Sue Rootenberg

UCMAS Sue Rootenberg
(Universal Concepts Mental Arithmetic System)
INTRODUCTION
I was walking out of a Supermarket one Saturday morning when I bumped into a friend
with whom I had been teaching, both at the Johannesburg College of Education (Wits
University) and at a Distance Education College. While catching up with our lives she
told me that her husband was involved with courses called UCMAS.
As a mathematics educator, there was something about her brief explanation of UCMAS
that appealed to me, and I decided to find out more about this system.
On looking back, that decision is in itself interesting: There are continuously “new”
mathematics programmes evolving and being marketed. With the dismal standard of
mathematics in S.Africa, many entrepreneurs have been using this large learning gap in
order to promote their systems. This programme, which involved the use of an abacus,
seemed different.
I asked myself why I was interested in UCMAS even before I had had an opportunity to
study the system and to ponder about its successes. In terms of my background and
lifelong experience in mathematics education, I wanted to explore how the use of an
abacus could result in other benefits, besides those of speeding up and rectifying mental
arithmetic processes.
And so I found myself in a class learning how to manipulate the beads of the abacus in
order to master the four operations (addition, subtraction, multiplication and addition)
with speed.
In this article I will discuss my own learning experiences while doing the programme, as
well as my observations of the learners in the classroom. Over and above the factors
listed in the UCMAS brochures and the results of studies reported in research papers, I
needed to use an experiential approach to look more deeply into the system, and then
relate my own findings.
I questioned myself as follows:
-HOW AND WHY DOES THIS SYSTEM SUCCEED SO WELL IN PROMOTING
SPEEDY MENTAL ARITHMETIC CALCULATIONS?
-WHAT IS THE RELATIONSHIP BETWEEN THE ACTIVITIES WITH THE BEADS
AND THEIR EFFECTIVENESS IN STIMULATING AND ENHANCING OTHER
AREAS OF BRAIN DEVELOPMENT (BESIDES THOSE LISTED IN THE
BROCHURE)?
-HOW CAN UCMAS BENEFIT S.AFRICAN LEARNERS, NOT ONLY IN THE
MATHEMATICS SITUATION, BUT IN THE WIDER FIELD OF THINKING AND
FUNCTIONING?
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MY BACKGROUND versus UCMAS
In order to put my findings and ideas in context, it is appropriate to first give a brief
overview of my qualifications and experience in the field of mathematical thinking,
learning and understanding. This will serve as a background to my interest in the effects
of the UCMAS programme, whose teaching methods, on the surface, are at variance with
philosophies concerning mathematical learning.
Besides having an Arts degree in languages, philosophy, politics, history of music and so
on, I obtained a B.Ed and an M.Ed. degree in Comparative Education (cum
laude).(WITS). I also gained a Post Graduate Primary Education Diploma (UCT) and a
Diploma in Special Education, as well as further mathematics qualifications (UNISA). I
realized early on that language and communication are important areas of mathematics
education and, with other disciplines, are vital elements in the promotion of sound
mathematical thinking and understanding.
I have taught in Primary Schools and a Remedial School where I developed a
mathematics programme. I also taught in High Schools and later at the College of
Education where I trained student educators in the teaching of mathematics in the
Primary School.
I created workshops for disadvantaged teachers in the rural areas who were upgrading
their mathematics teaching qualifications. This experience resulted in developing a series
of books consisting of workshops (using an outcomes-based approach) covering all
aspects of the curriculum in Primary School Mathematics. These books were also used at
UNISA until the contract expired at the end of 2006.
MY QUESTIONS RELATING TO THE REPORTED SUCCESS OF THE UCMAS
METHOD
This lifelong involvement in mathematics led me to focus on analyzing mathematical
thinking and the processes involved in successful learning experiences.
As stated previously, the purpose of this article is to examine how and why the UCMAS
system achieves success not only in mental arithmetic, but more importantly, how the
successful outcomes are manifested in other areas of functioning. Also, as stated, having
come from a different vantage point, I wanted to supplement the claims by making my
own findings.
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The following questions will be addressed in my enquiry:
(1) What is it about the system that caused me to dispense with my skepticism and to
continue to be motivated to practice the UCMAS system daily on my own?
(2)(i) How can this system work simply by following instructions and being given
rules on how to manipulate the beads?
2(ii) What are the experiences of young learners participating in the UCMAS
activities? The answers to this question are linked to the conclusions found in
question 2 (i)
(3) Finally, can the adaptation of this system in S.African schools have a positive
impact on learners besides their achievements in mental arithmetic?
BACKGROUND OF THE UCMAS SYSTEM
(a) Origin of UCMAS
UCMAS is described as “an ancient Chinese technique of co-ordination of brain and
body development using the ABACUS”.
This programme was refined by Dino Wong in Malaysia, the emphasis being on the need
to reach children during the time that greatest brain cell development takes place
(between five and thirteen years).
