# The Pebble Maths Blog!

## Holiday Workshop.

by Vera Stevens on 11/30/15

## Children's Winter Holiday Workshop 2015

by Vera Stevens on 07/14/15

We have had a very wonderful children's workshop in the second week of the school holidays. It was an ambitious undertaking as the programme included 2 hours of arithmetic in the mornings and 2 hours of fractions and geometry in the sand at the beach every afternoon. We had 7 class participants and myself. Two girls who have completed the Pebble Maths work studied 'Stairway to Heaven Step 1' with Amber and everyone else was with me.

Using the beach for the exploration of dimensions in geometry was particularly successful. For all the children the fraction work now is logical and understandable.

Thank you everyone.

## A Pathway for People with Perceived learning difficulties to embrace and succeed with studies in Vedic Mathematics.

by Vera Stevens on 05/23/15

__Introduction__

Until now people who do
not have a natural aptitude with the four operations in arithmetic have not had
an opportunity to enter the world of Vedic Mathematics. These people include
Dyslexics, certain people on the autism spectrum, children who have missed
schooling in the early years due to illness, family trauma etc., and those who
are primarily visual, kinaesthetic, tactile or auditory learners and for whom
the standard school approach in teaching arithmetic is a failure.

__History
behind the development of “Pebble Maths”__

In
1993 I began looking at the way Mathematics was being taught in high school as compared to my experience in the ‘50’s and ‘60’s, with a view to
helping children to be more successful in their studies. To my horror nothing
much seemed to have changed. I worked within the confines of the school system until
I was entrusted with the task of teaching a 12 year old boy who was on the
verge of being expelled from school for behavioural problems and who had
absolutely no ability with arithmetic. My challenge was to not only “teach him”
but to inspire him with the joy of mathematics and its potential as a creative
endeavour. I lived by the beach so we collected pebbles, painted numbers on
them and played with arrangements, initially in groups of 10. He enjoyed this
which was a most important factor in changing his attitude towards mathematics,
but addition still evaded his understanding. Counting tools were not enough for
him to grasp the essence of addition.

I feel that it was divine guidance that
brought me to explore the distinct nature of odd and even numbers as different
entities with different properties. I had discovered the key which enables
every child to understand number and be able to compute successfully.

I continued to teach Tom
for a term by which time he was able to return to class.

Tom now has a degree in
Business studies.

Over the course of two
and a half years during which time I had the opportunity to teach with complete
freedom in a privately run primary school, the children and I discovered all of
the patterning which later became the foundation of “Pebble Maths”. At the same time as working with Pebble Maths
I was also studying Vedic Mathematics. The first book which came into my hands
was Joseph Howse – “Mathematics without tears” it took me a full two weeks of
study to grasp very basic Vertically and
Crosswise multiplication and division techniques, yet I was totally fascinated
and wanted to learn more. I found the Vedic maths website and bought one of
James Glover’s books – Vedic Mathematics for Schools: Book 2, which I
recommended to those of my students who had completed the foundational work
which I later enumerated in my book “Pebble Maths.”

My next purchase was “The Cosmic Computer”
by Kenneth Williams and Mark Gaskell.

“Pebble Maths” continued
to evolve with each student and with each difficulty with which I was faced. I
knew very little about Autism and nothing about Dyslexia. I worked as a
volunteer in a school for Autistic children for 6 months. These children had
varying ability with mathematics. They all responded positively to “Pebble
Maths”. Since that time I have been teaching children on the autism spectrum
who all find Pebble Maths to be enjoyable and understandable.

In 2011 Kenneth Williams
encouraged me to write a teachers’ manual so that more people could have access
to this knowledge. I published my book in May 2012 and Pebble Maths is now taught
in Australia, New Zealand, Spain, Singapore, Africa, America and Great Britain
and possibly other countries as my book has been sold all over the world.

__Dyslexic
Students__

I had parents who informed me that their
children had a diagnosis of Dyslexia and were unable to understand the
teachings in literacy and numeracy as presented in school. In a very short
period of time all of these children became adept in mathematics and it
appeared that their literacy skills improved concurrently.

