“Math for Everyone” provides a framework to address the varied learning styles of different children, along with the varied teaching styles of educators through an intuitive interface. The typical digital learning interfaces replicate the drawbacks of a conventional physical classroom in the digitized form such as lack of room for student exploration of concepts, inability to individualize learning etc. “Math for Everyone” is based on the premise that every teacher, however good, has a preferred teaching style and hence children with differing learning styles may miss out. Infact interestingly every teacher we tested this with found it to complement their repertoire as a teacher in some or the other way. It allows for existing digital content to be incorporated seamlessly where this becomes a front end for the entire Math curriculum. Hence we see it as having a huge potential for changing the entire way of looking at classroom teaching. Attached is a publication presented at the conference Designing for Children hosted by IDC, IIT Bombay.

1. By: Manuj Dhariwal (04020512)
Guide : Prof Pradeep Yammiyavar FDRS 12th Apr 2008

2. Field Study
All classrooms have three prominent components
1. The Student
2. The Teacher
3. and the content floating between them

3. In the schools I visited …
the teaching methods were …

4. Teacher led classes
Demonstrations
PPT, Animations, Videos
Experiments

5. Inside the classroom …
Alice in wonderland
Slow learner
Booky, the bookworm
Pick me! I know the answer
meet...

6. Teacher led classes
Role of teacher:
The all knowledgeable
Body language of students:
Ready to ‘receive’
Not interesting for
non-participants
Able to address only the
middle spectrum

7. Powerpoint, Animations, Videos
• Interesting
though
• Easy to drift off
• Students not forced to
think
• Listening and taking
notes is difficult

8. Demonstrations
More interesting than before

9. ..but more like a museum or a fancy exhibition
Ancient Greek Vases!
Aladdin's lamp!
The sword of Tipu Sultan!
Beautiful!
Child feels at a loss at not being able to play with anything

10. Food for thought
So, where is the space for child’s own
experiences, musings, questions … ?
How will he personalize and internalize
all the knowledge?

11. Summary of my experience
Teacher led
Demos,
Activities
PPT,
Animations
• Inattention
• Observation is
limited, deceptive
• Lively during the class
• No space for child’s
own musings
• Interesting
• Passive learning

12. Video

13. Teachers are already using something to teach so how do they
incorporate my application in their teaching?
If this doesn't happen then the response is “Hmm .. it’s
a good idea” ….
……but just like so many other ideas it
never gets implemented
So I studied different teaching methods to see how it will fit.
How an idea fits in the overall teaching-learning process is equally (if not more)
important than the idea itself - just like a good idea for a product is not enough to
sell the product.

14. Teaching any Topic can be divided into 3 parts
1.Intro/History (Motivation for the
students to learn the topic) is mostly
ignored
Introduction
Concept
Teaching
Practice
Problems
2.Concept taught in one class through
any one of the methods depending on
the teacher (like paper cut outs,
history, writing the symbolic formula
for Pythagoras theorem)
the amount of time and importance
given is in ascending order :
3. most of the teaching time and
focus (espl Math) is on practice,
doing lots of problems from the book

15. This order should probably be in the reversed order
Practice
Problems
Concept
Teaching
Introduction 2.If the concept is ingrained in him
then its application to the problems is
more meaningful and better
1. If the child is motivated then
his retention and efficiency
increase mani-folds throughout
the topic
3. Thus it was decided to provide
Intro & Concept teaching as main
parts of the application

16. Motivation Application
Application
Extensions
CRIB
Math For Everyone

17. What is Concept Reinforcement Idea
Board (CRIB)?
CRIB is a tool to represent a
concept in different ways by
engaging multiple modalities, to
reinforce the idea catering to the
varied learning styles.
Real
Thing
CRIB
Symbol

18. What are the different components?
The different components tie the recommended Math deliverables with
effective learning theories such as Multiple Intelligence.
•Real thing : Hands-on activity
showing the concept.
•Story : Word problem on real
world situation
•Words : Spoken mathematical
statements and terms
•Virtual : Interactive application,
game, animation.
•Diagram, Number, Symbol, Demo
are self-evident

19. Subject Area
Topics
Concepts
Pre-K – 2 3 — 5 6 — 8 9 — 12
Number &
Operations
Algebra
Geometry
Measure
HOME TOPICS
Idea Board
Numbers (3-5)
Fractions
Ratio proportion
Percentages
Patterns
(V) CRIB in CLASSROOM INTRODUCTION

20. Real Thing
CRIB
Symbol
(a - b)2 = a2 + b2 - 2ab
Choose a field to view it.
Subject Area
Topics
Concepts
Idea Board
See how the study of ratios can help you Make
a delicious Shake!

