class IX. The students are not so comfortable in plotting points correctly on a graph paper. They normally commit mistakes while plotting the points and labeling even correct axes. This was bothering me, so I tried a new strategy for teaching this concept to the students. I used open source software Geogebra and created a video lesson using Cam studio. The complete activity was as follows
10 Points were generated on the x-axis and by observing the readings of the coordinates generated, the students quickly answered the coordinates of any general point on the x-axis is (x, 0)
10 Points were generated on y-axis and by observing the readings of the coordinates generated; the students were able to tell the coordinates of any general point on the y-axis.
10 Points were generated in the I quadrant and the students noted their coordinates and visualizing them they noted the observation of any general point in the first quadrant is (x, y)
Similarly points were generated in the remaining three quadrants to note the coordinates of any general point in the remaining 3 quadrants.
This is how I introduced this concept to my students.
Then I gave them the assignment based on the activity.
During the lesson, the whole class was attentive, because their attention was captured by the activity running on the screen. Few of my students have downloaded Geogebra at home, to explore more.

Different Proofs

In class X mathematics syllabus Pythagoras Theorem is taught. The students simply cram the theoretical proof of the theorem given in the N.C.E.R.T. book and thus could not do the application part of it. I think if we could provide the students with various proofs of the theorem, then the students would be able to understand it in a better manner.


Click on these links for Interesting Pythagoras theorem proofs
http://www.teachertube.com/view_video.php?viewkey=1540bc52912baf3aa709
http://sunsite.ubc.ca/LivingMathematics/V001N01/UBCExamples/Pythagoras/pythagoras.html
http://www.ies.co.jp/math/java/samples/pytha2.html
http://www.frontiernet.net/~imaging/pythagorean.html

elearning

I planned my math lesson of teaching angles and measurement using the interactive link elearning for kids given on the Shiksha portal.Firstly, I explored the site and selected the lesson ,then using a projector in my classroom ,I taught the lesson.In the lesson each and every concept related to the topic is well explained.Right from the introduction till the end of the lesson,the students were watching it attentively.They enjoyed the interactive part of the lesson very much.Although there was only one computer available, but I called upon few students to work on the interactive part of the lesson.Then I gave the following link to the students for learning the lesson from home also.
http://www.e-learningforkids.org/Courses/protractor/index.html
In general, the students are not very sure of measuring correct angles using a protractor.They get confused in placing the protractor at a correct place,to measure the angle. In this lesson the way to keep the protractor for measuring the angle is explained in a very appropriate manner. Even, I felt like attempting the excercises given.After the lesson was over, I could find, a smile on the faces of children. Thats what we want.

Info Rapid Knowledge Map

InfoRapid KnowledgeMap is a free mind mapping program and knowledge management system. InfoRapid KnowledgeMap can be used to draw knowledge maps, organizational charts, decision trees and work breakdown structures, taking down your ideas when brainstorming, or generating structure diagrams from XML files. Knowledge maps can be published on the Web or your intranet, can be added to WinWord, Excel and PowerPoint documents, and can be printed in almost any size you choose. The program contains a complete Knowledge Management System suitable for use at home, at work or on the company intranet. Its intelligent KnowledgeMap server analyzes text document content and integrates it with a knowledge map. The Private Edition is not functionally limited in any way and does not expire after any certain number of days. However, unlike the Professional Edition, the program displays a small reminder in the diagram that it has been created with InfoRapid KnowledgeMap. This bit of advertising is intended to acquaint a wider audience with the capabilities of the program, and is your contribution for using the program at no cost.

http://www.bestsoftware4download.com/download/t-free-inforapid-knowledgemap-download-clkrjyal.html

Mathscribe Lite

Mathscribe Lite is a free dynamic graphing and mathematical modeling program. It solves and graphs equations involving standard functions found in algebra, trigonometry and precalculus classes. You can also use it to mathematically model scientific data, either by typing in the data from scratch, or simply pasting it from a spreadsheet or other program.

http://www.mathscribe.com/mathscribe_lite.htm

C.a.R ...a geometry software

C.a.R. is a very useful geometry exploring program. It simulates compass and ruler constructions on a computer. The main screen of this software is shown below, having various tools which would help teachers as well as students to explore on geometrical facts.

