Mathematics Learning

e Mathematics

2011-12-17T13:43:00.000+05:30

Teaching Math through Games

2011-09-24T08:54:00.001+05:30

Math is one of those subjects that can be taught in an exciting way using the child's natural sense of fun to drive home concepts and facts. The teacher with imagination can make the task of learning about numbers easier and more welcome by using games in teaching maths.

Arranging the room to leave a large open space will provide room for playing math games. This may be accomplished by moving desks to the so that they form a large open rectangle instead of the more traditional rows. This also has the advantage of making each child instantly visible to the teacher who can more easily monitor activity and see when a student is struggling.

Besides being a teacher, I work part time in the marketing department of a lanyard factory. This gave me the idea that using colorful objects such as lanyards can help young students learn about numbers more easily. Many children are visual learners, so bright colors attract and hold their attention. Games played with brightly colored manipulatives will also help tactile learners, since they handle the objects.

Herd the Animals

Goal: Children will learn to group different numbers of animal figures in "cages" to equal 10 total animals.
Preparation: Obtain small plastic animals. You may wish to provide a different type of animal for each group of 4 children in the class. Also provide "fences" to make corrals. Cut out numerals 1-10. Make several sets of these and laminate. Give stamps or small pictures of animals to the children. Provide paper for each group to write down the combinations the find that equal 10.

Play: Divide class into groups and distribute 10 animal figures to each group. Let them manipulate the animals to find various combinations that equal 10 and place the correct numeral with the group of animals (for example, 3 cows plus 7 sheep = 10 animals.) For each new combination, have them write down the numeral with a picture of the represented animal in an equation. The group that discovers the most combinations is a set time wins. Begin with 2 corrals and add 1 more as children are ready.

How Many Can You Find?

Concept: Objects can be measured in several ways using different units

Preparation: Obtain lanyards of two different sizes and correspondingly different colors. The lanyards should be fairly close in length. One set of lanyards for every 3 students will be required. Give each team a piece of tagboard divided into 2 sections with colors corresponding to the lanyards. Two children on each team will measure, and 1 child will record results. Use construction paper in several colors to make squares, rectangles, and triangles with sides the length of the lanyards. Scatter these about the classroom and secure them to the floor using double-stick tape. Place a sticker on each piece to be measured, and a small box of the same stickers next to it.

Play: Divide into groups of three and distribute lanyards and recording boards. Team members will measure the objects placed around the room with the lanyards and place a sticker under the correct color. Add 1 point for each correct item and take away 1 point for each incorrect item. The team with the most correct items wins.

This game can be used to introduce a unit on measurement. Also take the class outdoors and investigate how many lanyards long the playground fence is, how many lanyards wide a window is, etc. Once the children understand how to measure with a whole lanyard, mark some lanyards in inches and help them record how many units tall or wide various classroom objects are. Then make half-inch divisions and play again.

Let's Go Shopping

Goal: Each child will learn to count money up to 1 pound. Children will understand how to combine coins to purchase a larger item than they could purchase themselves.

Preparation: Label cereal boxes and other items with "prices." Place grocery items on book shelves to create a store. Prepare grocery lists of different items that together add up to 1 pound.Make each list different from the others, and make enough lists so that each group of 4 children has a list. Give each child in the classroom coins so that each group of 4 has the equal of 1 pound. Provide 1 bag for each group.

Play: Divide into groups and distribute lists. Ask the children to shop for their groceries and bring them "home." Then have them write down the cost of each item they purchased and add up the cost.The first group with all items correct wins.
As the children get more adept at counting money and figuring prices, add to the items on the lists and increase the amount they can spend. In time, they will be able to correctly count out change and add coins.

Make mathma practice interesting for children by devising games for them to play using colorful objects. These activities are limited only by the teacher's creativity. Follow up the games with corresponding worksheets for children to use as homework. Next day, go over the worksheets in class and let the children use the manipulatives again to prove their answers. A solid foundation in math understanding can be gained in this way.

Dunya Carter is a primary school math teacher from Sydney, Australia. She enjoys coming up with ways to engage her students and help them learn math effortlessly and in a fun way.

Create a word search puzzle

2011-07-31T09:14:00.000+05:30

After completing a chapter, we can give word search puzzles to students for recapitulating the important terms related to the chapter. You may use a free online tool http://www.armoredpenguin.com/wordsearch/ for creating them . You may save the puzzle in various available formats. I have taken it as an image as shown below. This is a word search puzzle on geometry related terms. The words are placed in forward/backward and upward/downward directions. Find as many words as you can. The solution to the puzzle is given below.

Solution

NPSC Workshop for Maths teachers

2011-02-04T17:52:00.004+05:30

A one day workshop for Maths teachers of NPSC Schools was organised at DAV Public school, sector 14, Gurgaon on 19th January, 2011. Around 50 teachers from DAV and Non DAV Schools participated.
The Principal Mrs. Anita Makkar initiated the workshop by introduction of theme and the importance of Mathematics in daily life. Thereafter following sessions were held during the session.

Session 1: Formative assessment in Mathematics- tools and techniques
Session 2: Creating FA Tasks and Remedial Strategies
Session 3: Collaborative projects

Teachers participated in all the sessions with enthusiasm and shared their experiences. They created FA Tasks and created Math model of an icosahedron during collaborative projects session.

It was an enriching experience for me as I got an opportunity to interact with Maths teachers of different schools.

Play Ken Ken

2010-09-27T14:08:00.006+05:30

Today I found this interesting online game. It is named as Ken Ken. It is also a grid game. Rules for playing the game are as follows.

This is an example of 4x4 grid.

Here is the answer.

You can find the online game here.

Day number of a year

2010-09-26T21:11:00.004+05:30

Calculate DAY NUMBER OF A YEAR using this online tool

http://mistupid.com/calendar/dayofyear.htm

Snap it- Screen Capture Software

2010-09-14T18:21:00.000+05:30

SnapIt is easy to use screen capture software which allows you to easily capture
anything on the screen including windows, menus, full screen, rectangular regions,
web pages and take shots of moving images.

It is a very convenient tool for bloggers. When you write posts on your blog you need to
capture and crop images from different sources - this tool is for you.

- Supports hotkeys, auto-saving, clipboard
- Automatically copies screenshots to the clipboard
- Tracks capture history, auto-saves captured images
- Saves files in BMP, GIF, JPEG, PNG and TIFF formats
- Auto-names captured images

Here is the link:

Screen Capture Software

Making Math Fun

2010-09-08T19:51:00.001+05:30

The younger child learns through play. This is a well-known fact that prompts many fun ideas in preschool educators; but once children hit elementary school, the fun tends to slowly diminish over time. Hands on projects are replaced with worksheets that display fewer and fewer pictures as kids make their way into higher grades.
Because math is a difficult subject for many children to grasp, keeping the fun alive may just be a way to assist students in their quest for knowledge. Realizing that not all children learn in the same manner, it makes sense to pepper your math lessons with audio and visual tools. For some elementary aged children, there is a need to be very hands on for learning and retention to occur.
For the teacher who presides over 20 or so squirming second graders, it can be a bit scary to consider introducing new lessons that may get out of hand. Classroom control is always in the forefront of the elementary teacher’s mind; and rightfully so. However, an outdoor lesson that is engaging and fun can hold students’ attention even better than a lesson in which they are sitting quietly at their desks.
To keep children engaged, give them real-life objects to use for counting. This could be stickers, gold coins or skittles if they have been very good. Kids enjoy counting objects that are interesting and familiar. Colorful objects can be mentally stimulating and kids get a kick out of the novelty. A teacher can make changes to objects used for counting throughout the year as a way to consistently challenge students and hold their attention.
When teaching about money, it makes a difference what you use. Whenever possible, use real money to teach about this subject. Handling money is a real-life skill, and for children to adequately grasp and retain information, it helps to use real-life objects as much as possible.
It is always essential for a teacher to relate with their students. This is true regardless of the subject being taught. Fun math will include kids’ interests. This is why using small snacks such as colored candies, grapes, pretzels or marshmallows goes over so well with younger students. Planning a fun math lesson that includes snacks can be a great end of the week treat to reward children for a week of positive classroom behavior. Kids also love sports; which allows a teacher to utilize some of their favorite sports when teaching statistics.
Word problems prove to be a real challenge for many students. A teacher can help by creating fun word problems that students can relate to. For instance, use the name of a student in the word problem, and a real-life situation that student may encounter. “Sally had three pickles in her sandwich and ate two...”
Kids and math can be a great mix with a little planning and a focus on the fact that children learn through play. These tips for fun math can be used effectively throughout elementary school and even into junior high.

Emily Suess, who loves creating lanyards and a graduate of Indiana University-Purdue University Indianapolis, writes about recent school trend topics like conference tips and college issues. She has worked for over seven years as a freelance writer/editor and is now focusing on early childhood education. Her works have been published in Children’s Digest magazine and Indiana Insight magazine as well as on the web.

Enhancing Student Learning: The Applications of Formative Assessment in Mathematics

2010-07-14T22:04:00.002+05:30

In contrast to summative assessment (infrequent, long tests given well after material has been taught), formative assessment enhances learning by motivating students and by providing teachers with more extensive feedback. Consistent, short assessments conducted within a week of learning a new concept are direct manifestations of academic progress to both teachers and students. When students can visually map their progress using the empirical evidence provided by frequent assessments, they are more likely to be motivated and persistent in their studies. Teachers also get a clear picture of the efficacy of their instructional methods. Formative assessment is collaborative, interactive, and positive: three qualities that should characterize any type of education. Translating Formative Assessment into the Language of MathematicsFormative assessment means more than just frequent testing. Teachers must organize and analyze the evidence they gather from assessments, using it to develop more informed and successful methods and lesson plans. For math teachers, this means that formative assessments should be developed around goals for student learning such as increased accuracy, deeper understanding of concepts, correct use of vocabulary, logical application of knowledge to new problems, etc. Assessment results should then be analyzed in terms of the goals set by the teacher, and instruction should be modified accordingly. Math-Specific Teaching and Learning StrategiesWritten tests can be effective ways to conduct formative assessment, but oral tests and homework are also important focal points. In any of these cases, it helps to make the assessment more interactive:· Prior to teaching the meaning of new math terminology, have students write down their own definitions for the words. Have them re-write these definitions after instruction. Collect both versions and analyze for basic understanding before building upon this knowledge.· When teaching students to solve a new type of problem, write out a sample problem on the board along with three or four different answers. Have the students vote on which answer is correct, and then engage students in discussion: which mistakes led to the wrong answers? This strategy helps prevent errors and indicates the depth of students’ understanding of new problem-solving patterns.· Have students write out the steps they take from first viewing a problem to writing down the solution. This can help identify gaps in the problem-solving process so that they can be addressed by further targeted instruction. · Base summative assessments on insights gained from formative assessments. Write tests to analyze documented problem areas and watch for signs of improvement.

Bio: Alexis Bonari is a freelance writer and blog junkie. She is currently a resident blogger at onlinedegrees.org, researching areas of http://www.onlinedegrees.org">online colleges.

15 Places to Learn More about Algebra and Geometry

2010-06-23T12:22:00.001+05:30

15 Places to Learn More about Algebra and Geometry

There are many different sites around the web dedicated to helping students and teachers of algebra and geometry. Site resources often include tutorials, practice problems with explanations, worksheets, homework helpers, and problem solvers. Here are 15 places to learn more about algebra and geometry over the summer.

Algebra

West Texas A&M University Virtual Math Lab - The West Texas A&M University Virtual Math Lab offers more than 100 free tutorials for beginning, intermediate, and college level algebra students. Each tutorial includes an introduction, learning objectives, definitions, formulas, illustrations, step-by-step examples, practice problems, and links to additional resources. Some tutorials also include practice tests.

Algebra.com - The free tutors on this site have written algebra tutorials, problem answers with explanations, and many other resources for pre-algebra, algebra I, and algebra II students. Other resources on Algebra.com include interactive solvers for algebra word problems and a question board.

AlgebraHelp.com - AlgebraHelp.com provides an enormous selection of Algebra lessons, worksheets, and calculators. The site also posts sample problems with solutions.

The Futures Channel - The Futures Channel offers a large selection of algebra activities that include explanations, movies, and more. Just a few of the covered topics include fractional exponents, exponential equations and functions, linear equations and functions, quadratic equations and functions, coordinate systems, and variables.

xyAlgebra - This algebra and verbal problem tutor includes Interactive instruction, practice problems, and step-by-step help. xyAlgebra is free to download and includes executable demo programs.

Geometry

AnalyzeMath.com - AnalyzeMath.com is a good place to learn more about geometry online. The site offers beginner to advanced level geometry problems and tutorials. Other site features include free geometry worksheets and calculators.

GeometryFormulas.com - GeometryFormulas.com is part formula directory and part help center. The site offers an explanation of the different types of geometry as well as 2D geometry formulas, 3D geometry formulas, postulates, and theorems. Other resources include links to calculators, converters, graphers, and problem solvers.

OnlineMathLearning.com - This site offers geometry help through video lessons and basic explanations. Other site features include geometry word problems and practice questions.

Gamequarium - Gamequarium is a good site for students who struggle with geometry or don't like to study. The site offers dozens of geometry games that engage students while they learn.

All About Geometry - Created by Dr. Suzanne LeBeau, an educator and technology adviser, this site links to a wide range of websites that offer geometry help, formulas, tutorials, and more. Some of the most valuable links include a geometry resource guide, a geometry problem of the week, and interactive geometry problems.

Algebra and Geometry

Khan Academy - This not-for-profit organization is the ultimate source for algebra and geometry videos. Each video explains a specific concept in easy-to-understand language.

Math.com - Created for students, parents, and teachers, Math.com offers algebra and geometry homework help, practice, games, calculators, and other learning tools. The site also provides a glossary and a formula guide.

Cut the Knot - Cut the Knot is an award-winning math website that offers help with algebra, geometry, calculus, basic arithmetic, and more. The site explains many different concepts and formulas and includes interactive examples with each.

Webmath - This math help website can be used to solve specific algebra and geometry problems. Simply enter the problem into Webmath's generator and hit the solve button. The generator will display the answer along with an explanation of how the problem was solved.

The Math League - The Math League offers a mathematics help facility for students in grade four and up. The help facility includes an introduction to algebra and problem-solving tips for geometry.

Guest post from education writer Karen Schweitzer. Karen is the About.com Guide to Business School. She also writes for PharmacyTechnicianCertification.com.

How to introduce Coordinate Geometry?

2010-06-19T11:09:00.002+05:30

Students learn formulae for calculating distance between two points, area of a triangle when vertices are given , section formula etc. More stress is on learning formulae and solving questions.
On Mathematics 24x7 I initiated a discussion on How do you introduce coordinate geometry and relate it with daily life examples?