I was asked to run
workshops for the North Coast Dyslexia Association which were attended by
learning support teachers interested in finding a way to manage dyscalculia. These
teachers are experiencing extremely positive outcomes by teaching their
students Pebble Maths. They also report that progress in literacy improves as a
by-product.

When my students have
successfully achieved all aspects of the four operations (addition,
subtraction, multiplication and division) as well as fractions and decimals, I
teach them Vedic Mathematics.

The fact that the
techniques in Pebble Maths enable the students to calculate mentally, left to
right, use digit adding to facilitate understandings, always use and look for
patterning as a way to solve all calculations and work without limit- as
compared to school where multiplication is a matter of rote learning that has a
ceiling of 12 x 12, results in a seamless transition to the later Vedic work.

__What
Happens After Pebble Maths?__

Many of my students do
not stay beyond catching up with the level required by their school but some
wish to learn more. One of these students, Amber began with me in her first
year of high school with no understanding of addition. After four years she is
not only at the top of her year in school, but is a certified teacher of Vedic
Mathematics and is preparing to take an advanced course.

In 2014 Amber attended an
online course on “The Crowning Gem: One Vedic master-formula for powers roots
and polynomial equations” by Kenneth Williams.

Prior to this course
Amber had worked with me on the creation of my book ‘Stairway to Heaven’ which
is a preparation for my students to be able to reach their highest potential in
Vedic maths studies.

I quote Amber “I couldn’t
have understood the work in the Crowning Gem without having done the work in
the Stairway book.”

This student is an
example of someone for whom Vedic maths would have been completely out of reach
without the prior experience of Pebble Maths.

Amber will undertake the
highest level of maths offered at her school for her senior years. We are in
the process of ascertaining whether one line answers will be acceptable in the
final exam. If we are successful, even in part, Amber will be paving the way
for school students to see that there is a much simpler and more enjoyable way
to study and achieve in mathematics.

It is my assumption that
a student who is as well versed in Vedic Mathematics as Amber will be when she
sits her final exam, is in a position to show the examiners and her school
maths teachers that Vedic maths is indeed a far superior way to teach children.

I am sure that by
tutoring senior students Amber will be successful in promoting Vedic Maths.

I now have numerous
primary school students in the 9-12yr age group all of whom came to me with no
facility or confidence in mathematics. After varying lengths of time teaching
them Pebble Maths they are working in a group and embarking on Vedic maths
work. The first lesson that I gave them on bar numbers created so much
excitement that they asked for a workshop in the summer holidays specifically
on Vedic maths. Those of you who are school teachers will appreciate the
enormity of this request. Most school children want to forget about learning
during their holidays, however in my classroom the opposite is a reality.

I need to mention that
more than 50% of this group have a diagnosis of Dyslexia. In the past these
children would have had little or no chance of ever being able to compute
without a calculator.

__My
Hypothesis__

I observe my students
very closely and found it amazing that the Dyslexics are quicker in grasping
the concepts in Vedic maths then the children with no perceived learning
difficulties. This observation has now become a most important research topic
for me. My hypothesis is that all children, if educated within the principles
of Vedic mathematics from the very beginning can be not only successful with
Mathematics but foster their mental creativity which flows into all learning
areas in their life.

__Case
Studies__

__Loui.__

Loui was 8 years old when
his mother first brought him to me, the school had made him repeat kindergarten
and then repeat class one. By this stage he was suffering emotionally so badly
that his mother chose to home school him. He could not write numbers or letters
and he didn’t have the confidence to speak during our class. He was terrified.
I made a point of not writing numbers or presenting him with written numbers at
all. We worked only with the pebbles until he understood the creation of the
numbers and could see the patterning in adding and taking away 1s, 2s, 3s and 4s.
We proceeded to the number partners for 10 and because odds go with odds and
evens go with evens it was disarmingly simple for him to advance to higher
addition. Over the course of 9 months with 1 lesson per week with me and
practice with his mother between lessons, Loui has developed a remarkable
capacity to add, subtract, multiply and divide mentally. He now writes his
numbers perfectly and communicates with confidence. I began teaching him
multiplication above and below the base and was astounded that his
understanding of “how many places were needed in the answer” was a natural revelation,
he is now 9 years old and the youngest in my group. I began work with him on powers
and roots (refer my book Stairway to Heaven step 1).

