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MadMaths : The origin and the feel-of-need

MadMaths has been conceptualized by EduClub after dealing with hundreds of childrensince the past several years. EduClub felt that a lot many children suffer from lack of

fundamental strength in maths, thinking and logic, which if not taken care at the right

stage and age, leads to disastrous career setbacks. Hence we as an organization felt the

need of a concept-strengthening program to help young learners build a solid mathfoundation. EduClub then took the help of ASSET test to get a clear picture of the all

India level of math performance by students across the country. It was then; that EduClub

got a clear picture and more concrete results, showing that math is a big struggle area for

children all across the country. Hence the roots of MadMaths lie in the results of ASSET.ASSET is an objective test developed by E.I. (Educational Initiatives). EI is an

educational organization based in Ahmedabad and managed by 3 IIM-Ahmedabadgraduates. ASSET test (learn more on www.ei-india.com) checks for the understanding

levels of a learner in maths. This is currently available for students till grade 9. ASSET is

taken by more than 2 lac students across the country, every year. The results of ASSET

clearly show a clear pattern of how our students lack in basic fundamental strength,inspite of being high-scorers in their respective classrooms/schools. MadMaths was

conceptualized as a remedy to the problems diagnosed by ASSET. So if ASSET is the

diagnosis, then MadMaths is the preventive and/or corrective measures.

MadMaths : The Purpose

MadMaths is a unique endeavor of EduClub to help child visualize the why and howof math. Please take note of each of the highlighted words. A brief explanation of the

same is as below:

What is visualizing maths?

One of the basic problems of the way math is currently taught in our system is that there

is very little or none, correlation between theory and practical life. For e.g.: A studentmight know how to solve a problem presented in his textbook or practice book. But when

the same student faces a WORLDY problem of the similar nature, he/she fumbles. This

happens because the student is not able to visualize math in real life. He/she is unable totake the math out of books and put it to real-life scenarios. This made us think that a math

lab is must for students to get a real 3D feel for maths. So in MadMaths when a child is

made to solve problems hands-on, there is an immediate connection which happensbetween theory and practice. The MadMaths lab helps the student Visualize math rather

than just deal with math in black and white. This visualization is through a lot of math

manipulatives and/or games, trivias etc. which add color to otherwise boring math.

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The Whys and Hows :

Good learning can never happen without a lot of whys and hows involved.Whys and hows are an integral part of any learning process. In any typical classroom, all

across the globe : students can be divided into 2 categories:

1) who regularly ask questions in classrooms, get into arguments and debate with

teachers and probably sit on the front benches.

2) second category is of those, who are silent learners, hardly speak up to teachers orask questions in a class.

Now it can be easily assumed and argued that students of category one, those who ask

questions are less knowledgeable than those who never ask, because they are the oneswith lot of doubts, confusions and probably lack of confidence. We can easily argue that

the silent ones are probably more confident, know their subject well hence never feel the

need to ask any questions to their teachers.

But any experienced teacher will refute this explanation and tell you that it is the ones

who ask more, that score more and know more as well. This is the power of whys andhows. A student with lots of whys and hows in his mind, will always be a better learner

than another one who simply takes his teachers word without counter-questioning. In a

typical education system, there is little platform for teachers to encourage the students to

ask questions. In fact, most of the teachers, teach processes or theories to students in avery mechanical fashion, and then its upto the student to mug it up somehow and

reproduce it in the exams. Education has become a mark-oriented and result-obsessed

phenomenon, rather than a knowledge-oriented activity. And knowledge has deepconnections with asking questions.the whys and hows.

MadMaths runs in a very different fashion. Rule one is that hardly anything is spoon-fedto students. We make it a point to push the student as much as possible to get the student

to figure out the solution to a problem. This pushing results in germination of lots of

hows and whys in the students brain. The student gradually learns how to participate,how to ask, how to think and how to solve. And when the student sees the solution to a

problem as an outcome to his struggleits eureka in your classroom.

MadMaths : The Features

MadMaths is a programme to help children identify and appreciate the importance ofmath as a tool in real life problem solving. MadMaths helps children develop a

thinking mind.

The aim of this programme is to encourage the young brains to visualize the world of

math and hence providing them with the opportunities to use it logically in real world.

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The curriculum designed helps in developing the conceptual understanding in all theareas of math right from number sense to geometry, algebra and advanced problem

solving skills.

