revision

end of year..no more innovations as of now. but i find that a stiff 1 month revision, with revision tests makes them confident of facing the exams. we go over all topics. pause wherever something sounds greek to anyone (!) and make sure that before the finals, all topics are covered well in their minds.

website

check out www.numeracysoftware.com
they have a lot of good free downloads. i used their stuff on symmetry recently. i asked the students to download the ppts on symmetry lessons and pdf on symmetry worksheets. they had 3 days to understand the topic and work on the worksheets. then i gave an assessment.
self learning from the net...they loved the method!

chanting

ancient Indians used chanting as a method to transfer knowledge as there was nothing to write on. generations of students and scholars chanted away the mantras!

i use chanting in the class as a strategy, especially for children with special needs who find it difficult to hold on to new words e.g QUADRILATERAL or to rules such as SOH-CAH-TOA. we all chant together.

it is funny, we do laugh a lot. we chant with phonetic awareness.

great way to help them bond with the word! slowly, as they chant, connections form in their minds and the new words/properties just settle in.

so if you pass by my class and hear all of us singing "opposite, adjacent, hy-po-te-nuse"...you know what we are doing!

project - symmetry

project - line and rotational symmetry

1
a) You are a designer and have been hired to create eye appealing artwork for a company logo (you can decide what the company manufactures!).
Your audience comprises of the company’s CEOs. Your situation is to design eye appealing artwork for the company logo. Your product performance and purpose is to identify and effectively use mathematics of symmetry to create an aesthetic company logo.
b) Write in about 100 words justification for the logo. Explain the symbols used. How does it represent the product of the company?

2
a) Design a logo that represents of your life
b) Write in about 100 words justification for the logo. Explain the symbols used. How does it represent your life?


3 a) Click pictures from life – flowers, cut fruits, people etc and show the symmetry existent in nature.
b) Write in about 100 words “symmetry adds to the beauty of nature”


RUBRIC – 20 marks
Aesthetics of the design- 5
Use of symmetry – 10
Paragraph - 5

simplified math

SOH-CAH-TOA

SOH - sine x = opposite/hypotenuse
CAH - cos x = adjacent/hypotenuse
TOA - tan x = opposite/adjacent

plain and simple rule to remember sine, cosine, tangent of an angle. there are students who can't process information too well. they need 'simplified version' of math. these rules come in very handy for them!

i told my class of SEN children the rule. we sang it in a tune to remember it. i asked them to greet me me as soh-cah-toa each time we meet....all of this as a strategy to make trigonometry introduction a fun filled, fear free and happy one!

activity for pythegoras theorem

are our walls perfectly right angled? let us check using pythagorean triplets

Activity - Students will make a right triangle of thick paper using a Pythagorean triplet of their choice. Then they will go around the building to check if the walls are perfectly right angled.

activity with pythagoras theorem

for grade 6 or 7- using creativity to boost math

“The nile flooded and all the boundaries of the farms were washed away. A man was told that he can redraw the boundaries, but the farm should be a right triangle...”

write a story with this plot showing clearly how the use of Pythagorean triplets helped the man draw the boundary again. You can draw pictures to supplement the story

webpage for art and geometry

http://www.itap.physik.uni-stuttgart.de/~gaehler/tilings_gif.html

An excellent and simple web page for different kinds of tilings. you can easily create a project on art and geometry using the information.

a good site for math

www.mathgoodies.com
an excellect site for ideas and worksheets on teaching math. some of their stuff is for sale only but there is a lot of free one out there! grab it...

project - reviewing area and % using the newspaper

“HOW MUCH OF A NEWSPAPER IS REALLY NEWS?”

Tasks
· Select a newspaper – the main paper only (no supplements)
· Make list of 6 types of content categories contained in the newspaper-
News;Advertisements;Photographs;Entertainment;Sports;Weather · Choose at least 2 pages of the newspaper (you may take more)
· Measure the area covered by each category
TOTAL AREA OF ALL CATEGORIES =
Now find what % is each category area of the total area?
PRESENTATION
· Present initial work on this sheet only.
· Bring the newspaper that you have used also.
· Attach the R.W sheet with this sheet
· Final presentation artistic on a colour paper
THOUGHTS TO REFLECT:
§ IS YOUR NEWSPAPER MOSTLY ADVERTISEMENT?
§ Check any 5 other newspapers and compare them with yours. Comment!?

fun in geometry class

after finishing the topic on geometrical shapes, we asked the children to make 2 characters out of the shapes and write a story. grade 6

a girl created characters called 'machu' and 'pichu' and wrote a lovely story revolving around them!

