The teaching of Mathematics is a much discussed topic in
the sphere of education because too many pupils seem to develop an early phobia
for the subject and often, teachers also live in perpetual dread of having to
deal with the subject – it is often left to colleagues who are subject
‘experts’ to deal with. As a Class
Teacher in a Steiner-Waldorf school, one does not have the choice but to delve
into it and find the most creative way to bring this subject to one’s class in
a way, one hopes, will build a life-long love of numbers. Since a Class Teacher in a Steiner school
takes the class group from Class 1 to Class 8, one knows that this cannot be a
half-baked job, because the problems, if any arise from an inadequate
understanding in early years, will only have to be fixed by oneself later on!
The four mathematical processes of addition, subtraction,
multiplication and division – the foundation of all Math to be taught in the future,
are introduced simultaneously in late Class 1 or Class 2 and this is often a
time awaited with baited breath by parents and teachers alike. “What will it be like? Will the students get the concept of each process?”
“After all the storytelling and fun games are done, will they connect the
symbol to the operation?” “ When will
they make the transition to purely doing sums with the abstract symbols without
needing a story to understand the operation?”
“Will they see the wonder of Mathematics as relevant to all spheres of
life – not just as a concept to be memorized through a method?” As one of the pillars in the 3Rs, one cannot
emphasize enough the importance of bringing Mathematics to young students in a
creative way to help them then learn so many more things further in their
journey of education.
Lofty ideals and very obvious goals – but how does one actually
go about it? The one thing I do have on
my side is that the subject is brought to the class in a ‘Main Lesson Block’ of
two hours every morning for a continuous period of 3-4 weeks, allowing a deep immersion
into the subject and plenty of time to digest the matter and come back to it
afresh day after day.
It was very clear to me from the beginning that, like
everything else I do with my students, the children will understand through
images that they connect with and my role would be to bring life to these
images. So the preparation for the
Mathematics Block was in telling a story that had characters that the children had
built a living relationship with. The
characters in the story were myself and my six siblings, cousins and
friends. My class has got to know them
all over time with me through Class 1 and until now through anecdotes, photos,
even some visits by family members to my class!
The central characters of the story, however, are the 4 uncles, each
with a special quirk - one likes to collect, the other likes to give away, yet
another likes to make it more and the fourth likes to share equally
always. All along I shared the stories
with the awareness that a good combination of familiarity of the characters and
unfamiliarity of the plot would work very well for my students and me. The quirks of the 4 special uncles were
described with funny incidents during my growing up years (exaggerated to drive
the purpose of the story) and along with it the symbols were introduced.
The following day, the story unwinds, grandfather on his
deathbed, calls the four uncles to pass on the 48 gold coins that were given to
him by his father, which was passed on from his father. The gold coins were a reward by the village
lord for doing an act of kindness of building a canal to bring water to the village
and prosperity (seeds for another story for another time!). 48 coins are equally distributed in special
bags (physical bags are shown - green for +, blue for -, yellow for X and red
for ÷.) Addition uncle keeps coins safe, Subtraction uncle gives away to anyone
who needs; Multiply uncle ends up trying to make deals that will get more
coins; bringing in disharmony until Divide uncle comes in to ask all to put all
coins together to be shared equally!
The impact of the story was obvious. Not only was the excitement of the children
palpable at each turn of the plot, but also every little prop brought in
connected with their inner processing of the concept. The ‘Blackboard drawing’, another staple of
the Steiner teacher’s toolkit, when revealed to the class, was received with
immense recognition of every detail.
Unfortunately, I did not take photos of my blackboard drawing, so have
used one from a colleague here for illustration purpose only. The quality that each of the four central
characters represented in the story was taken in deeply by the children and
transformed into an understanding of the quality of the mathematical process
that it was associated with – exactly what the teacher wants to achieve through
the whole exercise!
In the 2 weeks following the story, students collected
items from Nature in the school grounds.
They were asked where it becomes more (+) and where it becomes less (—) to
register the idea of addition and subtraction as parallel processes. Similar exercise was repeated with many things
in the classroom. Each one wanting to
barter sets up shops – again, the concept of transference and therefore
addition and subtraction was highlighted.
An inventory of classroom articles and count of trees in school was made
(addition). Everyday life situations were
taken and addition, subtraction, division and multiplication were brought alive. Initially, the children are encouraged to use
their ‘counters’ (a collection of up to 100 identical small objects like Cowdie
shells, wooden buttons, glass pebbles) to aid their work. Slowly, they are able to wean themselves off
the physical counting aid and mentally count their way through their Math work.
Once the processes become fairly clear to the students
and a good foundation has been built, the journey is now taken to the next
level – abstraction. Symbol is
introduced along with the word (more, less, divide, multiply) which are slowly
replaced by the ‘function’ symbol (4 seeds and 3 more seeds becomes 4 + 3)
Children are given enough practice sums to get an
understanding of the function even with abstraction. Multiply function is introduced as repeated
addition and division as repeated subtraction.
Eventually they get to a point of creating their own sums of complexity
they are ready for (caterpillar sums/sausage sums - 2+3= tram sums - 3+4+5= and train sums or snake sums - 4+4+2+3+1+6+5+4).
And of course, particularly in Math as in most other
things, practice makes perfect. Four to
five minutes are spent just after the Morning Circle, yet another Steiner
school staple, to help as a warm up before the Main Lesson, doing mental Math
through situation sums that will have 2 functions as the key elements. 1st & 2nd graders
also delight in creating number sums on large scrolls of paper, on the floor,
in a story…. Any given opportunity…
In my mind I also keep the real purpose of all
‘processes’ alive – it is finally for the benefit of all…good economics to
benefit everyone. Therefore the stories
and incidents consciously carry the message across to sow seeds of good work in
future. On
a subtle level, I also want my students to, through the study of Mathematics,
understand Natural laws - Addition and Subtraction is a parallel process which
is constant, therefore they are not viewed only as gain and loss, instead they
are mere transference of one thing to another, or from one place to
another. This would lay the foundation, for
all future life situations, of an attitude of deep confidence in their ability
to do things without the fear of loss or lack and with the awareness that abundance
and opportunity are the other side of the coin.
Math Work 4 Process Blackboard
Math Work Story Props and Counters
Maths Main Lesson work
-----By Renu Bhatia & Smitha Mallya