I decided to introduce
bar number work to my group and had no pre-conceived notion of how it would be
received. There are 6 students in the class- 3 of whom are Dyslexic. Loui’s
brother who is 2 years older than him, and an excellent student with no
difficulties in any areas, ahead of his age group in his school work, is also
in the group. I began slowly showing with 7 pebbles on the table as I wanted
the children to see that 7 divided by 3 could be 2 remainder 1, could be 1 remainder
4, and could be 3 remainder. We spent maybe 15
minutes exploring in this way before I ventured into written bar number work. I
used Kenneth Williams “Vedic Mathematics Teachers Manual: Elementary Level”
lesson 9 page 85. There was no hesitation- no questions. Everybody understood.
When I showed the children how for example 49 times 7 could be a bit difficult
but 5 times 7 is very easy there were smiles of
understanding all round. I should mention that the children have all embraced
“All from 9 and the last from 10”.

I wrote numerous sums
on the board which the children had to copy and either convert or remove bar
numbers.

The amazing fact was
that Loui, my youngest Dyslexic Vedic student, was the first finished with 100%
accuracy.

__Maia__

Maia also began with me
from the beginning of 2014, she was 11 years old in her final year at the local
primary school. Maia, a twin, was diagnosed with Dyslexia at age 8 as her
mother was alarmed that Maia’s progress was so disparate from her twin. Even
with learning support at school Maia’s capacity with mathematics was
non-existent. Maia has a very positive attitude and wanted to
learn; she progressed well. The most
important change was that she could see that she could achieve in mathematics.
Maia looks forward to her lessons and practices conscientiously. It was she who
expressed so much excitement with the revelation of the bar numbers and how
they can make mathematics so easy to the point of asking for a one week
workshop specifically in Vedic Mathematics during the holidays. The other
children thought it was a wonderful idea, they all want to embrace further
studies in Vedic Maths.

I should also mention
that she will be a participant in my class for children who are about to enter
high-school to ensure that they have the primary numeracy curriculum well
digested. This class also runs for 4 consecutive mornings in the holidays,
which means that Maia of her own volition will spend 2 weeks of her leisure
time studying mathematics. It is fascinating for most people to see that my
students love mathematics and want to learn more and more. This is very
different from the reality in school where the study of Mathematics is for most
children boring, confronting and soul destroying.

__Daisy__

Daisy’s father was
referred to me by the father of one of my previous students. Daisy was 15 years
old at the time and in year 9 at high school. She was angry and frustrated
about all her school work. She shouted at me that she tries so hard and can
never achieve anything and her parents and teachers just keep saying that she
should do more work.

I told her that we could
make a big change and she calmed down. She sat down and picked up two pencils,
one in each hand to signify that she was ready. I asked her to write the number
58- she wrote 5 with the left hand and 8 with the right.

I asked her if she is
Dyslexic and she didn’t know what I meant.

We began with the pebbles
which is where I begin with all students irrespective of age.

Daisy progressed very
well and after 5 weeks (5 lessons) had her half yearly exam.

She scored 70%. It was
the first time that she had ever passed an exam, the first time that she was
not at the bottom of her year.

At about the same time
she sat the national numeracy and literacy exam which is compulsory in years 3,
5, 7 and 9 and scored the school average.

She was overjoyed.

When she began as my
student I asked her what she wanted to do when she leaves school. She told me that
she wanted to be an actress.

Six weeks later she
looked at me and said ‘I want to be an engineer. Can I be an engineer? Can I do
maths in years 11 and 12? (Senior school)
I told her that she can be an engineer if she wants to.

Daisy is now better able
to understand the new work that is presented in class. Her ability to
comprehend is improving steadily.

Her father has agreed to
have her tested for Dyslexia and Irlin’s Syndrome.

In 3 years’ time Daisy
will graduate from High School and it is my prediction that she will, if she
still wants to, achieve the marks to enable her to study engineering.

I shall teach her next
year and Amber will become her tutor for years 11 and 12.