Replies...
Colin said...
I mention some alternative approaches so that you have a choice. The Cartesian Coordinate System could be introduced from a historical perspective, mentioning the works of René Descartes who invented the system. Discuss why it was novel: it connected geometry and algebra, and why it was important: it enabled the work of Isaac Newton, to begin with. You could compare the rectangular framework of the Cartesian system with the circular framework of the Polar Coordinate System, explaining how they differ. I'm not suggesting that you try these approaches; I'm glad that I learned the chemistry of oxygen without being confused by the Phlogiston Theory. In teaching Physics to young adults, little introduction was necessary. I used rectangular and polar coordinates by way of examples, the trajectory of a cricket ball or of the International Space Station. I explained some basic conventions for describing the laws of motion. The y-axis usually represents the up-direction, but not always. The equations for a ball rolling off a table are easier if the origin is at the edge of the table, and the y-axis points downwards. All of this was explained using diagrams on the whiteboard, and I encouraged students to come to the white board and draw the diagrams from their text book.

The answers may lie in biology and psychology rather than in mathematics. According to two recent articles in New Scientist, fiddler crabs are good at trigonometry and humans can't navigate their way out of a paper bag.

Maria D said...
First, I introduce grid reasoning through combinatorial grids - both art projects (shapes horizontally, colors vertically, cool combinations) and, with older kids, guessing games like "guess my rule hangman" on a grid (e.g. 2x+y can be the rule, and the person who made it up tells answers to grid cells until others can guess the rule).

Coordinates themselves get introduced through map-based games, such as Battleship or Maze

Kids are just told to give pairs of numbers and see the results, and because games are goal-driven, the feedback loop does its trick.

The problem with coordinate geometry is that kids don't have strong coordinate reasoning foundations, especially the idea of CO-VARIATION. These early activities help with that.

Equations of lines is a good topic for a start of coordinate geometry, and the Green Globs game is great for introducing it: http://web.mac.com/ihor12/Math2.0/

For a first "areas through coordinates" task I would probably ask kids to program anything (Excel, Scratch, GeoGebra) to calculate areas of rectangles by coordinates of end points. This comes in cartography applications. I can imagine it as a game mechanic in games about conquests of territories.

Darren Said...
That crab article is my favourite suggestion so far. Display a picture of a Hermit Crab from the CC collection on flickr, share this little snippet of info in the article, walk the class through the problem, then (working in collaborative groups) tell them they're hermit crabs and they have a problem to solve: "Swiper the Hermit Crab is about to steal their home ..."

With a little modification this could be used to introduce the Pythagorean Theorem, the distance formula, trigonometry, analytic geometry, or, if we include something about the rates at which they (as crabs) and Swiper can move this problem can be explored in calculus classes as well.
Michael said...
My experience of teaching the coordinate geometry is to begin it when children already know the connection between the position of point and it`s coordinates. It is necessary that they will know about locus ( maybe intuitively ) - from euclidian geometry. I think that the coordinate geometry goes after euclidian geometry and basics of function. Many things are clearly illustrated on "checked" paper - parallel and perpendicular lines, slopes -
are taught as problems on construction. We may make use of similarity - in order to conclude about equal angles and the consequent parallelism of two straight lines. As a matter of fact - similarity already is somewhat algebraic. After this pupil became more convinced about the usefullness of algebraic method and can begin to speak about geometrical facts in the language of algebra.

How product of two negatives is positive?

2010-06-06T14:14:00.001+05:30

A query was posted by Madiraju on Mathematics24x7
when i was teaching in algebra class one of my students got the doubt how the product of two negatives will be positive?

Replies...

Useful Link

Senad said...
You could use basic reasoning and explain this :
For example, you are probably familiar with this one:

" The enemy(-) of my enemy(-) is my friend(+) "
" The enemy(-) of my friend(+) is my enemy (-)"
" A friend(+) of my enemy(-) is also my enemy(-)"

etc ...

But we all know it is a convention ( -1 ) * (-1) = 1 ...

Whit Ford said...
I prefer an expanded version of the (brief) number line explanation that was given:

- Multiplication represents repeated addition, so (3) x (5) represents three fives added together

- To represent this on the number line, I start at zero then move the the right by five units three times. I will land at (+15).

- If a negative sign is involved, it turns addition into subtraction... which would cause me to move in the other direction on the number line.

- To represent (3) x (-5) on the number line, I need to "add negative five" three times which is the same thing as "subtracting five three times", so I will start at zero, and move to the left by five units three times. I will land at (-15)

- To represent (-3) x (-5) on the number line, I need to "subtract negative five" three times. This reverses the previous example. I still start at zero facing left to move by negative five, but the (-3) means that instead of moving the way I am facing three times, I move backwards... to the right by five units three times, landing at (+15).

- The essence of this explanation could be turned into a physical demonstration in the classroom: Have someone stand up facing "forward". Ask them to walk forward for three steps = (3) x (steps). Ask them to, still facing forward, walk backwards for three steps = (3) x (- steps). Now ask them to face "backwards" and walk "backwards" for three steps = (-3) x (- steps). They end up having moved in the forward direction, and the rule about double negatives logically cancelling each other out in an English sentence should come to mind: they did not not move forward.

Senad said...
Well even though I'm not a teacher, and I even agree with what you said, I need to disapprove the second method (walking).

The best way I think is to go with my example, it is a basic principle that even a 5 year old would understand. It requires no previos knowlage, and you don't have to walk a mile to understand it. Certanlly, as a student- I appreciate correct methods that will produce best possible results in small amount of time.

For example, if (-1) * (-1 ) would be ( -1 ), if that was a convention, ( " The enemy of my enemy is my enemy " ) would be in contradiction to all things known to man, even politics doesn't work that way :). And try explaining distribution law, using your mentioned " walk " method... Or you coud try to explaing in what cases, (-1)^n would result in 1, or in (-1).

Whit Ford said...
I cited the walking example as a way to try help someone understand *why* a double negative is a positive. The rules you cite certainly are often used in life, but if a young student is questioning why the rules are true in the first place... well, that can be a tough question to answer to their satisfaction. I cited the walking example in an attempt to connect very concrete initial steps to an abstraction in the later steps: backwards. But hopefully students have enough personal life experience with "backwards" to have a decent and growing intiutitive sense of what it means and can stand for.

Once a student accepts that the product of two negatives is a positive, and has been working successfully with it for a while with simple multiplication problems, I would abandon attempting to connect increasingly complex operations, like exponentiation, with the number line or physical examples - and base explanations on the rules of multiplication that the students have acquired a comfort with from personal experience as you advocate.

I explain the sign of (-2)^n to students studying the laws of exponents by telling them to count the number of negative signs that will be in the final product (n), and recall that a double negative makes a positive. Therefore, I can use the associative property of multiplication to group the repeated multiplication problem into pairs of negative signs which cancel one another out. Since 15 or 16 year old students should be very comfortable with the concepts of odd and even by now, they are usually quite comfortable with visualizing pairs of negative signs cancelling each other out, therefore if n is even, the answer is positive... and if n is odd, the answer will be negative.

I find it helpful to explain multiplication as repeated addition, and exponentiation as repeated multiplication. This implies that exponentiation is repeated-repeated addition... the contemplation of which gives most people a headache! While this explanation is true, I agree that trying to take a framework too far in a completely concrete way can cause more difficulties than it solves. Does that mean the initial explanation should not be used because it will not extend readily (or perfectly) to all arithmetic operations? I think it has value nevertheless... because it helps a student to gain a strong conceptual understanding of the nature of a fundamental operation, one which they will depend on as they learn about increasingly complex functions which depend on the operations they first learned in grade school.

Carolyn said...
One of the visual examples I use for algebra students is on the two dimensional coordinate plane. If they label quadrants in counter-clockwise order of I, II, III and IV, then quadrant I and quadrant III are your positive quadrants.

Since I always show multiplication as an area of length times width, then if you multiply on the coordinate plane you multiply an area of X axis times Y axis. Therefore, by way of example, (-3) x (-4) means go left 3 and then down 4. If you do that you have just created a rectangle in quadrant III. Since quadrant III is positive, you have created a positive area of 12 square untis.

You can then reverse this into divison. If you draw a rectangle 3 x 4 untis, in either quadrant I or III you have a positive area of 12 square units. You then have two choices as to what the sides will be: (3) x (4) or (-3) x (-4). Therefore the area (12) divided by the side (3) is the top (4), or the area (12) divided by the side (-3) is the top (-4).

I don't know if it's the best explanation, but I try to use as much visual as I can. And this is the only way that I can think of to actually visualize the rules. It makes more sense to them than just saying "pos x pos = pos", "neg x neg = pos", etc.

The same principals then work in quadrants II and IV which are negative quadrants.... (-3) x (4) means left 3 and up 4. You now have a rectangle of 12 square units which has a value of (-12) in that quadrant. Again you can draw this in either quadrant II or IV. Your area of (-12) will have a length of (-3) and a width of (4) in quadrant II and your area of (-12) will have a length of (3) and a width of (-4) in quadrant IV. So again, I can reverse the multiplication into division.

I do all my multiplcation/division visually with area - even when it is multiplication and division of fractions. I like to be able to see as much as possible. I dont know if this breaks down as the math get to higher levels, but it works well from very, very easy concepts on through a lot of algebra. If I am dealing with problems that have all real numbers, I use if for completing the square and quadratics, etc. Beyond that I don't know... (A friend of mine who used to work as an engineer, but now teaches math, told me that when working with imaginary numbers I need to use the "a by bi" coordinate plane instead of the "x by y". However, I don't remember ever learning anything about a plane that used a and bi to visualize what to do with your imaginary numbers. In fact, I don't remember ever being shown an "a + bi" plane at all. So I am at a loss at to how to visually demonstrate anything with with imaginary numbers - except that the parabola doesn't have any x intercepts on the (x,y) coordinate plane.)

I was not ever taught math that way when I learned it. But once I realized that I could visualize things that way, (and that was as an adult learner, years after I had a math degree) I took it as far as I could in my mind. Since it has been many, many years since I took any kind of Calculus classes, etc., and since I now teach/tutor only up through College Algebra level, I honestly don't remeber enough of what you learn in those higher level classes to know if this would work well for an explanation at higher levels and finding areas under curves, etc. But for what I show students, it seems to help them visualize how the + and - multiplication/division rules work. And they can also use it for completing the square and they can use it for multiplying binomials.

Hopefully it does not prove to be problematic for them in levels higher than Algebra.... For those of you who teach Calc, etc. let me know if you think that visualizing that way on the coordinate plane would cause any problems later.

Bradford said...
The only true way two negatives will ever make a positive is for us to make friends with our enemies. That said, let's look at it another way. When we fold a circle in half we put any two imaginary points together and crease. This give us a diameter. If we call what we can not see negative (the imaginary points) and by putting them both together will generate a line we can see (diameter), that is positive.

John Faig said...
I like a simple applet to show how subtracting negative numbers actually results in a positive. The applet is from the National Library of Virtual Manipulatives (http://nlvm.usu.edu/en/nav/frames_asid_162_g_2_t_1.html)

Once they master this idea, they should be able to grasp the idea that multiplication is this subtraction of a negative numer repeated over and over.

Anita Sharma said...
interesting discussion!
Another thought-observe the following pattern
-5 x 3 = -15 = (-5)+ (-5 )+ (-5)
-5 x 2 = -10 = -15 +5
-5 x 1= -5 = -10 + 5
-5 x 0 = 0 =-5 + 0
-5 x -1 = 5 = 0 + 5
-5 x -2 = 10 = 5 +5
using fundamental def. of multiplication as addition we can conclude product of two negatives is positive

Deborah Leslie said...
I was also taught to think about multiplication of positive and negative numbers using money analogies:

(+5) x (+3) = receiving $5 three times = $15 more in your pocket = 15

(+5) x (-3) = not receiving $5 three times = $15 less in your pocket = -15

(-5) x (3) = paying $5 three times = $15 less in your pocket = -15

(-5) x (-3) = not paying $5 three times = $15 more in your pocket = 15

It might be confusing for some people, but relating math concepts to money also helped me understand the concept faster.

Bradford said...
(-)+(-)= (+)
Since movement is a right angle function; one line added to one line, when combined at right angles is a plus sign.
(-)+(+)=(-) the second line is missing to make a plus sign, so it remains one line.
(+)+(-)=(-) this is simply the inverse of the above.

Only two things to understand; two lines make a positive symbol. One line does not make a positive symbol.

Senad Ibraimoski said:
You could use basic reasoning and explain this :
But we all know it is a convention ( -1 ) * (-1) = 1 ...

Joshua said...
It's not a convention: it's required by the distributive law and so on.
0 = 0 * 1 = (-1 + 1) * -1 = (-1) * (-1) + 1 * (-1) = (-1) * (-1) + -1,
and therefore (-1) * (-1) = 1.

I don't expect this to be the best way to explain it to students, but I do think it's important to realize that it's not an arbitrary convention but rather a requirement for the properties of addition and multiplication to carry over to negative numbers.

I like the Ask Dr. Math link from Rashmi Kathuria. There's also Teacher 2 Teacher at the Math Forum.

Number-line type arguments are good, as are payment/debt type explanations.

I tend to reason from patterns. I think you can do something like this:
4 * -3 = -12
3 * -3 = -9
2 * -3 = -6
1 * -3 = -3
0 * -3 = 0
and then they can see why -1 * -3 should be 3 to continue the pattern. (I see that someone else below said the same thing, and pointed out that using multiplication as repeated addition we can see why we're adding 3, or if you prefer taking away -3, as you go from each line to the next - that's a good connection!)

The walking and facing method is pretty nice too.

Dylan Faulin said...
This is how I teach it. I just wanted to '2nd' this suggestion. It's hard for students not to see this pattern. By the way, I do the same thing when introducing negative exponents:

5^3 = 125
5^2 = 25 = 125 / 5
5^1 = 5 = 25 / 5
5^0 = 5 / 5 = 1
5^-1 = 1 / 5
5^-2 = 1/5 / 5 = 1 / 25

This also takes care of why anything (but 0) to the power of 0 is 1.

Challenges as a Math teacher

2010-06-05T13:53:00.000+05:30

What according to you is a greatest challenge faced by you as a Math teacher?

Taleese Walsh said...
It's funny, I've been thinking about this very question this month, as I've been preparing for my first workshop for pre-service math teachers. As a 6th grade math teacher, I believe my biggest challenge is to overcome built up fears, inhibitions, and an "I'm not good at math" attitude, prevalent especially in students who have failed to succeed in math so far. How do you take a failing student or a just getting by student and turn them into a math believer and a math achiever?

I think...
Yes, fear for learning Math is a challenge for contemporary Math educators to deal tactfully in a classroom. The strategy which I am using to deal with poor performers is using a selective study approach and appreciating even small things which these students are able to do. Then in the end of the say saying aloud "YES I CAN DO MATH" .It enhances their motivation level and keep the working with higher spirits than developing a fear.

Thaddeus Wert said...
For me, it is taking a story problem (hopefully a real-world situation), teaching my students how to develop an appropriate mathematical model of the situation, and then solving it. If a student is faced with a paragraph of information, then she often just shuts down, even if the problem is relatively easy.

Danny Clarke said...
Overcoming the "I hate math" attitude. Students do not realize how much this attitude cripples their ability to learn math.