(b) Right brain development through applying UCMAS
With the use of the abacus it is claimed that these activities develop the RIGHT as well as
the left brain. Left brain relates to logic, mathematics, language, facts and related
elements, while the right brain relates to creativity, arts, imagination, visualization, and
non verbal aspects.
The results relating to mental arithmetic skills as a result of the UCMAS system have
been documented on film. But it has also been found that, while improving learners’
mental arithmetic skills, this is not an end in itself. Development of the right brain has
been backed up by the administration of scientific neurological testing.
Research teams have found that other by-products are manifested. They include:
Enhanced concentration
Memory, the ability to store and recall
Visualization and imagination
Improvement of judgement through observation
Analysis and differentiation-application of concepts
These are but some of the improvements in mental development that have been noted.
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In the appendix I have added references relating to findings and information by
researchers who have studied the effects of the use of the abacus.
(c) Explanation given by the Malaysian programme developers as to how
UCMAS has assisted in the areas of brain development.
It is claimed that the use of both hands on the abacus initially ensures stimulation of both
sides of the brain. Learners begin with concrete and tangible concepts with regard to the
use of the beads. The combination of touch and movement relating to the numerical
concepts then leads to the visualization of an imaginary abacus. This in turn results in the
enhancement of many other areas of mental development as listed above.
ANALYSIS OF MY FINDINGS RELATING TO THE PRACTICE OF THE UCMAS
METHOD
(1) Question (1) on page 3 asks:
What is it about this system with the abacus that holds my interest and continues to
motivate me?
I began to observe the young learners focusing on the abacus while manipulating the
beads. I also monitored my own actions and responses while doing similar activities,
but at a slower pace.
I found the following:
Every time the beads are manipulated correctly, there is a feeling of success.
In other words, each time a movement with the beads is taught and applied, the
learner is confronted with a small challenge. Each small step, both in the learning and
the practice with the beads, comprises a situation where there is an on-going process
of challenge/success, challenge/success.
What is happening is akin to a bio-feedback situation. With each step there is
positive reinforcement. This is an important component in all learning, but especially
so in understanding mathematical processes. Not only is the learner able to see
immediate results, but he/she is working independently, creating a sense of
empowerment. He/she becomes less dependent on the educator or facilitator, thus
building a cycle of confidence and motivation. This psychological aspect of
mathematics learning cannot be over-estimated.
As is well known, many learners develop a negative approach to mathematics. As
soon as they become confused, they believe that they have no abilities and this
becomes a self-fulfilling prophesy. Their loss of confidence affects their performance
and the gaps in their knowledge widen, affecting even their self esteem. Learners
need constant motivation, and this is exactly what is happening with the positive
“small steps” feedback in the UCMAS system.
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Moreover, learners cannot move on to the next learning stage before mastering the
one before. There cannot be gaps in understanding as can happen in the school
situation. This factor further promotes the cycle of motivation.
In the school situation, problems emerge when a new concept is taught before a
learner has grasped its contributory concept. With large classes, it is difficult to
implement mixed ability teaching, which takes into account the different speeds at
which learners work .When learners have to keep up with the pace before they are
ready they develop a gap in their mathematical understanding. This gap blocks further
progress and the structure in concept development breaks down.
Thus, a secondary finding related to working with the abacus (and connected with
motivation) is that the learner moves on to the next phase only when confidently
understanding the phase before. This positive learning experience and its effects can
be attributed to the UCMAS system.
(2) Question (2)(i) on page 3 asks:
How can the system be successful if learners are given instructions and rules on how
to move the beads?
The above methods would amount to “rules without reasons”. I needed to reconcile
the “showing and telling” with methods where relational understanding of
mathematics is applied. In order to make sense of basic mathematical concepts
(whether in areas of numeration, operations, fractions, size or shape) a combination of
self discovery methods are used. These could include the use of teaching aids and the
verbalization of ideas. Thus an “outcomes- based” method of mathematics education
aims at creating independent thinkers who can transfer their knowledge, which has
been acquired in a meaningful way.
This is in contrast to the learning of a particular skill which may be an end in itself.
I questioned the method of learning the skills in the UCMAS system.
However, it has become apparent that the efficacy of the course with regard to the end
results, and the important by-products which evolve, over-ride any doubts relating to
the techniques taught. (See also Appendix relating to this).
Firstly, a vital factor which needs to be alluded to again, is the psychological one.
The “small steps” success, with its immediate feedback, creates a continuing
awareness by the learner of his/her progress and improvement. As any mathematics
educator will concur, this ongoing motivation is one of the greatest assets for learners
of mathematics.
Secondly, I want to suggest a further advantage related to the use of both hands when
working with the abacus. As described above, the Malaysian UCMAS team has found
that this activity promotes right brain development.