A CREATIVE PROJECT FOR GRADE 7

CREATE AN ADVERTISEMENT AND A STORY

A shop is putting all its items for sale. Create a colourful advertisement sheet for the shopkeeper to use. Take pictures of the items (from internet/magazines/newspaper etc), their real cost and decide discounts yourself.

Write a fictional story of Ramu who goes shopping in the shop. He buys 5 items. Create a bill for him showing the actual and the discounted price.
How much money is he saving due to the discount?

MARKS: 20
ADVERTISEMENT –5
STORY AND BILL - 10
AESTHETICS - 5

develop personality in math class

i asked a kid to explain something on the board to the entire class.
"no ma'am i feel scared", was the answer.
i grabbed the opportunity to make him face up to it. on a prompt, the entire class cheered him and egged him to go for it.
shyly he got up and explained the sum on the board..looking mostly at the board only!
but he did it! and we loved him for it...

shape walk

we did a SHAPE WALK the other day.

the children were sent to a club nearby to do a cross curricular work.

for math, they were asked to look at each object, identify the underlying shape and write any 2 properties of the shape they chose!

soon you had grade 6 kids looking at branches, bushes, swimming pools...

"there is math everywhere!"

math game

We played dumb charades in class the other day to reinforce geometry. 3 groups;
Group 1 thought of a shape.
Group 2 had to demonstrate it using their bodies!
Group 3 had to guess it.
A hilarious situation arose when group 2 gave a Nonagon (9 sided polygon/closed shape) to group 3, which had 5 children.
It took them a while to figure out a way of showing it...

vocabulary in math

how to make them remember all those words...?

ask them to think of each as a character, and introduce it. give it colour, form and use the imagination to give it a body.
"hello! i am Mr. Bisector...I am..."

the drama skills get wings to fly in the class. Math class becomes something to run to!

use the body

use the body...
ask the children to demo the various angles and shapes using their body. they can be solo or have 2 to 3 members in the group.
you can also play dumb charades through this - ask group 1 to give group 2 a shape to display and group 3 has to figure out what it is..

• everyone participates
• it is a lot of fun as they grapple!
• build the team feel
• they understand the properties 'kinaesthetically', an area sometimes difficult to bring in the math class
• watch with hilarity as the ones not so flexible try to twist to show angle 90 degrees or bisector!

top it up by asking them to describe the vocabulary/properties demo'd in their own language in the notebooks. the linguists get a chance to show.

prime numbers

http://www.answers.com/topic/sieve-of-eratosthenes
ERATOSTHENES SIEVE is an excellent way to work on prime numbers.
you can get the chart "1 to 100" from 'google images' (or see the link).give each child one chart.
instructions:
1.strike out all multipples of '2' (our head number)
2.now strike out all multiples of 3 (other head number)
3. next 5, 7, and so on...
when the list is exhausted, the 'head numbers' are the prime numbers!
.... they will have a lot of fun doing this!

revision by children

end of the syllabus and exams in a month's time!

i wanted to get away from the rigmarole of the usual revision. so i asked the students of grade 6 - 'would you like to teach'?

"me, me, me..." they all chirped.

we made a schedule and put it up on the wall.

so here we are, already on our 3rd topic. the children have divided the topics among them and in every math class 2 of them come forward and revise the chapter. some from the textbook, some get problems from the net or make their own. they teach, give problems to classmates to solve, correct the work and also grade it daily.

i step in only when required. they learn from each other!

it is wonderful...

creating a math magazine

PROJECT – CREATING A MATH MAGAZINE FOR SALE

This is a classic example of a project through which a girl, having found her niche, also found her relation with the subject. It is her magazine that is attached.
She came to my class very scared of math. So much so that she would start crying. It is through these projects that she overcame her distaste of the subject and went to the extent of taking a class one day and taught algebra!