Maria D said...
Lack of math in the culture surrounding us. Basically, you can't learn math as your "first language" if parents don't "speak" it. I am working on changing that, but it's slow going. This year is slightly better, because social media crossed the next adoption threshold and is mainstream now.

Crolyn said...
Attitude! Administrators are not embarrassed to say that they are not good at math, and excuse a lack of effort on the part of students. Math is not a priority, but art and music and sports are.

My impression of many elementary teachers is that they went into teaching because they want to work with young children and to help them learn to read, but when it comes to math, they share their phobias and dislike of the subject. Parents also echo the sentiment. Until something changes, it will be an uphill battle!

Steven Hsia said...
The over-dependency on calculators. While technology is nice, but the over-dependency on calculators drowns out the basic knowledge needed by my students. For most of them, single digit multiplication and their respective division problems takes 10 seconds without a calculator. Addition and subtraction takes forever without a calculator. I tried to form a competitive math team last year, but I felt dismayed watching calculus students unable to add 1/4 + 1/3. (They thought the answer was 1/7. And this was more than 1 calculus student.) While calculators provide a definitive answer, this answer can be wrong if the user is not careful. The over-dependency on calculators have erroneously eliminated the need for students to step back and think about whether their solution is correct or not. Once they are set on their thinking on how to solve a problem, if they get an answer from the calculator, they will assume it is correct even when the answer defies a logical sense. This over-dependency is mind-boggling.

I think...
Hmmm, this is really scary. Mathematical skills need to be learnt by writing and understanding of algorithms is essential. Use of calculators and other technology tools may be used for analysing situations like graphical analysis. Especially at primary and secondary level , children should not use calculators . You see, software developers are good in designing softwares because of the understanding of logic and algorithm of making it. All that need is deep knowledge of concept. So, I agree to you that over dependency on technology is a challenge for Math teachers.

Danny Clarke said...
I agree. Especially at the college freshman level, so many texts include sections on how to solve problems using the calculator. Of course, this is no help in solving applications (word problems), yet I still get students challenging the score they get on exams by saying, "It can't be wrong, I used the calculator!"

Cristy said...
My biggest challenge: teaching to so many different levels of intelligence in one classroom. I have over-achievers, B/C students, F students, students who don't care, and mentally retarded students ALL IN ONE CLASS.

I think...
Catering to needs of variety of learners is indeed the biggest challenge. A classroom is a blend of all types of students. A teacher has to maintain a balance to keep up all working. The strategy which I am using is giving specially prepared worsheets/assignments according to individual needs of learners. Also , different methods are used like chalk/talk , using multimedia , hands on etc which help in inculcating interest in the subject .

Michael said...
The challenge of teaching math is, IMHO, to study it in order to use it. Exactly as every craft.
In "our" time, that is in 50-s 60-s we didn`t think about our attitude to math - we simple learned it. Modern habit of continuous self - psychoanalysis instead of doing breaks the integrity of world view.
That is my starting point while thinking about the problem. I`m very interested in comment from Maria D. - is it the point?

PendeM.Venket.Kumar said...
hi ......as i know..maths cannot be enjoyed unless a student doesn't know the essence of learning it...what is the need ,application and outcomes.....i start teaching particular topic with the related examples in real life situations which enable the students to understand the real need of learning it.......that may diffuse fear of learning,hatred etc....

Monika Hardy suggested...
This is where tech does come in nicely. With the web - we should be able to cater to every differentiation needed in the classroom.. if we can come to grips with how messy that feels and appears.
Interactive and student made tutorials, small groups who need face-to-face - again led by peers, global groupings formed per passion with peers/college students/professionals, .... every kid can/should get one form of an expert individual tutor, so that they are reeling in constant personal feedback/encouragement.

Dr.Pragati said...
To reduce "Math Phobia" among students is the greatest challenge for Math Teachers. It is generally believed that math is dry and abstract subject. We people are trying to overcome this mentality at our level best. But it is rather difficult to teach each and every topic with the real-world situations like the topics of Abstract Algebra. Many students think that little mathematical knowledge is sufficient to enter into different careers. They don't know the wide applications of it.

Kari said...
Having the time to individually meet each students needs. Classes tend to be a "one-size fits all" because of size, differing abilities, and time constraints. I am unable to reach every student.

Whit Ford said...
To walk into every teaching opportunity with enthusiasm, a visible passion for the subject, an obvious intention to confer your passion to your students, respect for the students interests and talents, and ideas for conveying the day's material in a way that engages the students' interest: Why will this be important in your life? How is this topic connected to what students already know? Where will they need this topic in the future? What kinds of real world problems does this topic relate to, and how? How many different ways can we solve this problem? Can it be solved in a visual/intuitive way as well as in a procedural (algebraic) way?

All of the above is much easier to do for the first class of the day than for the last one...

Erlina said...
I think the challenge to us teachers relies not on how we can make math easy to learn but on how we can make our students love the challenge that mathematics presents.

Mnemonic devices in Mathematics

2010-06-04T13:25:00.000+05:30

Teaching in Harmony wrote on Mathematics24x7
I have realized that though many students struggle w/ remembering simple concepts in mathematics, simple mnemonic devices often prove to be helpful. Here's a poem which I recently discovered which makes distinguishing between formulas for the area and circumference of a circle much easier:
Tweedle-dee-dum and Tweedle-dee-dee,
Around the circle is pi times 3,
But if the area is declared,
Think of the formula pi "r" squared.
"Around the circle" means circumference.
Aside from some of the classics such as "All Students Take Calculus", "PEMDAS", and Chief"Soh-Cah-Toa" I wonder what other mnemonic devices you use in your classes.
Incidentally, years ago, when teaching order of operations to seventh grade students, I had them create posters using their own mnemonic devices using GPMDAS (Groups ...parentheses, brackets, braces, vinculum...Powers (or exponents)...Multiply OR Divide (whichever comes first in order from left to right)...Add OR Subtract (whichever comes first in order from left to right. To this day, I recall some of these:
General Patton Made Direct Air Strikes
Girls Prefer Magnificent Diamonds and Sapphires
Geepers, Pretend My Dog Ate Snausages

Replies...
Collen young said...
What about songs?!
......have you heard the circle song?!
This makes me laugh every time I hear it! I once met some students singing it the day I first played it to them in a lesson.
....and at my school everybody knows about the area of a trapezium thanks to a little song!

Some mnemonics shared by me...
I find this strategy very useful . Some of mnemonics which are used by my students are ...

1)Pi mnemonics are memory aids for remembering the first few decimal digits of Pi:
3.1415926535897932384626433....
The most common type of mnemonic is the word-length mnemonic in which the number of letters in each word corresponds to a digit. This simple one gives pi to seven decimal places:
How I wish I could calculate pi.
May I have a large container of coffee?
Counting the letters of each word gives you the value of pi to 7 places.
2)Please Excuse My Dear Aunt Sally
Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
3) Lucky Cows Drink Milk
The ascending order of Roman numerals: LCDM ...

Sandra (www.realmathinaminute.com ) said...
This is such an old corny one but The Quadratic Formula Song is still around.

There are lots of new tunes and versions of it on You Tube.

Kristen Fouss said...
It's silly, but the kids always have trouble with absolute value inequalities - what's "and" and what's "or"? I always tell them to think of "great-OR" to help them remember.

And we do the quadratic formula to the Pop Goes The Weasel tune. :)

Maria D said...
I would not use a mnemonic for circumference/area, because it's important to understand about lengths of things being proportional to first powers, areas to second, volumes to third and so on. It's cute, though :-)

I use mnemonics for things that do not have any internal math relations to names. One cute mnemonic for a "hard" multiplication fact:
5, 6, 7, 8
56=7*8
(Though it's not very easy to remember, either).

There is a "semi-mnemonic" explanation about order of operations: they go from the strongest to the weakest, mathematically. So powers go before multiplication/division and that before addition/subtraction. It kinda makes conceptual sense.

Sharad sure said...
I feel mnemonics are useful for teaching factual information, but when it comes to the conceptual knowledge it may not be sufficient. A concept have to be developed in the mind of a child.

Will Kimbley said...
Instead of PEMDAS we use GEMS - Groupings, Exponents, Mult/Div, Add/Subt.

For integer addition, we sing to the tune of Row, Row, Row Your Boat:

Same Signs add and keep.
Different Signs subtract and
keep the sign of the higher number.
Then it will be exact.

I created a Glog (online interactive poster) for integer addition that you can see here: http://willkimbley.glogster.com/Integer-Addition/

For integer subtraction, we use Keep, Change, Change then follow the rules for addition.

So, for (-5) - (-7) = we perform the following steps

Keep Change Change
-5 - -7

-5 + 7
then follow the rules for addition, (different signs subtract) so rewrite and solve the problem:
7 - 5 = 2
the sign of the higher number (7) is positive, so the answer is positive 2

Collen Young said...
In all of this I think we have to remember that we are all different - us and the children we teach.

No doubt that the understanding is the most important but then for some those mnemonics can help them remember things for exams which can be stressful. If a mnemonic helps them then so be it!

I find it is actually useful to discuss how we are going to remember key points with a class when we have completed something. If I ever tell them about some mnemonic I know about we then find out who it helps!
In my experience for any given mnemonic, some will find it helpful whilst it does nothing for others in the same class.

Teaching in Harmony said...
I don't think a mnemonic is particularly useful for teaching conceptual knowledge. It is, as its name implies, a memory device only. Keeping Bloom's taxonomy in mind, I always tell my students, "Memorization is the easiest form of learning." Given the choice between memorizing Quadratic Formula, or recognizing and applying its applications, I believe the latter has greater significance.

Sandra said...
I like the mnemonics as an additional teaching/learning tool. Sometimes when a student says, "Move this up and this down" and they have no idea what they are doing, I groan inside....however it does allow a weak student to continue and perhaps reach a point that does make sense conceptually to him. When I teach a student who strugges greatly with math, I appreciate anything that helps him move forward....even if it causes me to groan silently!

A student once told me that you couldn't divide by zero because if you put the eggs in the bottom of the grocery bag they would break. It was okay to have the eggs on top. He would always get this correct but thought it was all about eggs......groan....

Anirban said...
While I was a stuudent in class-3,I remember the mnemonic BODMAS (Big Old Dot Made A Shot ) while approaching Simplification sums to remember the seuence of function from left to right.

BODMAS -----> Bracket, Open, Division, Multplication,Addition, Subtraction.

Girishkumar said...
There is one to remember the conversion
King (Km)
Hitler (Hecto metre)
Died in (Deca metre)
Mumbai ( Metre)
Due to ( Decimetre)
Cholera and ( Centimetre)
Malaria (Milimetre)

Teaching in Harmony said...
I know EXACTLY what you mean, Sandra! *L* ...it's just another tool, though for me, teaching so that students truly understand the concept is most important! I have a friend who teaches students that the "sun shines ABOVE the horizon" and not "below the horizon" to show that division by zero is undefined! *shaking my head* In my geometry classes, I have reserted to pointing out the "SOS" in the word "iSOSceles" to show that help (SOS) is here to show that two Sides are congruent, the two l's in the word parallel to show 'two sides parallel," etc. ....so many others come to mind now that I am facing the beginning of another school year...and am once again in teaching mode!

Lim Ee Hai said...
I believe this form of teaching using songs, poem or otherwise is to trigger the left and right brain similar to mind mapping concept. We can always use or try whatever methods that the students can accept as long as they like them and enjoy them. It is indiectly reducing the anxiety for those facing problem in math. Triggering all senses is the objective, if possible.
But I like this method of poem to excite the students.

Teaching in Harmony said...
I have always told my students that the more they inolve their senses in learning, the easier it becomes....definitely thinking VAKT (visual, auditory, kinesthetic, and tactile) on this one!

Jerry said...
For the trig formulas sin(x+y) and cos(x+y) we had a cheer:

SINE COSINE, COSINE SINE
COSINE COSINE, SIGN SINE SINE

What do you think about mnemonic devices?

Interpretations of Geometric Mean

2010-06-03T12:57:00.004+05:30

Julia wrote on mathematics24x7
My students really struggle with Geometric Mean, and I am finding that many math teachers don't even know what this is. Does anybody have good suggestions for teaching this concept?

Replies:

This is how I teach the concept of GM.
Before teaching GM, students learn the meaning of Arithmetic Mean. Suppose we have a rectangle with sides x and y. Arithmetic Mean of x and y is (x+y)/2 , which geometrically is side of a square whose perimeter is same as the given rectangle. Isn't it? (Perimeter of given rectangle is 2x+2y and perimeter of square of side (x+y)/2 is also 2x+2y.
Once this idea is clear, then the concept of Geometric Mean is introduced.
Take a rectangle of sides x and y , then geometric mean is side of a square whose area is same as the given rectangle.
In both cases it is square root of xy.

Beth said...
I usually remind my students what they know about the arithmetic mean and show them how two numbers have an arithmetic mean that is the same distance away from both of them on a number line. They see that the two numbers are the same distance in an "addition/subtraction sense". Then I use a nice integer geometric mean and help them discover that the two numbers are now the same "distance" away from each other in a "multiplication/division sense." For example, the GM of 3 and 12 is 6; 3x2 = 6 and 6x2=12. Whereas the AM of 3 and 12 is 7.5; 7.5-3 = 4.5 and 12-7.5 = 4.5.

Michael said...
in the right - angled triangle the height dropped onto hypotenuse is the geometric mean between the segments of the hypotenuse which are created . The students must reveal this fact during learning the similarity in triangles - without any struggle, but by investigation, maybe guided by their teacher.
And, if we speak about another mean, arithmetic mean, so the midline in trapezoid is the arithmetic mean between it`s bases. And also , this fact we reveal and don`t put upon students in the final form.

Ryan said...
To make it relevant, Geometric Mean does have an application in artistic viewing. Using the width (and possibly height?) of a piece of an art (or nowadays flat-screen LCD TV's), the Geometric Mean actually is the exact location you should stand away from the artwork/TV to get maximum enjoyment. Research has proven this if you meander through the internet. Also, store like Best Buy are really starting to get into this with the increase in LCD TVs and home surround sound theaters.

All these are fantastic ideas. Try them out in your classroom. Make Math enriched and enjoyable.

Wallwisher in Maths Classrooms

2010-04-16T18:37:00.003+05:30

Wallwisher.com :: Words that stick via kwout

Here are some examples of how teachers are using Wallwisher in their Maths Classrooms.

What have you learnt in Maths class so far this year?
Tell me what you have enjoyed, what you know now that you didn't know before and anything else about your maths learning that you think I should know!
Geometry Resources Wall
This wall has all sorts of useful Geometry information about Polygons, Quadrilaterals, and Triangles
Look at these wonderful ideas shared by Tom Barrett

Mathematics bloggers

2010-03-03T13:48:00.002+05:30

Checkout what Mathematics bloggers are sharing.

Mathematics Bloggers!!! via kwout

10 Places for online Math Help

2010-02-17T17:56:00.004+05:30

The web is a great place for students to learn more about math online. There are a wide range of websites dedicated to providing lessons, games, problem solvers, and other resources that provide math practice. Here are ten sites to explore in your spare time.