MadMaths : Styles of teaching :

Mad Maths runs on 2 theories: myPace and iQuery.

The style myPace has been adapted from the very famous Japanese style of teaching:

Kumon, where the children learn on their own pace, and taking one step at a time,

complete the programme based on the pace at which they can think. (Detailed discussionwill be covered later on.)

The style iQuery is a very new concept of Inquiry based teaching, which is radically

different from how learning and teaching happen in typical classroom. (Detaileddiscussion will be covered later on).

MadMaths: Goal

MadMaths aims that after this program a child will develop reasoning minds towardsmath as a whole. Students will be facilitated to develop a mathematical understanding

in wide range of topics right from fundamentals like number sense and place value

system to probability/ decimals and problem solving. In addition, children will be assisted

with their understanding gaps in interpreting the math language and hence develop asense of problem solving. Furthermore the exciting and the challenging part of the

programme will be its brain benders which are designed to provoke the childsenthusiasm and cultivate the interest towards the subject.

MadMaths : Content

The topics covered are numerous ranging from premath skills and number sense in the

beginners level to decimals, probability and data interpretation in the advanced level.

Each level broadly covers topics from all the key areas

Numbers sense e.g. whole numbers, fractional number, decimals, etc.

Number operations e.g. four basic operations, algebraic problem solving, number

properties, etc.Geometry concept of point, line to properties of 2D and 3D shapes (area, perimeter,

volume, etc.)

Data analysis statistical representation and interpretation, probability

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MAD MATH KNITTING THE FIVE STRANDS OF MATH

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Pre-Contact T heories

The following theories/topics will be covered before the contact-base training sessions take

place. The teaching staff is required to go through this reading material before attendingthe contact-training sessions at EduClub.

Understanding our role as educators

Brain based learning

Constructivism

Styles of teaching : iQuery

Styles of teaching : myPace

Multiple Intelligences

A Mind at a Time

Differentiated Instruction

Problem Based Learning

Hands-On Learning

Mentoring

Intra-Interpersonal evaluation

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Understanding Our Role As Educators The Study Guide

Vision of Education

Education is more than reaching certain standards of learning; education is developing a desire to

learn, knowing how to learn, and implementing teaching practices based on how the brain

actually functions.

The Child - Recipient of Education

Each of us is born into the world as someone; we spend the rest of our lives trying to find out who

we are and what is the purpose of our existence. Knowledge is the key to our self-discovery,

leading us to our goals and final fulfillment of life. EduClub deals with knowledge impartment

focusing on young learners. Each child has a unique pace and style of constructing knowledge

where receiving lots of information may not add much to it. If children are to learn to their

fullest and if they are to benefit themselves and society, we must honor their own individual

learning systems. As Hamer and Copeland (1998) advise in Living with Our Genes: Why TheyMatter More Than You Think:

Educators as Facilitators and not teachers

Giving children love and knowledge is as essential as giving them food, but at some point,

parents [and teachers] must understand that children are already on a path beyond anyone's

choosing. Hence we as educators (parents and teachers) need to understand our role as facilitators

in a childs journey to explore who he is and helping him discover the strategies to maximize his

potentials.

If we rethink the term teacheras that of model and mentor, collaborator, facilitator, coach, andguide, the descriptions would cast a new light on how teachers view themselves and how they

teach students.

The process of teaching would focus on forming habits for lifelong learning, rather than just

acquiring discrete fragments of information.

A rose by any other name is still a rose, but rethinking the concept of teaching dramatically alters

what happens in the classroom and, consequently, what happens outside of it.

Outcomes of Education

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EduClub believes that every learning is a form of food/input to the character, mind and

brain of the learner. And every input should lead to a output. So what should be the outcomes of a

good education system ?

EduClub lists that a good education should cultivate the following in any learner :

Passion for learning.

Vision for seeing what is possible.

Intention for developing knowledge and skills.

Reflection for self-monitoring and staying the course

and hence facilitate children in their actions for

transforming dreams into realities.

Effective Classroom Practices An Essence of Some Theories of Education

Researchers theorize that the human brain is constantly searching for meaning and seeking

patterns and connections. Authentic learning situations increase the brain's ability to makeconnections and retain new information.

Teaching strategies that enhance brain-based learning include manipulatives, active learning, field

trips, guest speakers, and real-life projects that allow students to use many learning styles and

multiple intelligences. A relaxed, nonthreatening environment that removes students' fear of

failure is considered best for brain-based learning.