AIM:
To take an overview of the topics done in the 1st term.
To be able to express them in their own words.
To elicit inherent creativity of linguistic expression.
To improve the grip of the math concepts covered.

MATH INVOLVED:
fractions (addition, subtraction, multiplication, division, applications)
geometry – few properties
decimals (addition, subtraction, multiplication, division, applications)
directed numbers (adding them using number line)

INSTRUCTIONS GIVEN TO STUDENTS:
Make a MATH MAGAZINE for sale, explaining any one from each of the main topics listed above.
Your magazine should have:
A report/story/article explaining the topics
Pictures – drawn or cut-paste- with the explanations
Few examples of each topic
A headings/captions for each section
A bit of researched work on music and fractions – optional (tabla/piano/guitar/any other)
Minimum 5 A4 size papers, a cover and a back page.

RUBRIC:
Math explanations: 5
Examples: 5
Pictures: 5
Over all presentation: 5

SKILLS INVOLVED:
information on mathematical terminology
transference of knowledge
linguistic expressions
Research
application in music (optional)

self esteem and math

Warm evening, santoor playing in the background; sipping my favourite green tea, my thoughts run to my experiences in the classroom…

‘I know that I can’t do math! That is why I am in the core section.’

How did these children get this attitude?
Where has the self esteem gone?
It’s like a wall of resistance when I face them.
They have lost it…somewhere on the way…LCM, HCF, coordinates…all has become a maze of incomprehensible zamboree!

I realize that they need positive experiences. Experiences of ‘I could do it!’ Small size experiences where the joy of success is reiterated.
I look at the MATH that they have to learn and I break it into small chunks…as small as possible. ‘Digestible size of bites’. And I offer it bite by bite. When one is assimilated, I offer another…and so on.
As their grip improves, the confidence-lost among the years-slowly, tentatively takes its first steps, I slowly increase the bite size.
And this continues.

Slowly there is a change in the atmosphere. The emotional knots have loosened; the faces look happier; there is openness to relation with the math teacher.

Increase in self esteem has brought about a change in math abilities…

a case study of a group

A complete failure?
“Children in the middle school need extra attention in math. If that is taken care of in the middle school, high school is not a problem. So, in each of the classes 6, 7, 8 we will take out few children who need attention in math and have a separate teacher taking their classes. Shall we go ahead?”
Well, sounded like a great idea! I was all for it.
I got my bunch in a class, 4 kids. 1 new and 3 old students of the school. The new kid on a separate program for math.

We started...me brimming with ‘what a great opportunity we are giving to the students. They sure should be grateful for it!’
I also had great ideas of how small groups are always better than large.
‘4? Ideal! There is so much I can do’.

Nothing worked. Nothing moved. Math or relationship (or is it math and relationship!)
The children came in kicking and screaming. They did not want to be separated from their class fellows. The new child did not like the small group.
‘Yo! What a challenge. I must face this. They will change surely!’

I relaxed in the class. Gave them more space to talk about things they wanted to. And math? Well, that stopped moving! It was as if a dam burst and I saw 4 living attitudes in front of me that were baffling! A child not wanting to work at all; a child who knew it all and therefore rude; a child going through severe emotional disturbances, reactive and rude; and a child groping through the environment completely new and alien. The kids had deep comfort grooves in their previous spaces and were pulled out from it by our smart ‘experiment’. Cut loose from the umbilical cords, their needs crammed into my space. This remedial math class was 4 children going through a trauma and an adult not sure of herself, and filled with great ideas!
I was overwhelmed by it, yet feeling the need to do something about it kept me on and on. ‘Maybe I can make a difference! They are hurt.’
I talked to anyone willing to listen in the school for suggestions. Desperate and exhausted, but...
Rarely did we have a class which did not explode into something. Far from being grateful (what’s that?), the kids went into a leisure mode. I gave them an emotional space to work in, and that was the detriment of the entire program. ‘Can kids be so manipulative?’

I tried various forms of building a work space. Activities- cooking, outdoors measuring work; talking to them; talking to parents; document sheets...but the atmosphere stayed vitiated.