Mangahigh - Mangahigh is designed for schools and classrooms but is also open to individual students and families. Users who sign up for a free membership can play math games and compete in an international math league.

Webmath - Webmath is a math help website that generates answers to math questions. The site can also help visitors solve difficult math problems.

Ask Dr. Math - This free online help service provides answers to frequently asked math questions. Users who can't find the answer to their question can write to Dr. Math.

Figure This! - Funded by the National Science Foundation (NSF) and the U.S. Department of Education, Figure This! provides math challenges for middle school students who want to practice math at home. Challenges are available in English and Spanish.

Math-Play.com - Math-Play.com provides a wide range of math games that can be played online. Games are categorized by subject, difficulty level, and grade level.

Mathway - This free online tool not only solves math problems, it also explains how the problem can be solved. Problems and solutions can be saved for later reference, emailed to someone else, or turned into a link that can be shared online.

Wolfram Mathworld - Wolfram Research, the makers of Mathematica, provide this free online resource to people who want to learn more about math. Some of the interactive features that can be found on the site include pop-up summaries for 300+ math terms, 3D geometry applets, and a math search engine.

Mrs. Glosser's Math Goodies - This award-winning site has been providing online math help since 1998. Site features include interactive games, lessons, worksheets, puzzles, tutorials, and a discussion forum.

MathBits.com - Designed for junior high and high school students, MathBits.com provides a wide range of math lessons and activities. The site also offers math videos, slide shows, and computer programming lessons.

Math Baseball - This free game from FunBrain.com combines math and baseball to create challenges for students who are learning addition, subtraction, multiplication, and division. The game can be played with one player or two.

Guest post from freelance writer Karen Schweitzer. Karen is the About.com Guide to Business School. She also writes for OnlineDegreePrograms.org, an online degree resource.

Read Math quotes

2010-01-29T11:14:00.001+05:30

Added this Math quote widget .Read inspiring Math quotes.

Interesting Math widget !

2010-01-22T09:14:00.002+05:30

Today I came across this widget on timeline of Mathematicians. I think it can be used in a classroom, to let know students about Mathematicians in an interesting way.

Timeline : Mathematiciansgreat free widgetsWidgetboxMore info

Discussing common errors

2010-01-07T11:30:00.003+05:30

At the time of examination, students sometimes are not able to express their knowledge correctly. With the result they score less . Finally a disinterest in the subject is developed. To avoid this situation and helping students, a wise teacher can plan a strategy of planning a lesson with the integration of previous years experiences of students in the form of COMMON ERRORS COMMITTED BY STUDENTS. It really helps.
I have shared here, how this strategy is implemented with my Class X students.

Cool Widget!

2010-01-04T17:50:00.003+05:30

Stumbled upon this cool widget .Just added it here too!

Karma Implementor - Globizer - Free 3D Globe Creator via kwout

Try it out!

Make Drawing/Charts/Graphs

2010-01-02T12:04:00.002+05:30

Lovely Charts Free online diagram software - Flowchart & process diagram, Network diagram, BPMN diagrams, Sitemap, Organisation chart, Wireframe, business drawing software via kwout

Online Diagram Software - Gliffy via kwout

yEd - Graph Editor via kwout

sketchfu via kwout

Tux Paint via kwout

Photo editor online - Pixlr.com edit image via kwout

Photograph puzzle maker

2009-12-30T19:49:00.003+05:30

Create a Jigsaw puzzle using this online facility. It turns any uploaded picture to a jigsaw puzzle. You may use a Mathematical picture here.
Try it out!

Number triangle 1.1

2009-12-30T15:47:00.002+05:30

Number triangle 1.1 is a freely downloadable Math puzzle.

The purpose of this task is to get the largest total at the top of the triangle by putting in numbers in the bottom line. The rules are that the numbers on the bottom line must add up to a specified number, for example 10.

To get the number on the line above we have to follow simple rules
Odd next to an even number = Multiply them and put answer in box above.
Odd next to Odd = Subtract and the difference goes in the box above.
Even next to Even = Add them and put the answer in the box above.

General Features include:
Simple Type in the base numbers and the totals will be automatically worked out.
4 different levels with different Totals. (only 3 available in Freeware version).

Downloadable Link

Quad factor 1.0

2009-12-29T16:04:00.000+05:30

Quite an interesting tool for learning factorisation of a quadratic equation.

Download link

Math challenge 2

2009-12-28T16:22:00.000+05:30

Its a free downloadable digital flash card system that can be customised to the level of learner.
Try it!
Download link

Guidelines for teachers-Planning Formative assessment in Math

2009-12-17T11:22:00.002+05:30

Guidelines for teachers-Planning Formative assessment in Math -

Macro Plan: Formative assessment in Mathematics

2009-12-16T10:11:00.003+05:30

Formative tests: These tests are assessments/tools designed for learning. They are designed for the improvement in the knowledge and understanding of concepts of learners. Mathematics teaching learning requires focus on development of various skills viz. arithmetic, logical, analytical, drawing, plotting etc. A variety of formative testing tools are available which may test these desired skills.
In Mathematics students may have concept understanding difficulties resulting in conceptual errors ,may do calculation errors ,may wrongly interpret word problems etc.
All these kinds of problems are to be resolved at the right time for improving further learning. Based on the feedback of learning of students via various tools, problems of students are diagnosed .Continuing further, remedies are designed.

ASSESSMENT TOOL #1

C.W/H.W/ASSIGNMENTS:
C.W. /H.W. notebooks of students are to be assessed by the teacher in specified duration of each Formative assessment.
Following four parameters are to be taken care of:
1. Regularity: Submission on time (1 mark)
2. Maintenance/neatness (1 mark)
3. Completion of work (2 marks)
4. Correction work (if any) (1 mark)
Assignments:
Assignments are to be given in each chapter. It may include all types of questions according to the design of question paper (Multiple choice questions, Short answer type and long answer type).
Following four parameters are to be taken care of:
1. Regularity: Submission on time (1 mark)
2. Maintenance/neatness (1 mark)
3. Completion of work (2 marks)
4. Correction work (if any) (1 mark)
Note: Questions in assignments should not be a replica of questions given in the prescribed text book. The number of questions should not exceed 15.
Please Note:
Talk to students that C.W./H.W./Assignments will be assessed.
 Observe at least 4-5 class work / home work records in each Formative assessment duration

 If a child is unable to complete the work due to some reason, then give him/her time for the same.

ASSESSMENT TOOL #2

Oral test: (Class response)
It is quite a reliable formative testing tool. It focuses on testing understanding of concept, Logical thinking and speaking skills. In Mathematics children may be asked basic concepts, formulae, important results, theorems etc. The class response of students is observed while teaching learning of each unit and on the basis of observations during a period of each formative assessment students are given marks accordingly.

Some suggestive ways of conducting an oral test:
1. While teaching teacher may ask questions to students Roll No. wise and keep the record in the diary. The whole task can be distributed in the duration in which the unit is taught.
2. One day may be assigned for taking oral test. Students need to be informed before the test.
3. Oral test may be taken in the Math lab period also.
4. Teacher may initiate a discussion in the classroom on some general topics like use of Mathematics in daily life, brainstorming on the utility of contents of chapter taught, recreational Mathematics etc and observe the participation of students.

Please Note:
 Although it is quite a good tool for assessment, but at the same time it is to be kept in mind that it creates maximum anxiety in students.
 When oral assessment process is on, a teacher needs to show a high degree of patience.
 Our purpose of oral assessment is to help a child to learn and not to create any fear for learning.

ASSESSMENT TOOL#3

Pen and Paper test:
Total marks allotted for pen and paper test in each Formative assessment duration is 15 marks.
It may include classroom worksheets and class tests taken during teaching learning in each formative assessment duration. The number of classroom worksheets/class tests may vary according to the need of the chapter.

Classroom Worksheets (5 marks)
Teacher may prepare worksheets of 10 minutes duration which can be given to students either before a lesson (for testing previous knowledge) or after teaching a topic (as a recapitulation exercise).
Suggestive format for Worksheet Class Worksheet Type 1
Total No. of questions 10
4 MCQ’s
4 Fill in the blanks
2 True/False
Note: Design MCQ’s for testing understanding of concept taught, Fill in the blanks for testing arithmetical skills and true/false questions type for testing analytical and logical reasoning.
Class Worksheet Type 2
Crossword

Class test (10 marks)
Duration of each test would be 30 min to 40 min. Short answer type and long answer type questions may be asked.
Please Note:
At least one class test should be taken during one Formative assessment period.
If a good number of students do not perform well in a class test, then following remedies are suggested to
 revise the chapter and discuss problem areas
 Give some support material in the form of list of basic formulae and concepts, practice worksheets, practice tests etc.
If some selected students do not perform well, then they can be suggested to prepare well for the next test.

ASSESSMENT TOOL #4

Math activity /Math projects:

Math activities :( To be performed individually)
There are three parameters for assessing Math activities
1. File Record (4 marks)
2. Performance of activity (4 marks)
3. Viva (2 marks)

Please note:
 Each child is required to perform hands on activities as suggested by CBSE.
 Record of the same has to be maintained in a separate record file.
 Teacher is suggested to provide guidelines of performing the activities through activity sheets / a demonstration.
 Students are to be observed in Math lab while doing hands on .
 Teacher may ask questions in between related to Math concept learnt.

Math Projects: (Group work) (To be performed in a group of 3 to 4 students)
Suggestive Math projects:
1. Make a dictionary of terms in Geometry with figures. (Making a Pictorial dictionary)
2. Survey in Statistics

15 Places to Find Math Games and Activities Online

2009-12-04T08:20:00.002+05:30

Math isn't everybody's favorite subject, but it can be made more interesting with fun games that entertain and educate at the same time. There are dozens of board games made specifically for this purpose. There are also a number of math games that can be played for free online. Here are 15 sites that offer interactive math games guaranteed to engage even the most reluctant math students:

Tutpup - Tutpup is a fun site that allows kids to play educational games and compete with other children all over the world. Math games include addition, subtraction, multiplication, division, and algebra.

iknowthat.com - This free children's educational site provides standards based math games for PreK-6 students. Kids play in a social environment and are able to save scores, documents, and other accomplishments to show friends and family members.

Funbrain Math Arcade - The Funbrain Math Arcade features 25 arcade-style math games for elementary and middle school children. Visitors choose their learning level to play their first game. Every time a game is beat a new game is unlocked.

Math Playground - Created for elementary and middle school students, this comprehensive math site features math games, puzzles, videos, and other math activities that can be enjoyed online.

Illuminations - In addition to providing lesson plans and information about math standards, this NCTM (National Council of Teachers of Mathematics) site offers more than 100 different online activities preK-12 students. Activities are sorted by grade level and can be easily located using the site's search feature.

NumberNut - NumberNut is a high quality site devoted entirely to math. Visitors can choose from basic math activities and advanced math activities.

Cool Math 4 Kids - Cool Math 4 Kids is a Net-Mom approved site where elementary and middle school students can play math games and solve puzzles online. The site also offers virtual math flashcards for extra math practice.

National Library of Virtual Manipulatives - This Utah State University site provides interactive, web-based virtual manipulatives for preK-12 students. Covered subjects include measurement, numbers and operations, algebra, geometry, and data analysis.

Arcademic Skill Builders - Arcademic Skill Builders features arcade-style math games that can be played alone or with a friend. The games can be played online and also work with the Nintendo Wii gaming system.

Sheppard Software - This site offers a new math quiz for every day of the week. Other site features include games that teach basic math, fractions, place value, money counting, telling time, and pre-algebra.

Math and Reading Help for Kids - In addition to offering hundreds of helpful articles and links to math resources, this site also provides several different fun and educational math games for kids. One of the best is Math Search, which combines addition, subtraction, multiplication, and division with the traditional word search.

CyberBee - CyberBee provides several standards-based online math games for grades K-5. Visitors who are struggling with math can also use the site's visual math dictionary to gain a better understanding of various subjects.

Multiplication.com - Multiplication.com provides dozens of free interactive games designed to teach students multiplication tables. A new game is added each month.

Wired Math - Wired Math offers fun online math games, challenges, and exercises for grades 7-9. Activities are sorted by grade level and subject.

Math TV - This site features an extensive collection of math videos that can be played online. Videos cover a wide range of math topics, including basic math, algebra, geometry, trigonometry, and calculus.

Guest post from education writer Karen Schweitzer. Karen is the About.com Guide to Business School. She also writes about online school for OnlineSchool.net.

Free Mathematics Software

2009-11-27T09:31:00.005+05:30

Following Mathematics software are excellent for use in Math classrooms.
#1 GeoGebra

GeoGebra via kwout

#2 Graph

Graph via kwout

#3 C.a.R

C.a.R. via kwout

Different methods of starting a Math lesson

2009-09-07T22:13:00.005+05:30

Well start is half done!

If a teacher is able to capture attention in the beginning of a lesson then half of the job is done. This means the first two classes of a Math lesson are very crucial. There are various methods of beginning a Math lesson in a creative manner.

#1 Making a connection- Everytime it is not essential that we are going to start a new concept. Students have some knowledge about it earlier. So, forming a connection by asking questions based on previously gained knowledge of students is a tried and tested strategy which helps in motivating students for further learning.

#2 Showing a picture - A picture says a thousand words. In a math class, one may begin a lesson by showing a picture from surroundings showing the use of some Math concept leading to introducing new concept.

#3 Story telling - This helps a lot in the beginning of a lesson. I believe we as teachers need to capture attention of students so that their focus is on the new topic. Story telling is indeed a good way to start a lesson.

#4 Realising the need to learn- Why we are learning this concept ? Why it is important ? This must be answered in the beginning.

#5 Involving students - Calling students names in between , taking their help ,taking their examples helps in capturing attention till the end of class.

#6 Showing real objects - Sometimes it is feasible to carry real objects in a classroom. Students may be asked to look around themselves to observe things also.

It is the way how a topic is introduced which matters a lot.

13 Learning Times Tables Links

2009-09-05T20:04:00.001+05:30

Multiplication tables plays an important role in learning Mathematics. Children move away from learning them. Technology has helped teachers by offering interesting tools/games/software for helping children to learn concepts and practise.

Here are some interesting links
#1

1. Times tables generator You will get times table generated in click of mouse. Just type in the number and click...

#2 (Free and Downloadable )

Here is an interesting downloadable Math game which may be used for practising tables. I find it different and challenging too.Try it!

Valgetal Falling Numbers 3.23

#3 (Free and downloadable)

Another one is Multiplication Master...Free multiplication tables practice software.Fast, simple and easy to use for budding multiplication masters of all ages!Keeps your score so you can see how well you're doing.Single table mode lets you focus on one multiplication table at a time - the fastest way to improveRandom feature tests you against all the multiplication tablesIncludes reference tables to help you learn multiplication tables fastUnlimited use. Practice as many multiplications as you want, as often as you want.Completely free. No charge for this software - ever.Here is the link to download.