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Brain Based Learning

A major role of educators is to know enough about brain research to help students develop intothe best who they can possibly be. As educators, we can rely on the five major neurobiologicallearning systems to construct a well-organized educational framework that makes lesson planning

exhilarating and implementing our plans exciting.

Learning Systems of the Brain

Brain possesses five interconnected learning systems associated with emotions, relationships,

cognition, the senses, and assessment of self in one's environment. For each learning system, the

teacher/educator will have to assume different roles. The learning systems and educator-roles for

each emotion are as listed below:

1) Emotions: In brief, the emotional system determines personal passions, dreams, anddesires. Children love and hate their teachers based on this system which creates

emotions like frustration, hatred, threat, curiosity, etc. and hence develop passion or fear

towards the taskin question.

Desired Educator Role: Mentor

2) Relationships: Social learning can be either automatic or intentional. For instance,toddlers learn a language or develop bias and beliefs from family members automatically

or without conscious effort. When children work together to solve a problem, social

learning becomes intentional and collaborative.

Desired Educator Role: Collaborator

3) Cognition: The cognitive system interprets, stores, and retrieves information; focuses oninformation; and provides factual inputs for all other systems. This system functions best

when a person feels safe and secure rather than threatened. But the input and output of

this system is clearly connected to other learning systems.

For example, even though you may go to the library and research various car models and

decide which one to purchase based on the model's maintenance record and gas mileage,

a car salesman may say something to convince you differently by tapping into your

emotional or social systems. While showing you a car of lower standards, for example, he

may say, I can see you are a lot like me; you are thoughtful and deliberate in yourpurchases. That makes my job of selling you this car much easier.

The implicit desired response is, This salesman really respects me. He wouldn't sell me

a car with lower standards than I desire. Thus, although your cognitive intent is to

purchase based only on researched qualities, the salesman's expertise at triggering your

emotional and social systems may result in a purchase you later regret.

Desired Educator: Collaborator

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4) The Senses :The cognitive system gathers information through the senses, interprets it,and distributes it throughout the brain and body. The physical system is responsible for

transforming those interpretations into action.

Physical learning may take a long time to accomplish, such as when learning to ride a

bicycle, but once learned, you can jump on one and ride down the street after years away

from the trusty two-wheeler. In addition, physical learning can be reactive like the other

systems. For example, children who grow up with lots of hugs tend to become automatic

huggers. Those who grow up with physical abuse tend to become abusive.

Desired Educator: Coach

5) The Self: Thislearning weighs past, present, and probable thoughts and behaviors, andthen predicts future outcomes by asking self-directed questions. This monitoring system

plays a key role in determining how people function in society and how they construct

their lives.

Learning systems are active. They are constantly adjusting and adapting. And onceadjusted, the new learning is irreversible. There is no way to go back and unlearn,

something. The learning may be forgotten, but it cannot be unlearned. Try unlearning

how to tie a shoe.

Desired Educator: Guide

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Prompts for reflecting and writing on the Text Read

The questions listed below are meant to prompt the teachers of MadMaths to think and

come up with their queries, strategies and explanations. All teachers undertaking

MadMaths training are supposed to answer these questions.

These prompts can be answered in pairs or individually.

1) You are a grade 1 teacher. After reading this article how would you introduce

a concept of addition to the children of your class. Please write a lesson planand reasons for choosing the strategy.

2) Write 10 things about "The expected role of an educator as a facilitator."

3) What are 3 new strategies you would like to implement in your class to

cultivate passion of learning among children?

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Constructivism

Education is centered on themes and concepts and the connections between them, rather

than isolated information. Mathematics educators, for example, are concerned with suchcases as that of a 5th grade student. Her teacher asked her to explain the process in front

of the class:

Teacher: Who can come to the board and show us

how to solve the following problem?

[Write on the board.]

1/6 + 1/3 + 1/2 =

Student:I want...

Teacher:Please come and show us. But also explain as you proceed.

Student:First I see that 6 is the least common denominator, so I write 6.

... =/6

Now, it does not change the numerator for the first fraction, it changes the

second by 2 and the third by 3.

1 + 2 + 3 =/6

Now, I add the numerators and the answer is 6.

... = 6/6

Now, 6/6 is exactly 1.