21. HOME <BACK
Expansion of (a-b)2
Real Thing
CRIB
Symbol
Story Mode
Story
A florist grows flowers in a square
plot of sides 200m.
One night Mrs. Basu her
jealous neighbor cuts
down all her flowers at
the borders, reducing the
side by 50m.
Suggested Flow Next >

22. HOME <BACK
Expansion of (a-b)2
Real Thing
CRIB
Symbol
Story Mode
Story
What is the area of plot
now?
200m
50m
Can you think of your own story
for this concept?
Suggested Flow < Prev

23. HOME <BACK
(a - b)2 = a2 + b2 - 2ab
Real Thing
CRIB
Symbol
Story Mode
Real Thing
Lets see what could (a-b)2 represent in
reality and what would it mean for (a-b)2
to be equal to (a2 – 2ab + b2).
A
With a, b as lengths (a=6”, b=4”), cut out the
following shapes in one color (denoting +).
a2 represents a square (A) with sides a
b2 represents a square (B) with sides b
(a-b)2 is a square (C) with sides (a-b)
Cut the following shapes (denoting -) in
another color.
a*b are rectangles (X,Y) with sides a, b
Suggested Flow Next >
B
C
X Y

24. HOME <BACK
Expansion of (a-b)2
Real Thing
Story Mode
Real Thing
CRIB
Symbol
A
X
Y
C B
B
(a-b)2 = (a2 – 2ab + b2)
Step 1
A
X
A
Put C on one side and A, B, X, Y on other.
Now you have to put one color on top of
another (can’t put same colors on each other)
such that both sides look the same.
Try it yourself.
Suggested Flow < Prev Next >

25. HOME <BACK
Expansion of (a-b)2
Real Thing
Story Mode
Real Thing
CRIB
Symbol
Step 2
X B
A
Put X on A.
Put B on X.
Try to do the last step yourself.
X
A
Step 3
Suggested Flow < Prev Next >

26. HOME <BACK
Expansion of (a-b)2
Real Thing
Story Mode
Real Thing
CRIB
Symbol
Step 4
Step 5
Put Y on A.
Verify both are the same by putting C on A.
Using the same pieces and rules,
find out if a2 + b2 = (a-b) 2 + ab + ab.
Suggested Flow < Prev
A
X
Y
C
A

27. HOME <BACK
Expansion of (a-b)2
Real Thing
CRIB
Symbol
Story Mode
Suggested Flow
Number
Put in the given values of a and b to confirm
(a - b)2 equals (a2 + b2 – 2ab).
a=6, b=4 a=5, b=-3
(a-b)2 = (6 - 4)2
=(2)2
= 4
(a-b)2 = (5 - (-3))2
= (8)2
= 64
(a2 + b2 - 2ab)
= (62 + 42 – 2*6*4)
= (36 + 16 – 48)
= 4
(a2 + b2 - 2ab)
= (52 + (-3)2 – 2*5*(-3))
= (25 + 9 – (-30))
= 64
Find (a-b)2 for a=4, b=6 and a=-3, b=5.
Compare these to above examples.

28. HOME <BACK
Expansion of (a-b)2
Real Thing
CRIB
Symbol
Story Mode
Suggested Flow
Symbol
Two equivalent ways to represent (a-b)2
symbolically are given below.
(a-b)2
(a2 – 2ab + b2)
Can you think of another way to represent
(a-b)2 using symbols?

29. HOME <BACK
Expansion of (a-b)2
Real Thing
CRIB
Symbol
Story Mode
Suggested Flow
Diagram
A labeled diagram of the concept
is shown below.
(a – b)
(a – b) b
b
A
B
C D
What does the shaded area signify? [Refer
to the Real Thing]

30. HOME <BACK
Expansion of (a-b)2
CRIB
Select a Mode
Add Real Thing
Suggested Flow
Add Picture
Add Instructions
Add Picture
Add Instructions
Add Picture
Add Instructions
Add Picture
Add Instructions
Create
Real Thing

31. How to use this in the classroom?
The integration of this package with the current teaching practices is highly
subjective but following are a few suggestive ideas:
1.For introducing and developing concepts
(not for practice since it is time consuming)
2.Demo CRIB for a concept and then ask the
students to make the CRIB on their own, or
do another problem in similar manner.
3.On-going and continual assessment
tool to check student understanding
4.Pre-assessment tool to identify learning
preferences of each child

32. Why to use CRIB
Changes in the role of teacher
Saves time on writing and drawing
Overcome possible handicap of drawings
skills in terms of aesthetics, accuracy and
perspective
Teacher can now focus on essentials – from
‘How to teach’ to ‘What to teach’
Time to observe students and give
individualized feedback

33. Changes in the role of students
Active learning
Works independently
Able to relate to the content better since
multi-modal
Gains confidence since content includes his
strengths
Rich peer-to-peer interaction with ‘weak’
helping ‘bright’ ones

34. Why to use an e-Package
a Good idea vs a Usable idea
CRIB is a good idea like many other good ideas
Not clear how to integrate it with the current teaching
e-Package organizes material as subject areas, topic starters
Blackboard and e-Package
Medium allows animations, videos, virtual manipulatives
Word problems on Blackboard : Story problems in e-Package
Problems of illegible handwriting, small letters, inaccuracy or
lack of perspective in diagrams can be solved

35. User Testing
Dr Shailesh Shirali
Renowned Mathematician and Educator
National Award for Teachers 2003
Chairman of the Problem Committee, IMO 1996
Currently running Teacher Training at Rishi Valley School
Suggested to add structure to CRIB
Fields of CRIB
Remove Demo from fields
Add Words, Activities (Math games, field activities) to fields

36. Motivation Extensions
Application
Extensions

37. Extensions
Science CRIBs
Framework applies to other subjects especially Science
Example: CRIB for levers
Thematic Learning
Tap into student’s extra-curricular interests such as Sports
Interest based CRIBs for the same concept

38. Thank You