#4 (Free Junior edition)

This one is learn MathMatic JuniorMathmatic is a program for learning and drilling multiplication tables 1 through 12. It is dedicated to that unique task and it does it thoroughly. MathMatic generates and PRINTS DRILL SHEETS. The user can choose between Mental and Written learning modes and use the timer to measure performance. MathMatic's sounds and colors are fully user definable. The Junior Edition is Freeware and is directed towards young students (multipliers bound to low values).

#5
A free multiplication program for kids... MULTIPLICATION FACTS lets you learn and practice the basic times tables using the numbers zero through twelve. And it's FREE! MULTIPLICATION FACTS lets you work with any digit(s) you choose. Review times tables, see graphic representations of problems, or take speed drills. The program grades your performance and provides feedback. Print worksheets for practice away from the computer.

#6
Checkout Times tables activities,games and worksheets ...quite interesting!!
#7

Tables tree-an interesting game to practice multiplication tables.

#8

A complete website on multiplication for teaching learning multiplication facts.

#9

Visualising Multiplication tables using this applet.

Visual Multiplication

#10

Answer 10 multiplication questions. How much time did you take?

Tables times

#11

Multiplication flash cards on Quizlet.

#12

Interactive practice of times tables. Click on a box. Drag the right answer from the numbers given on RHS.

#13
Explore Multiplication tables in an interactive manner.

15 Places to find Teaching Resources and Math teaching strategies

2009-09-03T09:24:00.003+05:30

Trying to get a classroom of 20 to 30 individual thinkers to understand difficult math concepts can sometimes be challenging. Fortunately, there are many websites that offer lesson plans, activities, teaching strategies, and other resources to help you out. Here is a list of 15 sites that math teachers will find especially useful:

National Council of Teachers of Mathematics - The NCTM, a public voice in mathematics education, provides professional development strategies, lessons, journals, books, and other resources that can be used in a K-12 math classroom.

The Math Forum - This free online math warehouse offers lesson plans, activities, educational materials, teaching strategies, career development resources, and much more. The Math Forum also provides links to other resources that are useful for math education.

TeAchnology - TeAchnology, a huge database of lesson plans and classroom resources, is loaded with lesson plans specifically for math teachers. The lesson plans cover all grades, areas, and concepts.

Math.com - Even though this site was created to help students with math, Math.com features a variety of resources teachers can use as well. Under the teachers section of this site, you can find lesson plans, classroom resources, career information, standards, and other free resources.

Math-Videos-Online - This free online math site features math videos that teachers can use with their lessons to demonstrate important concepts. The site also offers interactive games, quizzes, and printable worksheets to be used in conjunction with the videos.

Rader's Numbernut - Rader's Numbernut is a site that contains interactive math games and activities for beginning and advance math. Teachers can use these activities within their lessons to illustrate important concepts.

Illuminations - The Illuminations site features a library of 103 activities that teachers can use with their K-12 students. In addition to the activities, this site also features over 500 lessons specifically for math.

TheTeachersCorner - Teachers looking for a wide range of online teaching resources will enjoy the lesson plans, worksheets, and activities offered on TheTeachersCorner. This site also features a message board, printables, bulletin board, and other general resources that teachers will find useful.

AAA Math - AAA Math provides a comprehensive set of lessons for K-8 students. The lessons come with unlimited practice to help students master concepts.

FREE - The Federal Resources for Education Excellence (FREE) features a huge list of teaching resources for algebra, data analysis, geometry, measurement, numbers and operations, and other math concepts. The teaching resources cover lesson plans, tools, learning activities, and more.

Discovery Education - Discovery Education offers free math lesson plans for elementary to high school students. The lesson plans are broken up into three sections for elementary, middle school, and high school children.

Mathematics Learning - This blog, created by an educator with over a decade of experience, provides math teachers with a place to find and share new strategies in the teaching of math. Throughout the pages of this blog, teachers will find resources, activities, and strategies that have been successful in other math classrooms.

Terri Husted - The Terri Husted site is designed specifically to give math teachers information and ideas on how to improve their teaching strategies. Throughout this site, you will find information on classroom management, new teacher resources, math activities, homework assessments, and much more.

National Library of Virtual Manipulatives - The National Library of Virtual Manipulatives is a free online activities site that teachers can use with their K-12 classrooms to visually demonstrate numbers and operations, algebra, geometry, measurement, and data analysis.

Math Drills - Math Drills provides thousands of free printable math worksheets that are great for assessing student's abilities, giving extra practice, and teaching new strategies.

Guest post from education writer Karen Schweitzer. Karen is the About.com Guide to Business School. She also writes for OnlineCollege.org, an online college resource.

ThatQuiz for teachers

2009-08-14T21:43:00.004+05:30

Children love to learn in a playway method. Why not try evaluating their knowledge using readymade quizzes ? Recently, I was exploring some recreational Math resources for teachers and I stumled upon ThatQuiz.

ThatQuiz for Teachers is a free testing service for teachers to use with their classes. Multiple choice tests and math tests can be administered to students using this website. All grades are immediately reported to the students. Teachers receive complete record keeping of test results, including all grades and wrong answers.

Here is the link.

Using online tools-Prime number calculator

2009-06-28T11:10:00.007+05:30

Web is expanding with information and creative tools for explorations. It has become easier for teachers to integrate readily available tools with classroom teaching. There are so many interesting tools which may be clubbed with teaching of Mathematics for creating not only interest in the subject but also extending a scope for further exploration. Say, for example when we are talking about Prime numbers in a classroom. Prime numbers are positive, non-zero numbers that have exactly two factors .Children normally see them upto 200 or a maximum of upto 500 as it is not expected from them to create a list by manual division process. And sometime they are not sure of correctness of what they have obtained.

I used Prime number calculator for checking whether a given number is Prime or not . This tool helped in finding next largest and next smallest prime numbers of a number. Prime number charts are created for displaying in classroom.

Other interesting links on Prime numbers

History

Eratosthenes of Cyrene

Prime number game using 100chart

Prime pages

Lesson

Eratosthene Sieve Interactive

Interactive prime number game

Clarity of a concept...number and a numeral

2009-06-12T12:40:00.004+05:30

Clarity of a concept is essential for creating interest in the subject. Children are often confused with ideas in Mathematics.

For instance take this example of...

What is the difference between a number and a numeral?
When we say there are six flowers in a bouquet, we are mentioning number of flowers.Numeral refers to the markings we use to indicate that idea of number.

That is in above case it is Six, VI or 6.

A number is an abstract concept while a numeral is a symbol used to express that number. How do your express the concept of fiveness…
· Five
· 5
· V
A number is an idea that is used to refer to amounts of things.
A number symbol is called a numeral.
This is what Dr. Math Answered…
http://mathforum.org/library/drmath/view/58756.html
Read 10 Rules for writing numbers and numerals.
http://www.dailywritingtips.com/10-rules-for-writing-numbers-and-numerals/

So, it is desirable to make concepts clear with proper examples and instances.

Realising the presence...

2009-05-25T14:32:00.003+05:30

Mathematics is considered as an abstract subject. Students find it dull and boring. There are so many on this planet who always say " Mathematics is not my cup of tea". Do you know the reason for this indifferent attitude towards Mathematics ?

Have you ever realised the presence of Mathematics around. One thing which is very interesting to note is...the people who say that they are afraid of Math or they hate Math or they try to run away from Math are using/applying it in daily life.

Aren't these people managing house budgets ?

Aren't they not paying bills for their dinner in a restaurant ?

Aren't all of them not using number manipulations, mathematical operations etc?

Aren't they not seeing/observing beauty of geometry all around?

There is not even a single place where the knowledge of Mathematics is not applied. It is very important to make students realise the presence of Mathematics around and how important the subject is in our daily life?

I have created a blog Exploring Mathematics Around where you can find pictures from daily life depicting the presence of Math everywhere.

Answering how???

2009-04-21T17:11:00.001+05:30

Answering how??? is very important for learning Mathematics. Say for example A teacher stated in a classroom - The sum of first n odd natural numbers is n² . In the next step students try to remember this result. After some days they forget the formula. Why it is happening? The main reason for this is cramming without understanding.

Mathematics is logical. It means it has valid reasons for what all it has in it as a subject. In the above example one way for understanding is showing visuals. This strategy can be made more interesting if students are participating in between for learning.

Given below is a slide show of pictures representing sum of first n odd natural numbers. Students try to see each one of the figures and come to the final conclusion by observing them in a sequence. Students answer the following questions:

Can we express 1 as 1²?
What is 1+3 ? Can we express it as 2²? and so on...
What is 1+3+5+7+....upto n terms?

Commiting Math errors...

2009-04-19T23:05:00.000+05:30

Who does not want to get a good score in mathematics? The perfect 100/100 is the ultimate. Mathematics learning and then applying is not an easy task for many. Learning ability of students may vary. It is dependent of many factors. There are many students who struggle for even passing the subject. They commit errors while solving mathematical questions. Errors can be logical, conceptual, arithmetical, misread type etc.

Reasons for committing mathematical errors…

• Forgetting the previous knowledge…Most of the topics done in the present class are normally based on knowledge gained by students in their prior classes. I believe Mathematics learning is cumulative. This means the new knowledge gained is linked to the previous knowledge gained.

Students tend to forget the basic knowledge of concepts learnt earlier. This cause a wide gap in further learning the concept as a teacher assumes that students have attained the knowledge level of previous class. At the same time the student is under pressure of learning what he has forget and has to work on hard enough to grasp the new unlearned concept. This increased pressure creates an imbalance in achieving the perfect result.

• Doing the bare minimum to pass… Mathematics is demanding. This means if we want to score well we need to work with it. Learning, practicing and revising are key steps for achieving better score. Some students have a fear of learning math because of lesser clarity of a concept in earlier classes. So they try to run away from exploring the subject and study just bare minimum to qualify the examination. This situation results in incomplete learning and hence is prone to committing more errors.

• Lack of involvement in the learning process…Mathematics is a subject which comes by continual practice. It cannot be learnt in a single day. There is requirement of consistent involvement in learning of the subject and then practicing the concepts as well. Students memorize formulae; geometrical results etc and tend to forget the way the memorized concepts are to be applied for solving the questions. In the process confusion is created which lead to an incomplete solution or wrong solution.

• Not related to daily life… While learning the subject its presence in daily life is not realized .This creates a gap between the subject and students. In such a situation students learn it as a subject Mathematics, which makes it more difficult to understand by students.

Importance of Mathematics in daily life

2009-04-17T11:44:00.000+05:30

Mathematics, Maths, Math...You say this in front of anybody , he/she would like to add something about it. Mathematics is an integral part of our life. Believe it or not " THERE IS NO ESCAPE"
Yesterday I floated this question on my twitter network."Where have you used Mathematics today?? One use...quick response will be appreciated

mcarls@rashkath Ouch, balanced my bank account online (double checked it) after vacation! Also checked about delicious math tags after your tweet
crthibodeaux@rashkath to calculate pages read by students in my classes.
MariaDroujkova@rashkath Not counting the Great Circles workshop, I had to approximate my trip there (on foot and by bus) - a bit of logistics today.
prodev@rashkath Making breakfast for my kids I measureed & then cut food into geometric shapes. Then I shared a % of My orange w/the dog
malinkaiva@rashkath Where have I used Mathematics today?? ...in Computer Graphics too: http://tinyurl.com/cyfkgl
malinkaiva@rashkath Hi Rash! Where have I used Mathematics today?? ... for example in device simulations:http://www.youtube.com/watch?v=QSUF1JudNS8&fe
elemtech@rashkath I've used math to calculate how many hours of spring break we still have left this week.
kolson29@rashkath in my daily life, used to calculate calories - in school used in math lesson on division and fractions!
JohnSW35@rashkath Looking around. Do you have any interest in Summer Math Reading? What does that include?
mrmackenzie@rashkath used maths to put numbers into standard form to save using a calculator
mrstucke@rashkath Calculating how many songs I could fit on a new hard-drive
Holtsman@rashkath Counting money at a drive through.
josepicardo@rashkath I used mathematics to realise I had been short changed at the sweet shop!
kaferico@rashkath I used math today when I made coffee this morning. The amount of coffee (ounces) I used was proportional to the amount of water.
jdwilliams@rashkath We looked at AZ Cardinals drive summaries from last season and added negative and positive integers. So in math class...
mikeheth@rashkath Figuring change for buying 2 coffees / 1 gal. of milk. Needed to estimate so I knew the change was right. No calculus involved :)
njtechteacher Use math today to estimate how much money I needed to give my sons to get groceries from the store.
teachernz@rashkath Hi thanks for following me. Where in India are you so i can stick a pin in my map?
langwitches@rashkath Google Earth Tour around our town. Students are looking for Geometric shapes in buildings & measuring distances in yards & meters
Fouss@rashkath figuring out easiest way to make change for $7 when I have $23.
lekahe@rashkath I have a day off and was shopping, so I added up how much I spent today :)
sgauthier@rashkath I used math in calculating my calories and fat in my breakfast
dmcordell@rashkath I used Math to estimate how much money to pre-pay at the gas station (tank capacity, % left, cost per gallon)
capohanka@rashkath I used math today when I checked to see how much time I had left on my laptop battery and decided I needed to plug in the charger.
dianadell@mcarls @rashkath I used math today to add check amounts together for a bank deposit.
glassbeed@rashkath I used math today thinking about temperatures and what I was going to wear for outer clothing (spring here is slow coming).
greenskunk@mcarls @rashkath Used #math for Spreadsheet calculations, Web Statistics, Timesheet and Web Design
teachernz@rashkath Had to take my son to his friends for the first time.. needed to look at postboxes to find the house-1311,1313,1315,1317,1319 Yay!
LParisi@rashkath How I used math today: I estimated how much milk I had left to decide if I had enough for a bowl of cereal. (I had just enough.)
NeilAdam@digitalmaverick @rashkath checking train timetables and when I need to leave the house
mrthomson@rashkath In calculating time for Kutcher / CNN to win battle to 1 million followers. Also rejigged finances, use of Excel/maths there!

Thanks to all those who participated.

Jigsaw Mathematical puzzles

2009-04-15T06:48:00.000+05:30

Students are always happy in doing something challenging. It is a pleasure sharing about a free Jigsaw puzzle maker Jigsawplanet . On this website you can create a Jigsaw puzzle using any image stored on your computer. I tried it with a picture of a Parabola that I clicked in a park (actually a watering pipe was lying in the park in the shape of a parabola). Here is the Jigsaw for you.

PARABOLA

You can create your own and put it in your blog/website.

Writing Mathematics Expressions

2009-04-11T10:38:00.001+05:30

Writing Mathematics expressions on a computer is not an easy task for teachers as well students. But at the same time, it is important to write correct Math expression for learning the same correctly. One of my colleagues on Mathematics 24x7 initiated this discussion and shared some interesting Math expression typing software/tools.

1. Sitmo equation editor (a Google gadget)

http://www.sitmo.com/latex/

You may embed it in your blog. Teachers/students can easily type in the desired expression .It is free.