__Further
Stepping Stones to Vedic Maths__

My contention that all
children, irrespective of perceived learning difficulties, can be good at and
enjoy mathematics is being supported every day by the successes in my
classroom, the classrooms around the world where Pebble maths is being taught
and in the homes of the children practicing the pebble work.

I made the decision to
write material for use after the completion of Pebble maths as a way for the
students to understand the unity of all aspects of high school mathematics;
arithmetic, algebra, geometry, trigonometry and calculus and for it to be a
mentally unchallenging pathway to
embrace the teachings of Vedic Maths.

In my experience and the
experiences of many of my school friends, maths was divided in several subjects
which seems to have very little, if any connection. This view of and attitude
to mathematics is not only untrue but makes the study of the subject laborious
and dependent on memory therefore rendering its success out of the reach of
many students who don’t have the capacity for memorising unrelated material.

Because the majority of
my students are visual learners the material must be presented in a way that is
harmonious for their thought processes.

The introduction of
Powers and roots as the entry point is very successful. The students create
very comprehensive charts making use of colour to differentiate the processes
including differences and differences of differences. The later work with
numbers to the third power requires one more difference to arrive at zero. This
revelation ties in with integration which I don’t introduce at this point. They work with the digit sums and differences
and discover patterns inherent in all the square numbers up to 100 squared.
They focus on number placement so that predicting the number of places in any
multiplication becomes a natural process, without thought. They learn various
Vedic multiply techniques including Duplex. The creation of the algebraic
formulae for the creation and differences of squares flows easily from the
arithmetic.

My method differs from
many in that I begin with the geometrical representation, followed by arithmetic
calculations and finally distil the algebraic formulae.

I find this way of
introducing algebra to be very successful.

When we have completed
the creation of the chart we study to numbers to discover how to recognize the
root of a perfect square. If allowed to explore and discuss, the students
discover much of the reversal processes themselves.

By creating the charts
which can take many hours of calculations and setting out, the students become
familiar with the numbers and patterns. In school no-one spends a term
calculating squares to a hundred, yet this process opens the mind , not only to
the maths in question but to further patterning which enables the future work
to be obvious. The learning becomes easier and easier, quicker and quicker.

It is my objective that
my students have the foundation to not only understand Vedic maths but to be
able to create for themselves.

__Conclusion__

My research with Dyslexia
and Vedic Maths is in its infancy at this stage. As I am becoming known as a
teacher who has success with overcoming Dyscalculia I am working with more and
more Dyslexic students. These children, at least those who stay with me beyond
managing their school work, will all be learning Vedic Maths.

My prediction is that
they will all become more and more confident, more and more capable and learn
with greater speed.

In the past it has been
all nigh impossible for people with Dyscalculia to overcome their incapacity
with number. These people can now not only manage the basics but can enter the
world of Vedic Mathematics.

People like my students
will have every avenue of study open to them. They will be able to study
disciplines such as engineering which would not have been a consideration prior
to their Vedic studies.

It seems that teachers
must eventually notice that children whom they have been teaching
unsuccessfully are now not only paying attention and learning but also
achieving high marks in their maths exams. Whether or not the school teachers
want to change their teaching methods is not something that I have any
influence over. However some of my students are saying that they want to help
other Dyslexics to achieve in the same way that they are and have the ambition
to become primary teachers.

It is an astounding
concept that the people whom society has thought of as being incapable with
mathematics may be a great power in changing the way that educators work.

I am happy to say that I
have sold approximately 500 copies of Pebble Maths to every corner of the
globe. Pebble Maths is being taught in several Maori language school in New
Zealand and will be translated for those children. It is also currently being
translated into German. I am also engaged in teacher training with teachers
from Spain to Singapore, from England to Australia, Africa, India, Saudi Arabia
and more every month.

## International Mathematics Conference!

by Vera Stevens on 03/02/15

## Another Wonderful Week at Noosa Pengari Steiner School!

by Vera Stevens on 02/17/15
Last week I had the pleasure of teaching at Noosa Pengari Steiner School. Once again I taught in class, small groups and had a whole day with the learning support team. It was a very fruitful week. It was wonderful to work with the teachers and children once again and I felt that the children embraced Pebble Maths with all their heart.

Thank you Noosa!