Finally...a complete emotional withdrawal by me. I could not handle it. I decided to be only a math teacher, and communicated it to them clearly. There was a silence as I said, ‘henceforth, talk to me only when there is a question pertaining to math. Nothing else.’
A wall comes over me when I enter the group space. They can’t penetrate it.

Have I failed as a teacher?

There is a perceptible difference in the atmosphere. Work is moving. There is a soft hi! And bye! from them. But something within me has switched off. The only connection is math. Teach and come back. There is a disinterest in anything else.

Is this a total disaster? Would someone else have been better? Could I have...would I have...should I have...? If I was matured...? The noise goes on.

I only wait for the end of the term.
The situation is still unresolved, but a lot of questions boil inside me.

Is it not that ‘math remediation’ is only a very 1-D way of seeing things? Can we see the situation without involving the emotional side of the children?
We get caught in the phrases ‘relationships’, ‘emotional support’...in our schools. Are these only catch phrases or do we have a clear understanding about them?
A relationship requires maturity and wisdom. Would be not be safer to be on the steady grounds of subject teaching and stray out only as far as one is comfortable?
But if only math, it does not satisfy! I need to touch deeper.
I relaxed the hold on math, for I felt the children needed something else. Only math was not satisfactory.

I wonder, am I clear? What are we doing here? What am I doing here?

...in the meantime, I only teach math! Safe on the nerves.

aha moments...

There is always a surprise waiting when a project is done in the class.
There is always some one child who is always quiet in the class and kind of left out, who finds a space to show his prowess and feels happy and connected with the class. someoen through poetry, someone through music or art...
The self esteem soars. The AHA! Moment…My effort in math classes has been for such moments. I hope each child gets a moment of this kind…

teach math to him...

He is a kid who is beautiful with the non-mainstreamed way. Give him his space and he blossoms beautifully. Creative, loving and sensitive.

And I? I have to teach him math! A subject that demands order, rigour and method. I sense the beauty and sensitivity in him, and also his inability to come to terms with the method part in life.
What do I do? How do I communicate to him the need for hard work, order, discipline without covering the sensitivity part in him? Is there a way that his sensitivity stays alive and yet the so-called ‘mainstreamed’ ways develop in him?!?!

conquering fear of math

Dialogue with Mr. Fear

It started with tug of wars.

She was trying her best to avoid math, I was trying to find ways for her to come to it! There was a resentment in her, which flared up each time she saw me, her math teacher. She was childhood diabetic and her insulin level went up when math class started!Well, the only opening I had, was her opening to a relationship, conversations, and we had plenty.
The first attempt was to ask her to do 10 min of math everyday at home. Anything involving math. She agreed, albeit a bit unhappy, but she tried.
In school we decided to repeat last years book once again. “So you can be stronger with the concepts,” said the ‘wise’ me. She started, and we went on to a daily grind of “please focus on the work”.
Change happened one day when I saw her sitting quietly, head drooping, bored, doodling on the textbook, and that was it! I suggested a complete abandoning of the textbook and switching over to few SMP (school mathematics project) booklets. Her face lit up the first time she saw them.

“Am I allowed to colour the pictures”?
“Of course.”

And the sun shone brighter in the class at that moment. Oof!
There was some cheer for the next few days.
Next dramatic shift happened when ‘Geometry and Art’ (making geometrical shapes and turning them to art pieces) was introduced in the class. Her natural flair for art opened her to the rusting tools of geometry (compass, ruler, protractor) that she carried reluctantly. Some colour was coming back on her face. As I saw her, sitting with complete focus, trying to draw a perfect circle, I felt a sense of wonder coming over me.

It’s possible for years of patterns to break…!
(Art and geometry was a regular event in the class. The other event was math plays. )

They did a play, she and her friends. Something about a beauty parlor and prices. I had never seen then so happy; they had made so many props.

SMPs and art went on for a while…then we shifted back to the textbook. Seeing her love for art, I asked her to start afresh, with graphs.

“Of course you can colour your graphs!”
“Thanks aunty!”

Now came the real difficulty. Mood swings depending on the work were regular occurrences. I would sit next to her while she worked, quietly and unobtrusively. Other kids would come and go with their doubts.

Then quietly, our conversations started.