2. Online equation editor

http://thornahawk.unitedti.org/equationeditor/equationeditor.php

3. Mathematical formulae on Web

http://www.univie.ac.at/future.media/moe/formeln.html

This is quite interesting. It generates HTML Code which can be easily added as a part of blog post with no complexity of uploading image of expression. Maths online offers a tool which makes the generation of HTML code for Maths formulae a fairly easy matter. Earlier I use to write a quadratic equation as ax^2 +bx+c=0, a not equal to 0, a , b, c are real numbers, but now by using HTML code , I am writing it correctly (as it is given in textbook ) ax² +bx+c=o , a¹0, a , b, c are real numbers.

Here are some softwares shared by Mathematicians via Twitter

Lekahe there is Open Office Math to be used with Open Office Writer. MiKTeX is a visul LaTeX editor, but maybe hard....

montgorp re writing math expressions: we use fx equation. Better than mathtype but only works on windows

samjshah MathType (in MS Word) and LaTeX

awbaggaley latex for maths on computer

dansmath for expressions and equations I use Mathematica and save as tiff then paste into Apple Pages. Whole algebra book done this way.

k8nowakusually MathType, sometimes LaTeX.

Fraction-Decimals converter

2009-03-16T11:06:00.004+05:30

In a Math classroom manually children convert fractions to decimals upto a limited number of decimal places.
Do you know 1/9801 is purely recurring with a period of 198 digits?
1/9801 = 0.0001020304050607080910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061626
36465666768697071727374757677787980818283848586878889909192939495969799..

You must be surprised how I have calculated this. This is done on a click of a mouse button using an online converter.
Explore it yourself and find interesting Math.
Here is the link.

Pi Day March 14

2009-03-13T13:27:00.002+05:30

March 14 is celebrated as Pi Day. Teachers and students all across the world celebrate it in different ways. Here through this blog post I am sharing some Pi Facts

• The symbol for pi was first used in 1706 by William Jones, but was popular after it was adopted by the Swiss mathematician Leonhard Euler in 1737.

• Mathematically, Pi represents the ratio of Circumference of a circle to its Diameter.

• The value of Pi up to 75 decimal places is 3.14 159 265 358 979 323 846 264 338 327 950 288 419 716 939 937 510 582 097 494 459 230 781 640 6286

• A very simple mnemonic to learn the value of Pi up to 7 decimal places is “HOW I WISH I COULD CALCULATE PI” Count the no. of letters in each word…

• Here is another mnemonic for the decimal expansion of π. Each successive digit is the number of letters in the corresponding word.

How I want a drink, alcoholic of course, after the heavy lectures involving quantum mechanics. All of thy geometry, Herr Planck, is fairly hard...: 3.14159265358979323846264...

• Pi is an irrational number. It cannot be written as a simple fraction or as an exact decimal with a finite number of decimal places.

I really liked this creative way of celebrating Pi Day Making Pi Necklace

Find where is your birtday in Pi ???? Where is your Birthday?

Send a Pi Card to wish your friend. Send a Card...

Online Puzzle Maker

2009-03-12T10:36:00.006+05:30

Children are always happy in learning in a play way style. Learning through puzzles is an interesting way to learn Math. A variety of puzzles can be easily created using ONLINE PUZZLE MAKER .

There are plenty of options available viz. Word search , criss cross , double puzzles , fallen phrases , math squares , mazes , letter tiles , cryptograms , number blocks and hidden messages.

Now , it depends on you to choose a suitable one for your kids. This is a sample Word search puzzle created on Geometry related terms.

Try it!

Twitter Poll:Do you like Math

2009-03-04T08:58:00.004+05:30

Yesterday I had a Twitter Poll "Do you like Math? If yes...if No...share one reason". I would like to thank all those who participated and shared their views. I am glad to share it here with all of you.
Here are the responses ...

1.Rubrai @rashkath Twitter poll math: no I don't, I had a lousy math teacher in primary school and there's stuff that still baffles me
2. dwsm@rashkath I love Maths, particularly calculus and algebra - it was cracking the code and making sense out of the seemingly random
3.pdonaghy@rashkath I love Math because it is so logical :)
4.lizbdavis@rashkath I love math because I love mathematical and logical thinking. I like solving problems and using numbers to figure things out.
5. kathyfavazza@rashkath Yes - I love to figure out patterns
6.murcha@rashkath Yes I do like maths as I like working with numbers and enjoy the challenge of getting a solution
7.Allanahk@rashkath I understand & like maths now as I teach it (Year4/5)- never did when studying it although did quite well in exams.
8.awbaggaley@rashkath love maths because it's in everything we do. Unfortunatly my love is being tested as I struggle to write up my thesis!
9.susant@rashkath no just couldnt learn it
10.theother66@rashkath I love maths - probably because I 'get it'
11.lekahe@rashkath I fell in love with Math when I was 14! The love has only been growing since.
12.loonyhiker@rashkath yes, i like how the answer isn't a subjective answer - i can depend on it being the same every time
13.mathheadinc@rashkath I LOVE math. The beauty of math. The logic of math. The ubiquity of math. The challenge of math. The infinity of math...

If on your networks anybody has replied for this poll, pls share it with me.

Thanks

Celebrating Special Days

2009-03-03T12:44:00.003+05:30

Every day is special. Some days are very special. Children celebrate their birthdays . We also celebrate special occasions and days associated with them. Why not use this strategy for learning Mathematics. Say for example today is 3.3.09 .
What is so special in it???
The date and month are both square root of year.
If you notice this particular date then you will see special Mathematics is attached to it.
We say 3X3 = 9 OR square of 3 is 9.
Such a special day is celebrated as SQUARE ROOT DAY.
Do you know???
Last time it was on 2.2.04.
When it will be next???
4.4.16
Square Root Day occurs only nine times in a century.

Exploring Mathematics Around

2009-02-27T09:09:00.001+05:30

Mathematics is an integral part of our life. To make realise this fact, it is important to prove it. Children are always fascinated by pictures.Visit my new blog Exploring Mathematics Around where I am posting real pictures from daily life.

Exploring Mathematics Around via kwout

Mathematics Learning Wordle

2009-02-26T14:36:00.003+05:30

Created using http://wordle.net

Playing with Geometrical Shapes

2009-02-23T06:58:00.003+05:30

In primary grades students get to learn about basic geometrical shapes viz. triangle, square, parallelogram , trapezoid etc. To make them familiar with these shapes an activity of making designs and patterns using shapes really helps. Children make different patterns by fitting given geo shapes.

Here is an online applet which may be used by students at home for making different designs using geometrical shapes.

Playing with geo shapes

How to use it?

Mathematics in daily life

2009-02-11T08:36:00.006+05:30

Mathematics is an integral part of our life. Right from the time we wake up in the morning till we go to sleep, invariably we are using mathematics in one or the other way. Teaching mathematics in classroom using pictures from daily life can help students in understanding a concept in a better manner. For instance, when a child is introduced the concept of 3 dimension , he/she is not able to visualise it. Learning of this concept can be made simpler and interesting by showing them actual objects or their real pictures. It will surely help in not only understanding but also retaining the same for a longer time.

One of my students went to a cinema hall and clicked the following pictures showing 3Dimensional shapes and geometry.

Blog on IM Magazine

2009-02-04T11:53:00.000+05:30

IM Magazine, an international online magazine that has a unique concept: to show the best things in the world... for a better world recently put online a blogs platform. During their research they found this blog, which seemed to them very interesting, reason why they put it into IM platform.

For viewing you can access through the link:

http://immagazine.sapo.pt/eng/blog2009.html

Learning from errors

2009-01-25T19:32:00.004+05:30

While evaluating examination papers , plenty of math errors are noticed which are commited by students. Some of them are purely conceptual which reflect no clarity of concept or using wrong math concept , some are misread type- students show carelessness while performing calculations, addition operation is mixed with multiplication ,figures are not correctly drawn, word problems are not properly translated to mathematical equations and so on.

Learning from mistakes is a strategy for improving oneself. Why not try this for improving mathematics concept learning?

I have created a new blog http://mathematics-errors.blogspot.com/ for this purpose.

Please reflect your views on it.

Conference:Best teaching practices using ICET

2009-01-06T14:56:00.010+05:30

I am glad to share with you, about conference on Best Teaching Practices using ICET which was organised by NIIT institute of Information Technology (TNI) on 22nd and 23rd Dec 2008 at India Habitat Centre, New Delhi.

Teachers from all across India participated. They presented their papers on using ICET in classrooms. Out of 31 presentations 4 were from our school. I presented a paper on e Mathematics using offline and online tools. I am happy to share that my paper was ranked at First Place.

It was indeed an enriching experience .

Formulator Tarsia- for creating puzzles

2009-01-06T12:44:00.009+05:30

Challenge your students ...they will learn in the process.

Solving Math puzzle is a dynamic strategy in learning process. Formulator Tarsia is a free software which allows you to create puzzles based on jigsaw activities. The students are given a set of tiles which must be matched edge-to-edge to complete the shape. Mathematical questions are given along these edges. Jigsaw puzzles can be created based on triangle, square, rectangle, rhombus, parallelogram, hexagon and parquet patterns of tesselating shapes.

Click to Download .

This is one sample which I have created for revising algebraic formulae. Students are asked to cut triangles on page 1 and page 2.

They are then asked to arrange triangle cutouts to form the following shape. In the process, students use math concepts (here formulae ) as hint for making the desired shape.
Here is the solution...

Share your puzzles at http://passionateteachers.ning.com/

Interesting Game

2008-12-31T18:12:00.002+05:30

I liked this game so much that I could not resist myself for talking about it.
I will not say anything.
Just play it yourself and decide .

Estimation of Angles

2008-12-16T18:05:00.005+05:30

Play 'n' Learn

Teaching and learning of mathematics is fun. While teaching my daughter about angles , I used an e tool which is basically a game of start and stop of a stop watch kind of a thing. This tool is available here. Here is a screenshot of estimating 45 degrees. It is much closer to accurate result, so the score is 10 points. Try this!

Errors in Mathematics

2008-12-16T11:13:00.011+05:30

Students of Grade 8 committed following mistakes at the time of examination.

1. Cancellation of numerator and denominator terms

2. Solving exponents

3. Numerical transformations ...70 is not equal to square of 35

4. Importance of putting brackets

Making a 5x5 Magic Square

2008-12-15T19:03:00.003+05:30

Children love Magic Square making activity. Numbers fascinate all of us. Look the following picture and learn how to make a magic square of order 5x5. This is top right approach of making a magic square. Follow the direction of arrows from 1 to 25. The challenge is that by watching this path try to make Magic Squares of other odd orders.

Measurements in Math

2008-12-10T19:43:00.005+05:30

Learning about measurements is an integral part of learning math concepts. Be it about measuring length , mass or time, all play a significant role in mathematics.

I stumbled upon this interesting website on learning measurements when I was exploring some readymade e resources for teaching my daughter.

Here is its screenshot

menu via kwout

Math in surrounding

2008-12-06T11:47:00.004+05:30

Relating mathematics to surroundings proves beneficial while teaching math concepts. Students easily relate objects which they see daily to the concept learnt in the classroom. While teaching 3 dimensional shapes like right circular cylinder, right circular cone , sphere , hemisphere etc students are motivated to give examples of things which they see in their surroundings similar to these shapes.

Here is a slide show of some objects clicked by a teacher.

An interesting puzzle maker

2008-10-25T14:48:00.005+05:30

Are you creating Jigsaw puzzles on your own???

Formulator Tarsia known earlier as Formulator Jigsaw is an editor designed for Teachers of Mathematics creating the activities in a form of jigsaws or dominos etc for later use in a class. It includes the powerful equation editor for building the math-expressions for the activities. An advanced feature of text placement along the side of the shape makes this tool irreplaceable software for fast activity creation. Formulator Tarsia became a powerful tool for learning activities since it supports the activity templates. It enables easy support of teachers and gives them new perspectives to development of their teaching activity.

This tool is very interesting!!!

To know more...Here is the link

Enhance Arithmetic Skills

2008-08-02T15:02:00.006+05:30

In mathematics, improving arithmetic skills an essential step right from the beginning. I found , Reken test , a freeware , easily downloadable ,an arithmetic testing and practicing tool. This one is so cool, that students under age group 8-12 would surely love to practice and play using it. You may download it from here.

Try it!

3D Visualisation Applet

2008-07-27T00:03:00.004+05:30

It is no longer a question now, how visualisation is important in understanding 3 dimensional concepts? Recently, while exploring some software , I stumbled upon this interactive applet.
It is basically to have an idea of spatial geometry.
The title is Rotating Houses.
Try with kids. They will like to explore.

Mathematics in Playground

2008-07-22T09:23:00.005+05:30

Students of grade 10 performed mathematics experiments in playground on calculating heights and distances using an isosceles right triangle. They used trigonometric ratios in calculating the height of basket ball pole and a building nearby the playground. It is amazing to share that they calculated the values corrected upto 2 decimal places.

Firstly, they prepared their isosceles right triangles using a cardboard.
They worked in groups and measured the heights of each group member using a measuring tape.
They were told to hold t triangle with one edge parallel to the ground with hypotenuse angling up from their eye to the top of the object. They used the hypotenuse as the line of sight and moved backward/forward on the straight line drawn on the level ground, until the top of the object coincides with the top of the hypotenuse of right triangle.

It was altogether an enriching experience for me as a teacher because even in our school days we did not learn by these kinds of real experiments.

Creating aptitude puzzles

2008-07-02T20:57:00.010+05:30

Mathematics learning is not just developing numerical solving skills of students. There are lot of skills like logical thinking, aptitude, knowledge and understanding enhancements which are an integral part of learning mathematics.

Here I am talking of developing aptitude in students of observing patterns and generating the next in steps. Children , specially of grade 6 to 8 love to do mathematical pattern based questions. I have created puzzles based on mathematical patterns and spatial arrangements . The images have been set to panorama view using an open source software Irfan view.

Following are some samples of playing with match sticks.

What we do with these pictures?

Show them to students and ask the following:

Guess the next figure and draw . Find a relationship between number of match sticks between consecutive steps . Try to formulate a general expression for the nth step.
Following are some samples of playing with unit cubes:

Guess the next figure and draw . Find a relationship between number of unit cubes between each consecutive steps . Try to formulate a general expression for the nth step.
Have fun learning mathematics using technology.

Animated mathematical figures

2008-06-20T22:29:00.014+05:30

In an e teaching workshop organised by CII Shiksha, I got to know about a cool animation tool UnFREEz. The addition of this e software to my directory helped me to add life to still mathematical figures. I experimented with this software in creating some animated mathematical stuff.
Have a look.

The following three figures are created to explain the properties of a rectangle viz. both pairs of opposite sides of a rectangle are equal, each angle of a rectangle is a right angle and diagonals of a rectangle are equal.

The figure given below may be used to understand the concept of vertices of a cube. Observe the pink dots. My students were making mathematics project on optical illusion . I thought of creating animated illusions using UnFRRez. Two parallel lines turning into a pair of intersecting lines ... Two equal lines turning into unequal lines...

Do you want to download it?

Here is the link.

