Klahanie School
Montessori Philosophy and Practicum: Math & Language Foundation Understanding
written by Emily Graham
AMS Certified/Montessori Education Institute
of the Pacific Northwest
Dr. Maria
Montessori Introduction
Dr. Maria Montessori believed
in the development of the child, spiritually and intellectually. Follow the child was and is the
foundation of the Montessori method, began and noted in 1906 at Casa dei
Bambini (Children’s House) in San Lorenzo, Italy where she began her quest to
assist in the success of children through practice of observation, presence,
respect and care of the individual.
After great research, passion and time Dr. Montessori established clear
goals for education, which has become the defining Montessori path. These include; to help the child reach
his/her highest potential, help facilitate normal development of the whole
child and assist in the development of the child’s intellect emotionally,
socially, cognitively and physically.
Dr. Montessori believed that living the goals listed through the
practice of concrete curricula and awareness of developmental stages (Practical
Life, Sensorial, Language, Math, Absorbent Mind, Sensitive Periods,
Concentration, Coordination, and Order) would enable that child to grow to
his/her full potential.
Her profound insight into the soul of
the child; her long and varied experience; her scientific outlook combined with
a maternal tenderness and sympathy; the lucidity of her discourses and their
originality…the passion of her devotion to her mission-all these combined to
make her a perfect advocate of her cause, which was the cause of the child (Her
Life and Work, E.M. Standing, 65-66).
Understanding
Developmental Stages of the Child
From the moment we humans
open our senses to the world we are engrossed with the wonder of exploration,
experimentation, examination and dissection in order to begin to understand
what is presented from the world.
A child is born an explorer.
“The child is a philosopher before he can talk, an explorer before he
can walk” (Standing, 102). Dr.
Montessori broke the stages of life into three categories (First Stage Birth-6yrs,
Second stage 6-12 years and Third stage 12-18) to help understand the
developmental transitions one goes through. The first Epoch of Development (Birth-6 years) is termed The Absorbent Mind. From Birth-3 years the child is in a
state of Unconscious Mind, constantly
absorbing impressions from the environment and yet does so without knowing that
he/she is doing so. “In the first
year of its life, then, a child takes in the whole of his environment unconsciously. In this way he accumulates the materials
from which he will later build up to his conscious life” (Standing, 111). We adults cannot teach this
directly. This mysterious process
of humans passing from unconscious to conscious is independent of us
caregivers; we can only assist in providing conditions that will nurture the
child during this transitional period.
The second sub-division of Absorbent Mind, 3-6 years, in a move
from the child’s absorption of the world through his unconscious intelligence
by merely moving about in it, to the second stage where the child takes in the
environment consciously by using his/her hands to educate. “The hand has now become the instrument
of the brain; and it is through the activity of his hands that he enriches his
experience, and develops himself at the same time” (Standing, 112). During this time the child passes
through a defining period in which they reveal intense and extraordinary
interest and attention on certain aspects of his/her environment to the
exclusion of others to develop order and distinction to their understanding
which is called Sensitive Period. During the 3-6 years there are
different Sensitive Periods
emphasized for Order, Language, Interest in Small Objects, Learning Grace and
Courtesy in the world and Refinement of Senses. We as caregivers must support the area of interest focused
on by the child.
The
Development of the Mathematical Mind
Piaget, along with Dr.
Montessori, believed through observation a child must do a lot more work before
counting is to begin. Much of this
belief is due to research that showed children’s understanding and absorption
of information is more effectively created when a child works from concrete to
abstract. Thus, all Montessori
materials and lessons are facilitated at the beginning very concrete and later
moving towards a more abstract. As
seen in research, the concepts of abstract are not developed until age seven
and beyond but usually not before.
It is believed that we cannot directly
teach logical mathematical concepts such as number. Children form this type of knowledge from their experiences
in the world…. Encouraging young children to observe, compare, contrast,
ponder, question and think is a far more powerful way to support their
development than drilling them on numbers and math facts. Maturation of brain structure and ample
experience manipulating and thinking about objects in the environment are both
essential for a child to understand number and the underlying processes that we
use arithmetic (Mary Schneider, 1).
Understanding counting on a
one-to-one correspondence is a crucial component in knowing how to count
rationally. Counting rationally is
a foundation for understanding concepts and practice of numbers. Rational counting includes five basic
understanding. First, count
groupings of similar and/or different objects. Second, recognizing stable, sequential order of numbers
(two, three, four, etc.). Third,
practice and understanding the concept of one-to-one correspondence—assigning
one number per item (quantity) asked to count. Fourth, the idea that when counting items in a group, it
does not matter which item is counted first or last as long as all items are
assigned a number with one-to-one correspondence. Fifth, realization that the last number said in counting in
one-to-one correspondence is the total number of items—also referred to as
“cardinal principle” (Kathye W. Unglaub).
Suggested activities for introducing pre-counting/math are songs, finger
plays, books, poems, puzzles, games, toys, cooking and introduction to “more”
and “ “less.”
Research continues to show
that an important element in educating is through conversation about concrete
experience, all to encourage the child’s cognitive process.
Most three-year-old children understand
singular and plural and groups of things (sets) better than they understand
one-to-one correspondence and accurate counting. If we could, we should, really further develop
three-year-olds’ understanding of sets before introducing them to counting
(assigning numbers words of things); it’s children’s interest in comparing sets…that
stimulates interest in learning to count elements to ascertain ‘the answer’
(Polly Greenberg, 79).