“You know dear, you are not doing math. You are doing something bigger than that. You are facing your fear. Is it not awesome?”
Thoughtful expression on her face...
“There! It has come again. Mr. Fear! Don’t see it as a math sum. It is Mr. Fear. Are we not going to face it or are we going to let it swallow you?”
Smiled softly. “Yes aunty.”

Somewhere in that quiet corner, between all the art, coloured graphs and chats, something happened. The time spent on work increased in span; the self-check of work became regular; the need for chats became lesser and her natural sense of neatness and order prevailed into math work ‘also’. The rhythm of work established itself. There was a joy in her when she worked.

And then one day she said, “You go. I’ll call you when I need you.”
I was awestruck!

An avalanche of old patterns has broken...

What happened in that space? Is this what is called learning? Or this is blossoming? Is this what J.Krishnamurti (an educator and philosopher) meant when he asked, “Can you bring a child to joy through geometry?” is this this or is this that, the mind wonders. I know not…for what I feel is only a sense of wonder and fascination over the whole phenomenon.

Well! It not over, the work goes on and onwards!
At the parent teachers meeting, when she was asked, “Do you feel the need to be stretched in any subject?”
“Yes. Math. I can do more”

The other day she and a friend took a challenging game of Math based on graphs, and decided to understand it. It took them three classes and a demonstration, but they did not give up. Till they go it! Of course the game graph was full of colours…

2 months down the line… “Aunty, can I do the next class’s work? I am done with repeating last years work.” She is enjoying the work!
She is on her way…Mr. fear is out of the way!

Her mom came the other day to meet me. With tears in her eyes she said, "In these past 8 years, this is the firts time that I see my daughter volunteering to do math..."

art as the window to approach geometry!

ART FOR GEOMETRY

AIM
Art has a universal appeal. Geometry has an inherent perfection and its own beauty. I thought that if a student works on geometry by creating a perfect form, it may bring the perfection in the fingers that work upon the design!
Also, one will learn to work with the tools of geometry – protractor, ruler and compass – and weave the beautiful creations…

STRATEGY
To be done in the math class on Thursdays. The Thursday class was converted into project class.

Pair work
each pair of students was given one geometric design
they were asked first to figure out how it was done
using the geometry tools – ruler, compass, protractor, pencil – copy it to perfection
‘Colour it as you wish’. Convert it to an art piece!

CONCEPTS
Geometrical constructions

INSTRUCTIONS
Figure out the geometry of a design given
Copy it with perfection
Colour it and turn it into a design
Make a presentation to the class. Explain how you drew the design, giving all the geometrical processes and rules involved.

RUBRIC
A clear rubric always helps students to organize their thoughts.

perfection of geometry – 10 marks
Art work – 5 marks
Verbal presentation - 5

multisensorial work-intro

math can be abstract!
i wanted the students to have that one special moment in the class, where they felt they had something to show off their skills with!
hence was born the idea of using multi sensory modules of teaching math. of creating moments in the class that were creative for students too. to give them a chance to express their creativity.
the following pages would have some samples of such lessons and how they affected the little ones! or the grown ups too...

she...

she was 10 when she came to my class...shivering for she feared math more than anything in the world!
i started slowly. letting her do the amount of work she could in the class. giving her a work of '5 questions a day' for HW. the aim building her confidence and her math slowly over a period of time. we made a bond and that led to an increase in her determination to work harder.
then came the projects in the class (will be shared in later blogs). based on art, drama, language...her favourite strengths. and she blossomed...attacked math with a frenzy.
then came the best day of our lives. she said, "i do not fear math anymore"..."i want to teach". and she took a topic 'brackets in algebra' and taught the whole class!
a moment in our lives...

introduction

"i am a math teacher". this is how i generally introduce myself. what i am unable to express is the wealth of creativity that lies underneath it! i am not a mathematician...i am a teacher of math..somewhere on the borderline. the entire spring of creativity comes through this channel of 'teaching math' making life an enriching experience rather than a mechanical mundane existence.
thus i begin a series of sharings...lesson plans, plans gone great, thoughts on math and its teaching, and most important why the fear and anxiety for math and how i have faced it and overcome in many children, making them happier human beings...
if you find anything helpful...do share.