I feel that whatever is not possible manually in a classroom can be easily done by using this software. Its my personal experience, that this tool has provided lots of opportunities for self exploring on various math facts which are not there in our text books but are utilised for various research projects .We are able to visualise them by just clicking the mouse button.

Some features....

1. Ruler and compass constructions can be changed by dragging one of the basic construction points. Immediately,it shows the construction on the screen by which one can check the correctness of the construction . It helps the students to gain new insight.
2. Tracks of points and animated constructions can help to understand geometric relations. Tracks can be used as new objects to explore.
3. With the macros of C.a.R. very complicated constructions become possible. Macros are also a way to organize the geometric thinking.
4. Hiding construction details and using colors make constructions clearer to read. In C.a.R. lines and circles can also be reduced to the relevant points.
5. Arithmetic computations, numerical solutions, curves and functions go beyond classical constructions. It is even possible to construct in 3D using advanced macros.
6. Other geometries, hyperbolic or elliptic, can be explored.C.a.R. is a Java driven program running on all modern platforms. Constructions and assignments can be embedded into web pages easily. It can be used free of charge.

To know more about it

http://www.z-u-l.de/doc_en/index.html

Cam Studio...technology in education

Technology is playing a great role in the betterment of education process. Today we are not restricted or bound to follow the traditional methods of teaching in the classrooms. We are provided with innovative methods of teaching which are very interesting to first learn by the teachers and then used for teaching in the classrooms for the students. There are abundant resources available on the web. A correct guidance and skill to use them effectively is only required. Earlier, monetary constraints were bothering the schools to use only the proprietry softwares, but now due to the explosion of open source ,the problem has been solved. Now, only great thinking mind and a group of like minded people are required to fully utilise them to improve upon the education in India.

CamStudio is a free software by which you are able to record all screen and audio activity on your computer and create AVI video files and using its built-in SWF Producer can turn those AVIs into lean, mean, bandwidth-friendly Streaming Flash videos (SWFs) .
You can use it to create demonstration videos for any software program and share it with your friends and students.
You can create video tutorials for your classroom teaching.
You can use it to record a recurring problem with your computer so you can show technical support people.
You can even use it to record new tricks and techniques you discover on your Favourite software program, before you forget them
Download it from
http://www.camstudio.org/

Watch this video for installation procedure.

http://www.camstudio.org/video/install/

Geogebra...a great open source math tool

Geogebra, I must say is a very good tool for learning geometrical facts and lot more. It is an open source tool . Many of the mathematics teachers all round the world are using it and recommending to others for using it.

To know more Go to www.geogebra.org

Picture lessons in mathematics

Children are always fascinated by coloured pictures. Actually, photographs/pictures attract our mind and capture our attention. I am developing some picture shows for my students on http://www.bubbleshare.com/. It is a very interesting way to share the pictures.
In mathematics, I have developed some of the math lessons in the form of stories through pictures. In the beginning, I did not find the relevant pictures from any of the resources, and then one day, I thought of drawing the pictures and taking the photographs of them using a camera. It was an enriching experience for me to click the pictures and then transferring to computers. I must say, technology has provided us with a solution of everything which we want to do.
Working on http://www.bubbleshare.com/

1. Firstly we have to create an account.
2. You will receive an e-mail from them ,confirm your genuine e-mail ID
3. Start making slide shows .Write the album name, browse the photographs,
4. It can be a public or a private album.
5. You can edit the album by adding a caption, clipart, gizmos, audio, video caption.
6. Share the album through e-mail.
7. Add it to your blog by copying/pasting the code generated.

