Teachers views on Vedic Mathematics and its overall influence on the Students Community

V IEWS ABOUT V EDIC M ATHEMATICS USING F UZZY M ODELS

4.2 Teachers views on Vedic Mathematics and its overall influence on the Students Community

We held discussion with nearly 200 teachers from urban schools, rural schools and posh city schools. Also teachers from corporation schools and government schools were interviewed.

We could not ask them to fill a questionnaire or ask them to give any write up. Some of them had not even seen the Vedic Mathematics book.

Only very few of them had seen it and some had taught it to students. So the crowd which we had to get views from was an heterogeneous one and they belonged to different types of schools some of which promoted Vedic Mathematics and some of which strongly opposed Vedic Mathematics. Thus we got their views through discussions and noted the vital points which will be used to draw conclusions about the course on Vedic Mathematics to the students.

The majority of them spoke about these 8 concepts in one way or other in their discussion.

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D1 - The mathematical content of Vedic Mathematics.

D2 - Vedic value of Vedic Mathematics.

D3 - Religious values of Vedic Mathematics.

D₄ - Use of Vedic Mathematics in higher learning.

D₅ - Why is it called Vedic Mathematics?

D₆ - Vedic Mathematics is a waste for school children.

D₇ - Vedic Mathematics is used to globalize Hindutva.

D₈ - Vedic Mathematics will induce caste and discrimination among children and teachers.

These eight attributes are given by majority of the teachers which is taken as the nodes or concepts related with the domain space.

The following were given by majority of the teachers about the standard and use of Vedic Mathematics.

R₁ - Vedic Mathematics is very elementary

R₂ - Vedic Mathematics is primary school level mathematics

R₃ - Vedic Mathematics is secondary school level mathematics

R4 - Vedic Mathematics is high school level mathematics

R5 - Nil (No use in Vedic Mathematics education) R6 - Hindutva imposition through Vedic Mathematics R7 - Imposition of Brahminism and caste systems

R8 - Training young minds in religion without their knowledge

R9 - Has some Vedic value R10- Has no mathematical value

R11 - It has neither Vedic value nor Mathematical value R12 - It has Hindutva / religious fundamentalist agenda R13 - Absolutely no educational value only religious

value

We make use of the FRM model to analyze this problem.

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These 13 nodes / attributes are taken as the nodes of the range space. All these nodes in the domain and range space are self-explanatory so we have not described them. The following directed graph was given by the first expert.

R₂

R₄

R10

R₁₁

R12

FIGURE: 4.2.1

R13

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The expert is a teacher working in a school run by pro-religious revivalist Hindutva trust. We use the directed graph of the Fuzzy Relational Maps and obtain the 8 × 13 connection matrix.

The attributes related with the domain space are along the rows of the matrix and that of the range space attributes are taken along the column. Let us denote the 8 × 13 matrix by M1.

Now we study the effect of the state vector X from the domain space in which, only the node D4 alone is in the ON state and all

‘→’ denotes after updating and thresholding the resultant vector got from X₁M₁. Now

Thus the hidden pattern of the dynamical system given by vector X = (0 0 0 1 0 0 0 0) is a binary pair which is a fixed binary pair of the dynamical system M1.

When only the node (D₄) i.e. use of Vedic Mathematics in higher learning is on we see all the nodes in the domain space come to ON state.

In the range space all nodes except the nodes Vedic Mathematics is secondary school education level node R₃, Vedic Mathematics is high school level node R₄ and R₁₁, it has neither Vedic value nor mathematical value alone remain in the

OFF state. The binary pair is given by {(1 1 1 1 1 1 1 1), (1 1 0 0 1 1 1 1 1 1 0 1 1)}.

Suppose we consider a state vector Y = (0 0 0 0 0 0 1 0 0 0 0 0 0) where only the node R₇is in the ON state and all other nodes are in the OFF state; Y is taken from the range space. We study the effect of Y on the dynamical system M₁.

YM₁^T = (0 0 1 0 0 0 1 1) = X (say) XM₁ → (0 0 0 0 0 1 1 1 1 0 0 1 1) = Y₁ (say)

Y₁M₁^T → (0 1 1 1 1 1 1 1) = X₁ (say) X1M1 → (0 1 0 0 1 1 1 1 1 1 0 1 1) = Y2 (say) Y2M1T = (1 1 1 1 1 1 1 1) = X2 (say) X2M1 → (1 1 0 0 1 1 1 1 1 1 0 1 1) = Y3 (say) Y3M1T = (1 1 1 1 1 1 1 1) = X3 (= X2).

Thus resultant of the state vector Y = (0 0 0 0 0 0 1 0 0 0 0 0 0) is the binary pair which is a fixed point given by {(1 1 0 0 1 1 1 1 1 1 0 1 1), (1 1 1 1 1 1 1 1)} when only the node R7 in the range space is in the ON state and all other nodes were in the

OFF state.

Thus we can work with the ON state of any number of nodes from the range space or domain space and find the resultant binary pair and comment upon it (interpret the resultant vector).

Next we take the 2^nd expert as a retired teacher who is even now active and busy by taking coaching classes for 10^th, 11^th and 12^th standard students. He says in his long span of teaching for over 5 decades he has used several arithmetical means which are shortcuts to multiplication, addition and division. He says that if he too had ventured he could have written a book like

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Vedic Mathematics of course baring the sutras. We now give the directed graph given by him.

R₂

R10

R11

R12

FIGURE: 4.2.2

R13

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Now using the directed graph given by him we have obtained the fuzzy relational matrix M2.

M₂ =

Thus the resultant is a fixed point given by the binary pair {(1 1 1 1 0 1 0 1), (1 0 0 0 1 1 1 1 1 1 0 1 1)}.

Now we consider the same state vector of the range space given by the first expert.

Let Y1 = (0 0 0 0 0 0 1 0 0 0 0 0 0).

Now we study the effect of Y on the dynamical system M2.

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108 Y1M2T = (1 0 0 0 0 0 0 1)

= X1 (say)

X1M2 → (1 0 0 0 1 1 1 1 0 1 0 1 0)

= Y1 (say)

Y2M2T = (1 0 1 1 1 1 1 1)

= X2 (say)

X2M2 → (1 0 0 0 1 1 1 1 1 1 0 1 1)

= Y2 (say)

Y2M2T = (1 1 1 1 1 1 1 1)

= X3 (=X2)

X₃M₂ → (1 0 0 0 1 1 1 1 1 1 0 1 1)

= Y3 (say).

Thus resultant is a fixed binary pair given by {(1 0 0 0 1 1 1 1 1 1 0 1 1), (1 1 1 1 1 1 1 1)}. From the teacher’s view-point we see that they are least bothered about the primary level or secondary level or high school level in Vedic Mathematics or whether it has a Vedic value or any mathematical value because what they are interested is whether Vedic Mathematics has no mathematical value or even any true Vedic value, that is why they remain zero at all stages. What is evident is that the introduction of Vedic Mathematics has ulterior motives and it only has a Hindutva background that is why in the dynamical system itself all these terms R2, R3, R4 and R11 are zero.

Now we have used several other experts to derive the conclusions using the C program given in [143].

The set of experts were given an option to work with NRM described in section 3.5 of this book. Most of them were reluctant to work with it. Only seven of them gave the NRM for the same sets of attributes. All the seven of them gave the relation between the node D₂ and R₁₁ as I. Some gave D₂ with R₁₀ as I and some other gave D₂ with R₉ as I. All these NRMs were constructed and using these NRM connection neutrosophic matrices hidden patterns of the suggested ON state of nodes as given by the experts were found and included in the chapter 5.