Mathematics and image editing

2008-06-17T14:25:00.019+05:30

Technology has given a magical toy in the hands of teachers and students to explore and learn interesting facts with ease. I have been exploring the internet based tools and softwares from past 2 years and had deeply felt its power in enriching learning level of students.

In our mathematics laboratory, we have been exploring on mathematics based activities using pictures. It is interesting to note that by using tech tools and softwares , we can do many mathematical experiments with a click of a mouse button. There are image editing tools and online programmes which can add/remove effects to a picture . This can bring in an incredible change in the existing image/picture leading to unusual results. I believe , a teacher or a student must take advantage of this facility . It would surely inculcate in learners the interest in the subject and developing creative skills. May be one day we may find a hidden mathematician.

Here I am sharing some interesting observations

Transforming a tangram to a curvy tangram. I talked about this experiment in my previous post on image editing.
Experimenting with illusions is an interesting activity which may be performed easily using image editors. Observe the given pictures... This is an optical illusion

In the above picture ,there are pink squares bounded by white and green squares. The presence of white and green boundaries around pink squares has changed the tone of pink shade. It is observed that when pink squares are bounded by green squares then they appear to be darker in shade. And when we remove all the green squares then we found that all the pink coloured squares are of same tone.

I was astonished to see this illusion. But you know, I wanted to try it for some other colour combinations. Manually, it is quite impossible to check on drawing, shading and then observing. So, an idea came to my mind to try using image editing tools. And here is the result...

I first tried with turning all pink squares to orange.

then to blue and so on I experimented with 5 different colours.The I tried to remove the green squares using eraser tool and got actually verified the result. In the figure given below, observe the part from where the green squares are completely removed. You will find that tone of blue colour is same . Ans there is a change in the tone of blue shade in the portion which is bounded by green squares.
The following pictures are edited using irfan view , a wonderful image editing tool. I took the following picture. I wanted to change the green coloured squares to some other colour to verify the experiment. Through Irfan view it was made posible. I edited the picture successfully.

Here is the result. I was amazed to see the fact that when green squares are turned to black, then also the illusion effect in yellow squares was there.Using a swap colour option, just by a click of mouse button, Yellow coloured squares are changed to blue. Exploring and learning the wonderful facts using technology is an enriching experience for me.

Check this one which I posted on Figures Speak.

Reward and Motivation

2008-06-14T13:43:00.003+05:30

Reward and motivation for students is a key for self improvement and growth in life. Being a teacher , I have felt this many times that in a classroom, only good teaching is not sufficient for students.

Are you motivating your students ? No problem. There is an easy way to reward your students.

I found something interseting ...an online certificate creater.

All you need to do is type the name of your student ...choose a style...and print.

Shapes 2D, 3D

2008-06-09T16:32:00.006+05:30

Today I was discussing about geometrical shapes with my daughter. After finishing the chapter from the book, I wanted to give her some extra knowledge and visual experience.I explored the internet and found these useful resources for making learning easier and fun filled.

Visualise 2D and 3D Shapes
Exploring 3D Shapes Interactive tool
2D Shapes and lines of symmetry
Practising 2D Shapes Guess my name
Have Fun! Play with Polygon Shapes

Although this information is available in the text book but learning from a text book is not sufficient . We need to have other resources for providing ample opportunities to a young learner for gaining knowledge. I have realised that online interactive games and tools have a lot of potential in not only capturing learner's attention but in creating an interest in the subject.

Online Math time Tools for kids

2008-06-03T22:06:00.005+05:30

I am so impressed with the amazing power of freely available web tools. It is indeed like a magic wand in the hands of a teacher to fully grab student's attention and create wonderful learning environment. I have explored the internet and realised that there is so much and so much which can be integrated in our teaching-learning environment with ease. The most important thing is implementation of what we are exploring and learning.In the begining it is important to learn the available strategies. Then the next very important aspect is to use it for students. I believe, not every mathematics teacher can prepare creative resources for students , but at the same time I believe, yes every mathematics teacher can use prepared creative resources.

Here I am going to share some online web resources which may add a flavour to teaching mathematics in a classroom.

This is a link of available online clock which I used with my daughter for teaching her about time related concept.
Practice the concept of time through this available interactive time puzzle.
This one is so interesting with which you can play and learn time concept.Children love to learn while playing and getting scores. So try this one.
Wow! This one is like a clock in our hand. Try playing with it.

Love your profession and enjoy each and every bit of it.

Making e Snowflake

2008-05-24T00:43:00.003+05:30

Today, I thought of sharing with my students , making e snowflakes as their mathematics project. I made a screencast using camstudio on how to make an e snowflake on the given link.

The sreencast created was in .avi format and it was quite a heavy file. I was in a hunt of some software to shrink the size ,restoring the quality and sound effects. I left a message on twitter. In this process I got a solution to my problem from a twitter friend Pdonaghy .

I downloaded Rivaencoder and converted .avi format file to .flv . After this I tried uploading the flash video file to Blogger/Ning ....but could not. Then I again asked Pdonaghy for help. She is so kind to suggest me to upload the file on You Tube. I tried and succeeded in uploading the video.

Here is so called techventrous video...

I am happy to see it here. Thanks Pdonaghy.

Tips 4 teachers

2008-05-21T09:44:00.006+05:30

This is what I have realised...

If you are a beginner...

1.Before you use the technology with students, first use it for yourself. Explore ,learn and then experiment with students.

2. Feel free to share and learn together. Sometimes students are smarter. Let them come forward for help.

3. Use Networking sites for exchanging ideas and learn from experiences of others.

4. Make a mind map of what you exactly want to achieve , your constraints and plus points.

5. Learn both offline and online applications.

6. It is not essential to use a tool,if it is there. Plan a need based strategy which suits to your subject demands.

7. Be mentally prepared for spending extra time and effort with a positive attitude. This is a kind of investment, which would pay you interest in later years.

8. When you experiment ,create or innovate ,your greatest support is your intrinsic motivation.

9. It is not necessary that one successful experiment with one group ,will be successful with the other one too. You need to learn all possible e strategies before experimenting with students. Always be ready for a change.

10. Keep in mind to be focussed to achive learning objectives. One must not be vague.

11. Try to tahe benefit of what students are comfortable in. There are many students who can be like a leader for helping other students.

12.Do not restrict the use of technology for teaching only. Let it involve all aspects like reading,writing,brainstorming, note making, mind mapping, quiz, crosswords, timelines ,record keeping, communicating, interacting,collaborating,sharing etc.

13. Take a regular feedback from students and parents .

14. Never be scared of using technology. It is meant for you to make things better.

15. Learning is a never ending proces. Keep experimenting new things,atleast a new thing each year.

16. Try to use a tool which is easily available to students even at their homes. Go for some open source solutions.

Ning -Thing

2008-05-20T11:11:00.012+05:30

Sharing my experience of Students network on Ning ....

Mathematics , say it in front of 100 people, 80 would say ...Oh! I am not so good in mathematics or I hate mathematics or something which is not in favour of mathematics teaching or learning. I always wanted to teach mathematics differently because I have a strong feeling that it is the way in which is presented to students which create an interest or disinterest in the subject. So, I accepted it as a challenge to myself as a mathematics teacher to deliver the content to students in an interesting manner and to inculcate in them a habit of self learning.In my journey of teaching, I got an opportunity of exploring e tools ,open source softwares ,web based platforms (blogs ,wikis,podcast ) etc through a non profit organisation CII Shiksha . And in the process I created Mathematics Learning blog (which you are reading) , Planet Infinity , Figures Speak, Slide Shows , Podcasting House etc for teaching learning mathematics. Blogging added a new dimension in my teaching ways. It expanded the boundaries of the classroom. That was for the session 2007-2008 students.

Now, the new session has started. I wanted something new to explore with students. So, I thought of setting up a platform for students where we can interact , share ,discuss and engage in teach learn mathematics in a creative manner. By creative manner I mean to say , students are using various means (wikis/podcast/blogs) etc for sharing and learning. In the month of April 2008 , I created a social network for my students of grade 10 on Ning. It is KHMS e Mathematics .

How I planned the whole thing and How it is going on?

Firstly I planned the whole project on a paper and cross checked it for all pros and cons. I created a class poll in which I asked my students on having computer machines ,internet connection , how much time they spend on learning through computers etc. Then I took review from some selected parents regarding the use of internet by their ward in education .Then I asked my students to create their e mail ID's in a special format which highlights their name,class/sec and roll no etc.I took one and half hour session in our multimedia room in our school with each of my section and explained to them how to create an account , add to a group, start a discussion, to comment , to reply , to upload a file etc on the Ning.For each of my class/section I created a special group. For each and every chapter we are learning in the classroom ,there is a separate group for having a discussion and sharing. In each class/section , further I have divided the students in groups like group1_xb , group8_xg etc , for having project discussion and submission.A very special feature of this network is its Query section, where students post their queries in mathematics and I provide them the solutions of problems in mathematics through written text , mp3 audio files, videos etc.

This is not all, the journey is still on.

Math Fest in my school

2008-05-09T14:43:00.007+05:30

We celebrated an inter school fest, exploring hidden talents in our school on 22 April and 24 April 2008. During this celebration, on 24-04-2008, various inter school mathematics competitions were held. On this day the whole event was organised by Mathematics Club, The Planet Infinity.

The idea behind organising this event was to enhance creativity and provide an opportunity to the students to explore the beautiful world of Mathematics.
The following competitions were organized during the Arcade 2008:
· MathEnact Class XI-XII
· MatheArt Class IX – X
· MatheQuiz Class VII – VIII
· MatheWorld Class IV-VI
· MatheBook jacket Class IV-VI
· MatheAttire Class III
· MatheGeoshapes Class I -II
Various school students from Delhi and NCR regions participated with full enthusiasm and zeal. In each event they showed their talent and love for mathematics.

Event MatheArt. We set up the following rules for each school.

1. Each School sent one team comprising of two students.
2. The participants were required to make a collage of math art objects using strategies like origami, kirigami, curve stitching in one and a half hours duration.
4. The participants brought their own material for making patterns for the collage.

Here is a slide show of children making MatheArt...

Mobile has changed my way...

2008-04-07T23:23:00.004+05:30

Technology has greatly impacted on the ways of teaching learning. I believe it has provided teachers with lots of new options to explore and utilise effectively in delivery of lesson content in a more effective way. Gone are the days when students use to copy from the blackboard and do mathematics just with a monotonous chalk 'n' talk. Time has changed , so are the ways of teaching and learning.

Mathematics is a subject of hidden incredible creativity. Since I joined this profession, I keep on trying different ways for teaching my subject and delivering the content.I am very fascinated towards picture based learning techniques because I believe visualisation of a concept is essential for better understanding . I have lots of electronic gadgets which I keep on experimenting and using in my teaching. I have a camera mobile Nokia 6681. I thought of using my camera mobile for this purpose.

Here I am sharing my experiences…
In the beginning I use to click photographs from my surroundings showing mathematics. e.g. Photographs of boards and banners having different geometrical shapes, leaves of a tree showing some patterns of numbers, 3 dimensional architectures etc. When I showed these pictures to my students then they easily correlated them to what they learnt in their textbooks. I found it to be a quite useful strategy for learning and relating to daily life.
Then I gave it as a project assignment to my students and I received a incredible response from them. They used their mobiles for clicking each and every step of the procedure of their project work. I have uploaded their work on my blog http://mykhmsmathclass.blogspot.com/ . I would like to share links of some incredible work done by them. Here are the links :

Making a dodecahedron
Making of Platonic Solids
Making of a GeoBoard
We have a mathematics laboratory in our school. In mathematics laboratory we use to learn mathematics through hands on activities utilizing various strategies like paper folding, cutting and pasting etc. One day while teaching in the laboratory I thought of using my mobile for clicking photographs of each and every step of the laboratory activity. Experiment showed miraculous results. I made a slide shows on http://www.slide.com/ and a digital Photostory using the clicked pictures. You may view the slide shows http://mykhmsmathclass.slide.com . Then I upload them on my blog. With pictures and explanation, now math activities are more fun.
I have created some short videos of short cuts in mathematics using my Nokia 6681 mobile like this one. It is quite useful and helpful for students as well as teachers. Also videos created by mobile are easily transferred to computers and uploaded to blog. Here are the links of videos.
Recently I thought of creating some paper folding steps for making some math stuff. Then again I used my mobile for recording the steps in the form of a video.
The blue tooth facility of a mobile is amazing. The data can be transferred to another blue tooth enabled machine in a fraction of seconds.
In the end I must say creativity has no ending, one must strive for exploring new techniques and do something different for making learning a memorable journey for students.

My day with Kids

2008-03-16T23:08:00.005+05:30

Yesterday was full of exploration,experiment,excitement, entertainment ,enthusiasm and enrichment. It was all because of 7 special kids Prachi,Ishani ,Vishrut ,Sidak ,Rajpreet , Kanav and Aditya. These kids helped me in my new project of using e tools for new session 2008-09 for primary kids. We did the following ...

Firstly I clicked their individual photographs and started with my experiment which was using http://www.blabberize.com/ and asked all of them to introduce themselve .They loved this activity and laughed so much after watching their flipping mouths .
Then, I gave them a project work on having a discussion on the topic "Polybags are harmful" They came up with an excellent report. I recorded their project work which is uploaded on my daughter's blog.
All of them were so happy to do this activity. I think , if a teacher would try these kind of small small new strategies for teaching then surely there will be enhancement in learning . Also there would be an added life in the class environment.

I would like to thank all of them for raising my confidence in making my experiment successful and presenting this idea.

My this idea may be used by a teacher for teaching mathematics also.

A teacher can make a difference! All kids are special!

Learning experience

2008-03-12T15:09:00.010+05:30

Today, a group of teachers from our neighbourhood area school (Maharaja Agarsen ), visited our mathematics laboratory. The purpose of their visit was to to have an interaction regarding "knowing different ways and strategies of teaching learning mathematics". In our mathematics laboratory "Planet Infinity " we are trying our best to utilise as many new ways/strategies/techniques for learning mathematics especially through hands on and using technology.
We shared the following things:

It is now high time that we shift from a classroom with only chalk/talk based teaching learning to an environment with enormous techniques and stategies .This means , a new set up having better possibilities for visualisation and understanding of a concept is the prime need. Also, it is to enhance learning according to the needs of the students. In our discussion, I showed to them, some pictures which do not require any explanation and which can be directly used as an instructional aid for learning. Here is the slide show
- Then , I showed to them some digital photostories for understanding math concepts.
- I talked to them about various e tools by which a teacher can easily create quizzes , crosswords etc.
They shared with me how they teach mathematics in their classrooms and now that they are planning to set up a mathematics laboratory . I feel happy to see teachers with enthusiasm and a will to learn and share.There are wide and varied possibilities which are available for a teacher which can enhance the learning process to the maximum. Sky is the limit.

Incredible Patterns

2008-03-08T22:38:00.009+05:30

Mathematics is a subject of incredible creativity and hidden symmetries. Geometry patterns are so fascinating and captivating. As a teacher I believe, it is important to realise the beauty of mathematics. Students must be given a chance to atleast visualise and appreciate the geometrical presence all around. There are variety of shapes and patterns. I am not going to deep into the details but yes, would name few of them. During my exploration of e journey, I came across an interesting online symmetric pattern generator in which one can freely experiment with wallpaper patterns, Rossette and Frieze patterns. I find it quite interesting and amazing too!