Mind maps

A pedagogical tool for better learning…
Mind mapping…
Mind maps are self created helpers which promote logical thinking .They are like a guide map which could help our mind to memorise the content of a chapter in a systematic manner. Ever since I came to know about this technology evolution, I am working on its utility in mathematics learning. From the internet I came to know about various open source mind mapping tools which the people all over the world are using in various occupations. Its application is not restricted to business or public/private sectors, but people are using this tool in education field also.
This technique focuses on starting the map with a centralized concept/ idea and then emerging from it are various branches which are related to the main concept.It trains our mind to start from a main idea and then to generate suitably the upcoming nodes, linking with each other in a structured manner explaining about the whole idea.It is like a help which is mapping knowledge for remembering a concept for future reference. In a mind mapping tool we have a freedom of using lines, colours, arrows, branches or some other way of showing connections between the ideas generated on the mind map. There are lots of symbols available which helps us in making a structured mind map from a central idea to its evolving branches.Mapping may be seen as a type of brainstorming.For the students it can act like a master tool for preparing for the contents of a subject during the examination time..
Watch a video about Mind Mapping with Tony Buzan

http://members.optusnet.com.au/~charles57/Creative/Mindmap/
Make online mind maps .

Go to http://www.mind42.com/

Freemind is an open source tool for making mind maps.

http://freemind.sourceforge.net/wiki/index.php/Main_Page

Read more about mind maps

http://en.wikipedia.org/wiki/Mind_Mapping

Geometry master 3.0

I am using Geometry Master 3.0 , which is a very useful software to enhance the geometrical learning skills of the children.

• It has in it, drawing tools, geometry terms & shapes.
• This software runs on all Windows systems .
• It has multiple Drawing Tools, Color Fill Options and Custom Shape Tools.
• It also can save the images in GMT, JPEG or BMP format. The output Image can also be printed out to the Printer.
• It is free!

The Screen of this software is shown below...


Go to http://www.caltrox.com/products/geometry.htm
to know more about it.

Roadkil's Graph

Know about a freeware graph tool

• Roadkil's Graph is a freeware application that draws graphs from algebraic formulas entered by users.
• Functions such as sine, cosine, tan, log, log natural and powers can be used.
• The x and y range displayed on the axis can be altered to zoom in and zoom out on the graph.
• Grid lines and value labels are displayed on the graph for easy reading.
• Graphs can also be printed on any standard printer.

Go to http://www.softpedia.com/progDownload/Roadkils-Graph-Download-44235.html

to download it.

This is the main screen of the tool.

You just have to write the function and click on draw, graph will be obtained. I am using this tool ,just to visualise the shape of the graphs of various functions.

Creating online graphs

You can create online graphs of various types.

Go to http://nces.ed.gov/nceskids/createagraph/default.aspx

For creating algebraic graphs
Go to http://www.terragon.com/tkobrien/algebra/

For creating free online graph papers
Go to http://incompetech.com/graphpaper/

Using Graph 4.2

I am using the open source tool Graph 4.2 for teaching plotting graphs and analysing them further. This is a very useful tool. With the help of this tool we are able to plot the functions on a coordinate plane in very less time and are able to analyse various plottings on the same graph by making small changes in the functions.
Example 1

• Ask the students to plot the equations y=2, y=5, y=-3 and y=-5 simultaneously using this tool.
  
• The following graph will be obtained.
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
• It is clear from the graph that all these lines are parallel to the x-axis.
  
• The students will observe this fact themselves and they will note down the observation that the general equation of a line parallel to x- axis is y=+k or y=-k where k is any real number.

Example 2

• Ask the students to plot the graph of x=2, x=6 and x=-3 using the tool.
  
• The following graph will be obtained.

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• It is clear from the graph that all these lines are parallel to the y- axis.
• The students will observe that the equation of a line parallel to the y-axis is x=+k or x=-k, where k is any real number.

The best part of this tool is we can plot y=0.5, y=-6.7, x=7.9 etc equations which otherwise in a classroom are not usually done.

Example 3

• Plotting linear inequalities in one variable x>2, x<5,>4 etc

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• Plotting linear inequations in two variables 2x+3y>6 etc.

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• Like this we can plan various graph excercises for the students.
  
  Your suggestions are welcome. Add a comment.

Beginning...New ways of learning mathematics

Hello everybody,

Inspired from various teachers mathematics blogs , I have created this blog. The main purpose of this blog is to share all the new techniques and methods which are available for the teachers and the students for teaching and learning of mathematics. Mathematics is always considered as a very difficult subject to understand. I think, if the concepts are taught to the students in a way according to the needs of the students,it will definitely improve upon the present situation. I wish, through my blog I could share what all I know and contribute my piece of job to the society.