... = 1

Teacher: Very good. Now, look at this drawing and

explain what you see. [Draws]

Student:It's a pie with three pieces.

Teacher: Tell us about the pieces.

Student: Three one-thirds.

Teachers: What is the difference among the pieces?

Student: This is the largest third, and this is the smallest one-third.

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Sounds familiar? Its clear from the above example that the child is easily able to solve

the fraction-addition sum, but cannot define the 3 pie-pieces clearly. He calls them as 3

one-thirds, which is far from truth. A student with clear understanding and strongconcepts would have said that one pie-piece is 1/2, one 1/3 and one 1/6th .

This forces us to think and analyze that why students often understand mathematics in a

very rudimentary and prototypical way. Why even rich and exciting hands-on types of

active learning do not always result in real learning of new concepts?

Constructivism is an approach to solve this problem to a large extent. Constructivism isteaching based on research about how people learn. Many researchers say that each

individual constructs knowledge rather than receiving it from others.

Constructive teaching is based on the belief that students learn best when they gain

knowledge through exploration and active learning. Hands-on materials are deemed to be

more effective instead of textbooks in constructivism. In this approach students areencouraged to think and explain their reasoning instead of memorizing and reciting facts.

Although deep understanding, not imitative behavior, is the goal of constructivism, the

downside is that it is very easy to teach via imitation, but capturing other personsunderstanding is quite difficult. However appropriate intervention can overcome these

possible problems.

Teacher intervention is an essential component of all instructional strategies. But one ofthe major problems found while using constructivism was that children do not sometimes

realize and appreciate the hands-on method. This is one of the effective learning

strategies to construct understanding at their own pace and in their own way.

Hence it becomes important for the teacher to help children understand the nature ofmathematics. Mathematics need to be communicated to children as a set of tools which

have been developed by human beings and have a logical mystery behind them. This

logical mystery, if understood helps us apply these mathematical tools right from simple

addition to complex algebra, while solving a problem in a real life situation.

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How a brain looks at mathematics

Constructivism clearly says that each brain is unique and makes the best interpretation itcan, according to its previous experiences and the limited information available. Once the

interpretation is made and approved to be logically correct by the teacher, this

interpretation made by brain on its own is stored inside it as a structural change in the

learning (cognitive refer brain based learning) part of the brain.

This is the permanent change which could be forgotten but not erased. This is what a

child should achieve with the help of appropriate teachers interventions.

Role of a teacher in the constructivist classroom:

In a constructivist classroom, the teacher searches for students' understandings of

concepts, and then creates opportunities for students to refine or revise theseunderstandings by posing contradictions, presenting new information, asking questions,

encouraging research, and/or engaging students in inquiries designed to challenge current

concepts.

Desired Qualities of a teacher for the constructivist classrooms:

Teachers value students' points of view. Teachers who consistently present the same

material to all students simultaneously may not value individual thinking and point of

views. The teacher may even view them as interfering with the pace and direction of thelesson. In constructivist classrooms, however, students' point of views in the form of the

answers, they give are teachers' clues for deciding the pace of learning.

Classroom activities challenge students' suppositions. All students, irrespective of age,

enter their classrooms with life experiences that have led them to presume certain truthsabout how their worlds work. Meaningful classroom experiences either support or

contradict students' understandings and hence help children construct their knowledge.

Teachers pose problems of emerging relevance. Constructivist teachers structure

classroom experiences that foster the creation of personal meaning.

Teachers build lessons around primary concepts and "big" ideas. Students memorizethe material needed to pass tests. But many students, even those with passing scores, are

unable to apply the small concepts in other contexts or demonstrate understandings.

Constructivist teachers often offer academic problems that challenge students to grapple

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first with the big ideas and to find the important topics which need to be further analyzed

and understood.

Teachers assess student learning in the context of daily teaching. Constructivist

teachers don't view assessment of student learning as separate and distinct from the

classroom's normal activities but, rather, embed assessment directly into these recurrent

activities.

Prompts for reflecting and applying the text read

How is constructivism mode of teaching and learning different from theconventional method of learning and teaching ?

What are the initial steps as an educator, you would take in order to practice

constructivism in its true sense, in your daily class?

If you are a grade 1 teacher and you want to introduce the concept of

place value to your students, what would be your lesson plan like? You have

to ensure you practice the theory you have read.

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