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In comparing the use of concrete aids in the school classroom with the UCMAS
method, the school activity is not a continuous one. For example, when using
Cuisenaire rods, sucker sticks, Dienes’ blocks or any other aids, the tactile experience
is only part the activities. With the abacus method, the activity is on-going; the
participants touch and move the beads continuously. This would account for continual
brain stimulation over a lengthy period of time, until the abacus and its movements
can be visualized.
In this respect, it may be interesting to consider the correlation between music and
mathematics. Playing the piano continuously with both hands can be compared to the
abacus activity and right brain development. The continuous “touching and moving”
process results in the visualization of the piano keys.
Another similarity with the piano and the abacus is that the notes and scales of the
piano are introduced in a similar way of “showing and telling”. No meaningful
explanation needs to be given, yet with ongoing practice, the learner is able play and
progress.
(3) The third question to be addressed relates to the feasibility of adapting the
UCMAS programme in S.African schools.
What are the advantages?
How can the system work in conjunction with the school curriculum?
The following discourse is closely linked to what has already been discussed in this
paper.
As is well documented, there is a dire need for experienced mathematics educators in
this country. The causes have been made patently obvious, the most serious one being
the second rate education allowed for teachers during the apartheid days. In addition,
many teachers have left their professions, resulting in unqualified teachers being
called upon to teach mathematics. Although issues relating to the learning and
teaching of mathematics are world wide problems and are not specific to S.Africa,
it has been found that the standard of mathematics in this country is amongst the
worst in the world.
Since the official “outcomes based” curriculum was introduced, not only teachers
from disadvantaged backgrounds, but also experienced teachers, became confused
with the “new words” and new systems of lesson preparation. Introducing different
terminologies and lesson plans could not alone produce better results or foster
change. The presentations needed to be workshop oriented, using mathematical
classroom content, rather than explained in isolation. Many NGO’s and learning
institutions stepped into the breach, but due to practical realities, financial or
otherwise, no long term, in depth system for teachers countrywide has yet been put in
place.
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Mathematics teachers need to be extremely versatile in their understanding of
concepts, so that they are able to analyze and interpret learners’ thinking processes.
This can only come about after many years of skilled, in depth training.
As the implementation of these systems will take many years, large numbers of
learners remain the casualties of these problems.
Other pro-active measures are called for, and here the implementation of the UCMAS
system can be an exciting and relevant addition in any primary school, whatever the
ability of the learner.
Firstly, this system does not intrude with, or contradict, work in schools based on the
curriculum. Its value is that it both complements and supplements school activities
related to learning. As mentioned, by developing the right brain as well, imagination,
creativity, judgement, and memory are improved. All these attributes promote greater
levels of functioning in other areas of learning.
Moreover, lack of concentration and focus has become rife amongst today’s youth.
This impedes on all aspects of their school work. As shown, the activities with the
bead movements on the abacus create situations where consistent focusing becomes
apparent.
Secondly, with practice, learners are able to find answers even more quickly than
with their calculators. The positive feeling of success experienced is a great step
towards mastering many other areas of mathematics.
Thirdly, as confidence and motivation build up with each successive step in the
UCMAS process, the learner becomes more empowered and independent in his
actions. These psychological factors, as shown, are of vital importance in promoting
effective and meaningful learning.
CONCLUSION
This paper has recorded my own additional findings concerning the value of the
learning activities in the UCMAS programme, with a stress on the psychological
factors.
In addition, this system provides other significant outcomes:
I have alluded to the fact that many educators are confused concerning the meaning
and application of “outcomes based” education. I would suggest that using the
UCMAS model would not only have the benefits as listed above, but would also
illustrate, clarify and give meaning to the very concept of “outcomes based”.
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APPENDIX
Below are examples of some of the research done with regard to the abacus method
of calculation and the right brain.
(1) Ms. Shizuko Amaiwa, a Professor at Shinshu University, College of Education,
has been engaged in abacus research from the perspective of a psychologist. In
her paper (January 20, 2001) she shows how the use of the abacus provides a
beneficial ripple effect on other disciplines.
(2) Dr. Toshio Havashi is a Doctor of Engineering and Professor at Osaka Prefecture
University. He is Director at the Research Institute for Advanced Science and
Technology (RIAST).
In his lecture presented on July 30, 2000 in Nikko Kinugawa, Tochigi, Tochigi
prefecture, he says: “Thanks to the development of cerebral physiology and
machines that can accurately measure the amount of blood flow in the brain,
recent studies have proven that the abacus method of mental calculation is
extremely effective in activating the right brain”
(3) Ms. Kimiko Kawano is a researcher at Nippon Medical School, Centre for
Informatics and Sciences. She and her team were engaged in the study of brain
waves (EEG) of the brain activities of students.(Paper dated July 14, 2000). When
measuring the brain waves of abacus users with high ranks they made a breakthrough
discovery: The b waves appeared on the right occipital region, showing the students
were calculating using the right brain.
As with the preceding findings, Ms. Kawano explains how the ability to visualize can
be put to use in other areas of learning and behaviour