Here is the link.

Kali: Symmetric Sketching (Science U) via kwout

Here are some sample pictures...created by me

Enjoy exploring patterns...

Image editing is fun

2008-03-06T10:14:00.009+05:30

Image Editing
Today, on my passionate teachers network Kelly shared about an image editing tool Phixr. As usual, I could not wait for a long and started doing some experiments on it. I found quite an interesting feature in it , swirl, which changes the original picture into curvy pictures. Then, I tried doing an experiment with famous tangram puzzle picture. I got amazed to see a wonderful observation. A square cut into 7 curvy shapes instead of 7 regular ones as in a tangram

( 5 isosceles triangles/1 parallelogram and a small square).
This is the original tangram picture...

And this is a curvy tangram...

Then I thought of experimenting with the shape of a cat which is formed by joining seven cutouts of original tangram.
I uploaded it on Phixr and then again used the swirl feature. A curvy cat is the result.

Workshop for Primary teachers

2008-03-05T13:31:00.006+05:30

Today, with my colleagues of the primary wing grade 1 to 3 of our school, I shared about using pictures as a teaching tool. I believe, all of us are fascinated towards colourful pictures.Specially children are more attracted towards pictures. In primary grades we can teach various elementary topics through pictures.Earlier, in my previous workshop I talked about using an offline tool Photostory 3 for making a digital story.Today, I talked about various free online facilities which are available for making slide shows. We explored Slide.com.
I asked them to select a topic of their choice and using some image search engines ,to select save some related pictures in a folder. Then, I gave them instructions for making a slide show . We created a common account by the name kulachiprimary1to3 on slide.com. You may visit the link to view the work done by them.

Using online applets

2008-03-03T19:02:00.005+05:30

Learning Geometry is Fun!!

Lots of children are having a phobia for learning geometry. I have analysed this fact many a times that during the examination, students are nervous in solving geometry based questions. This fear is due to lack of visualisation or non clarity of concepts /geometrical theorems. Students tend to cram the geometrical results which leads to lesser clarity and a doubtful situation. Even questions based on simple results such as "sum of interior angles of a triangle is 180 degree" are attempted wrong sometimes.

I experimented on teaching geometry using online available interactive applets for learning middle school geometry .It proved to be beneficial as students were able to experiment/explore on basic geometrical facts using the interactive applets.

I believe as a teacher, we must keep on trying new solutions according to the needs of the students.

My day with teachers

2008-03-01T12:59:00.009+05:30

Today, I went to the Primary wing of our school, for having an interaction with teachers teaching grade 1 - grade 3 . The purpose of this workshop was to make teachers aware of the following...

Imparting knowledge of using technology beyond using just presentations in the classroom.
Utilising free tools/software which are available free e.g. Pivot Stick Figure
Using Search engines Google Image Search and Flickr Storm for downloading useful educational pictures (talked about copyright issues )
Using MS Photostry 3 for creating interesting digital stories. Shared some interesting ideas of making stories by involving students.
Discussing various possibilities of voice recording and adding music to photostories and slide shows.
To encourage the use of readymade resources .We have EFK (e learning for kids )Content provided to us by CII Shiksha.
Utilising useful online links for students of grade (1-3)...e.g.
Dance Typing Mat
Up to ten
Learning Planet
Storynory Free Audio stories for kids...an excellent audio resource etc.During the workshop ...
Firstly, I asked all of them to write the Mission of being a teacher. They wrote fantastic thoughts and ideas . I am sharing few of them... Kanika Sharma wrote"I feel it's proud priveledge to be a teacher by which I am not just only be able to expand my potentials but also excel further with my students. The utmost responsibility on my shoulders is to cater to diverse needs of my learners which I think I'm able to do through innovative strategies".Sangeeta Agarwal wrote "I am a teacher. My mission is to make our students good citizens by giving them proper education, by teaching them good moral values."Kalpana Kumar wrote "To build up a new life who can face all the challenges worldwide, with complete confidence. To make students aware of all the information besides the four walls of the classroom. As a sculptor tries to carve its image to its perfection so, will I to make the students to have their own perfection in all the spheres"Madhu Tandon wrote "My mission is ...to make students a good citizen and involving them in every moment and activities. Real presentation will improve their thinking skills. In this way they will learn about their culture with good values."
Teachers were given a feel of importance of learning in a connected environment which is not just limited to the boundaries of school .

All of them said in a louder voice "Together we can " . " As we are connected here, we will still remain connected through cyber world".I Shared some of my experiences of being connected to teachers worldwide through various networks and platforms available.

Then they were given a desirable knowledge for downloading and installing a software. I gave a demo to them "downloaded Pivot and installed it to my machine." Teachers were then asked to download the same and do the installation to their machines. Actually, I feel, a non- tech teacher is to be trained by hands on exposure...that's why I asked the to do it for themselve. They were happy after the successful installation. Then we played with Pivot Stick figure animator.
After this we downloaded few images using image search engines and learnt to make a digital photostory. It was an enriching experience.

Learning in life is non terminating...Keep on Learning.

Multiplying numbers nearing 100

2008-02-24T14:34:00.004+05:30

Short Cut Tip# 2

This is a short cut technique to multiply two numbers nearing 100. You may use it to find square of a number nearing 100 , e.g. 99^2 , 102^2 etc.

Note : For numbers more than 100 ,on R.H.S. just write (+) ,and in place of diagonal subtraction ,do addition .

Muliplying single digit numbers.

2008-02-22T14:59:00.003+05:30

Today, in my school I thought of creating videos of using short cut techniques for calculations.Here is a video for a short cut method of multiplying any two digit numbers.

I thank my friend Ankita for helping me in recording.

Thinking Blogger Award

2008-02-16T16:26:00.003+05:30

In the month of january 2008, I got an e mail from my cyber friend Leena from Finland who was rewarded with Thinking Blogger Award by her friend Hanna.
I congratulate Leena on behalf of Planet Infinity.
And Now ....She has awarded my class blog with Thinking Blogger Award.
She wrote on her blog "Rash Kath, whose passion in mathematics blogging has made me convinced that I’ll start a real mathematical blog to my students. My current Finnish blog concentrates on the entertaining and beautiful side of math, like this one. Rash Kath also created a group named Passionate Teachers and the amount of knowledge shared there is even too much for me to swallow instantly. Now I know what I will be doing next summer on my vacation."
I would like to thank Leena for this appreciation. I feel proud to put this badge.

About the awardThe participation rules are simple:1. If, and only if, you get tagged, write a post with links to 5 blogs that make you think,2. Link to this post so that people can easily find the exact origin of the meme,3. Optional: Proudly display the 'Thinking Blogger Award' with a link to the post that you wrote (here is an alternative silver version if gold doesn't fit your blog).In addition there is a note: “Please, remember to tag blogs with real merits, i.e. relative content, and above all - blogs that really get you thinking! "
I feel from my side I would like to share with this world about 5 genius people...who are doing excellent job in the field of education.
Now, 5 blogs which make me think ...

1. Lizbdavis ... Wellesley, MA, United StatesShe is a dynamic, passionate Instructional Technology Specialist and TV/Video teacher at the Wellesley High School in Wellesley, MA, a suburb of Boston. She believes in the power of educational technology to help students and teachers succeed in the 21st century. I got to know about her from a post on classroom 20 regarding Twitter. Since then I am learning from her through her sharings on various web platforms.

2.Kwhobbes... Kelly Christopherson, a principal in a K - 12 school in Saskatchewan. He is a great administrator , educator helping and guiding teachers to use techology in classrooms . His posts are inspiring and very close to our daily life routine realities. He is guiding many teachers all across this globe on Passionate teachers ning also. Read his discussions, you will surely experience a new thing.

3.Kolson29 ...Kate Olson , a 21st century Business education teacher ,an e teacher, a self explorer .She is a teacher who has always inspired me through her continual explorations. I am following her on twitter too. She shares her knowledge with the community.

4.Murcha ...Anne Mirtschin is another passionate teacher. Visit her blog ,you would come to know about her interesting sharings about her classroom experiences and explorations. I always appreciate the work and experiments which teachers do for manking teaching learning a joyful experience.

5.Suryaveer...Suryaveer Singh ,India. He is a passionate geographer. He has created a wonderful blog and a wiki in his subject geography.Also, he is continuously exploring e tools and various e strategies to make his subject interesting for students.
I was given this opportunity by Leena, Finland.Now, this award will travel through India to many other countries.

Congratulations to you all for your great contribution in the field of education.
Keep Sharing.

Best Regards

Rash Kath.

Blog in News Channel

2008-01-27T13:42:00.002+05:30

After the news in Hindustan Times Jan 5 ,2008 , teaching on Blogboard....
My class students and myself were interviewed by News Channels CNN IBN and Aaj Tak. The programme on Aaj Tak got telecast on 13.1.08 .
It was all about using blog as a teaching tool . Students shared their experiences of using Planet Infinity ...mathematics activity blog .

Exploring GeoGebra

2008-01-22T17:25:00.000+05:30

Geogebra is a very useful software for teaching learning and exploring mathematical results based on Geometry and Algebra. Today, in our school teachers from 6 different schools ,discussed lessons/resources for teaching mathematics using Geogebra. It was an enriching experience. We all , had a discussion on preparing instruction sheets for students, so that they may use it at their homes . (GeoGebra is freely downloadable ).

e Teachers maths club meeting on exploring GeoGebra .

BubbleShare: Share photos - Lead Free Toys

More on mind mapping and mathematics

2008-01-08T17:59:00.000+05:30

This information was shared as a comment.Ifind the links useful, so sharing.
http://www.mindomo.com/view?m=3ff8623d06851945926c6d8cb7ba122d
http://heuristixx.wordpress.com/
http://www.scribd.com/doc/952780/Mind-Maps-and-Math-Problem-Solving

Exploring mathematics ideas

2008-01-06T15:30:00.000+05:30

Explore Mathematics
Recently,while surfing useful mathematics resources, I noticed the website for exploring mathematical concepts.The link for the website is here.

The other one is an online graph creator.

This is something at home with mathematics.

Proprietary to Open Source

2008-01-04T20:47:00.000+05:30

Teachers all over the world are shifting from using proprietary softwares to Open Source. Read what they have to say...

Norfolk Blogger: The vested interests and hypocrisy of Microsoft and UK schools

Click on

Passionate Teachers Network

2007-12-25T13:24:00.001+05:30

I have created a group of passionate teachers on http://passionateteachers.ning.com/

If you think ,teaching is not just a job but a passion for you, Join this group and add your drop of knowledge.
All the Best.

Workshop for Maths teachers

2007-12-15T18:12:00.002+05:30

I was invited to Notre Dame School ,NTPC Badarpur ,by Pearson Longman, for conducting a hands -on activity workshop in mathematics for teachers. Its an enriching experience sharing new teaching strategies with them. Teachers showed so much of enthusism to learn. They performed various activities .I discussed with them about mathematics teaching and various teaching strategies.

We explored activities based on unit cubes and paper folding for grade 1-7. Teachers learnt to create basic paper folds in mathematics, making an equilateral triangle, a parallelogram etc. They got exposed to creative mathematics projects of creating 3 Dimensional solids using their nets. Also, I shared with them utilising play way puzzle creating/solving strategy for learning/remembering formulae and results. During the workshop, there was lot of brainstorming done on various mathematics related issues.

Podcasting Projects...

2007-12-14T18:29:00.000+05:30

My students worked on different mathematics projects in this session. I asked them to prepare a summary on their project and their general experience. Then I thought of recording their work as podcast. Not all students are confident in speaking or expressing themselves .But since it was mandatory for all of them to record their voice ,so they practised and gained confidence also. I felt happy when students were helping their friends and motivating them to speak in front of mike. Its really interesting to know that in the process, they learnt from each others work .Its an enriching experience for me also. Although, it was painful for me as I had to sit at home for long hours to upload their podcasts on http://mykhmsmathclass.mypodcast.com/ and then setting up a link on the class blog http://mykhmsmathclass.blogspot.com/ , with my routine teaching work, but I managed. But I enjoyed.

Podcasting Projects...

2007-12-10T16:57:00.000+05:30

My students recorded some mathematics projects using mypodcast recorder and we uploaded them on www.mypodcast.com.

The URL of podcasting house of planet infinity ...our mathematics laboratory is http://mykhmsmathclass.mypodcast.com

The students also shared their views about learning mathematics through activities and their class blog http://mykhmsmathclass.blogspot.com

I enjoyed recording their work.

Uploading Mindmaps

2007-12-07T19:32:00.000+05:30

I am using www.freemindshare.com to upload mind maps created .

Links of mind maps created...

Quadrilateral http://freemindshare.com/map/bcdjls17HT/
Strategies teaching/learning mathematics http://freemindshare.com/map/fjnqry8GLR/
Class X Mathematics http://freemindshare.com/file/dvxy125DMS/

Useful online mind maps

2007-12-03T15:59:00.001+05:30

While surfing internet, I get to know about some good readymade mind maps. Here are the links of them...
1. On Pythagoras theorem http://agutie.homestead.com/files/pythagoras/pythagoras_proof_mind_map.html

2.Geometry help
http://agutie.homestead.com/files/mindmap/geometry_math_com_help.html

3.Euclid's elements
http://agutie.homestead.com/files/mindmap/mindmap_elements_000.html

4.weblog
http://agutie.homestead.com/files/mindmap/mindmap_blog_weblog.html

5.Optical illusion
http://agutie.homestead.com/files/mindmap/optical_illusion.html

Mindmap Instructions:
To see a note, hover over a note button above.
To Fold/Unfold a node, click the node or right click a Node and select Fold/Unfold all from Node. To scroll the mindmap above, drag the map's background and move it around, or click on background and use the arrow keys.
To link to another page, click a link button above. Buttons above: Search, Go to, Zoom in or CTRL '+', Zoom out or CTRL '-', Reset (center), Shadow On/ Off, FreeMind, BG color.

Mind Mapping

2007-11-25T13:04:00.000+05:30

I have created Mind maps using an open source mind mapping tool Freemind. It has helped students in learning,making short notes, remembring results/theorems and much more. In a subject like mathematics, students tend to forget important results and theorems, so they are not able to apply them in the related questions. This results in poor marks. But with mind mapping tool, one can remember the results in an order. This technique is very beneficial for learning and organising notes.

I have created mind maps in many chapters. One of them is probability. On one page ,the concept, related terms,sample space etc are collected/represented. It has helped students in attempting questions related to the topic probability. The map is stored in permanent memory. Now, students can relate the questions asked and answer them correctly.

Mind maps created using Freemind may be uploaded on www.freemindshare.com

Practising Venn diagrams

2007-11-20T13:40:00.001+05:30

Click on the given link to use the online tool for practising about venn diagrams .

http://mathdl.maa.org/images/upload_library/3/Jimenez/VD3_Numbers-NOTATION_01.html