The focus is on developing
the child’s ability to group sets according to different attributes (size,
color, shape, etc.) to stimulate the ability to create sets using blocks, beads
and other objects of quantity as well as the introduction to compare whether or
not sets have an equal or unequal number of elements. At any age, even as young as toddler, children incorporate
counting assignments in play and motor activities. “They initiate the counting as they play” (79). Thus, we as caregivers and teachers
assist in creating an outlet where math can be introduced but not forced.
The
Montessori Classroom: A Preparation for Math
Creating success in the math
experience takes ample time and concentration in Practical Life and Sensorial
parts of the Montessori classroom.
Practical Life and Sensorial are fun and rich experiences needed to
discover math. Thus, the Practical
Life and Sensorial areas of the classroom hold numerous pre-counting activities
to create a clear and easy-to-bridge foundation.
Sensorial and Practical Life
incorporates sequencing, matching, comparison, pattern, sorting/classification,
order, coordination, concentration, independence and measurement, all of which
are foundation components in the math area. Materials are gateways to practice of concrete understanding
of abstract ideas. The following
Sensorial and Practical Life lessons are examples of setting clear intention
for bridging a child’s understanding to the next level of math concepts.
· Sewing
· Red Rods (longest to shortest), Pink Tower and Broad
Stair (largest to smallest/broadest to thinnest)
· Geometric solids
· Geometric cabinet
· Binomial/Trinomial Cubes
· Knobless/Knob cylinders
· Plastic Decanomial
· Food Preparation (measurement)
· Spooning and Tweezing, sorting (matching, sorting,
transfer/subtraction and addition)
Montessori
Math Materials: The Purpose and Common Characteristics
A key concept and belief from
Dr. Montessori was the role of the subconscious. She believed through observation of varying children that
all experiences are stored in the subconscious and leaves a defining mind
trace, also referred to as an engram.
Although a person may not immediately respond on a conscious level to
these memories, the engrams are permanent.
Thus, a sensory experience in early
childhood, according to Montessori, can be counted on to help a child both feel
more comfortable with certain materials and activities and provide a sensorial
basis for more abstract concepts…The indirect aims of the Montessori materials
are thus based on the idea that different aspects of the child’s experiences
can be called upon at a later time to make the learning of new, more abstract
concepts easier…provide specific sensory experiences that can later be
elaborated into new concepts (Chattin-McNichols, 98).
The point of the Montessori
curriculum is for exposure. The
child may not understand an algebraic equation but through sensorial movement
and memory, the lesson of why and how such an abstract idea can be concretely
remembered will filter in through the subconscious to a conscious level when
the information is needed.
The Montessori curriculum
allows extensive use of manipulatives so the teacher may demonstrate concepts
in a clear and concise manner.
Through isolation of difficulty, materials are designed to teach the
child one concept at a time (i.e. introduction to multiplication includes
numerous materials and lessons rather than teaching the multiplication
facts). Throughout the math
curriculum a child is exposed to a “web” of indirect preparations in order to
assist the learner during critical times with new materials and concepts. Lastly, the Montessori concept of
abstract holds great weight and materials the child uses change as the child
matures, becoming more abstract and less concrete. “This process of abstraction is an ‘Ah-ha!’ experience for
the child…The learning is truly the child’s own. Montessori describes this as a creative act, even though
these abstractions are not the first: a child is creative who discovers the
formulae, even though it is already known to mathematics” (Chattin-McNichols,
115).
To summarize, main features
of the Montessori Math Curriculum are as follows:
· Concrete manipulative activities
· Well defined, elegant, sequence from concrete to
abstract
· Definite purpose (Direct Aim of a lesson) to each
activity/lesson—clear isolation of difficulty and concept
· Web of preparation (Indirect Aims of a lesson)—the
activity/lesson work together to show new levels of findings
· The focus is on Process rather than mastery or
memorization (the product)
Understanding
a Child’s Acquisition of Language and Montessori Theories Behind It
Rather than the teaching of
language, Montessori education emphasizes the development of language. Dr. Montessori believed that language
development follows specific “fixed laws” that are universal to all children
(Chattin-McNichols, 117). “One of
the earliest and at the same time the most wonderful of the sensitive periods
in the child’s development is that which is concerned with the acquisition of
spoken language” (Standing, 121).
Without any formal teaching or conscious effort a baby learns to
pronounce the language of his/her environment. The sensitive period for a child begins long before he/she
can speak or walk, much of the learning is done through observation and
absorption. Montessori philosophy
stresses the importance of acknowledging “… for a period of its life, the child
is endowed with a special sensibility towards a certain element (language) in
its environment which enables it to establish a new function—speech. Furthermore, this sensibility is
transitory, and once gone never returns (121).
To honor the needs of the
child so he/she may acquire adequate space to develop language skills we as
educators and parents must recognize that a child holds an innate drive (horme)
to learn language.
Montessori referred to the potential of
language learning as a ‘nebula’; she felt that each experience undergone by the
child results in an engram or memory trace stored permanently in the child’s
subconscious. These engrams
interact and produce new learning which on occasion rises to the conscious mind
(Chattin-McNichols, 117).
Around two years, the child
experiences an explosion of vocabulary in words. A little after two the child begins the process of combining
words to create sentences and discovery of syntax (pulling together new words
into ordered functions).
Montessori
and Current Research
One of the areas criticized
and heatedly discussed in the Montessori curriculum is the sensitive periods in
the language area. What we are
seeing in current and earlier research is that findings shown through
observation of general sequence of developmental language stages in a child are
very similar to Montessori proposals and theories. In 1970 Dr. Slobin, researcher of Psycholinguistics and
grammatical development in children, stated in one of his studies “The picture
we are now beginning to form, however, is that of a child who is creatively
constructing his language on his own, in accordance with innate and intrinsic
capacities—a child who is developing new theories of the structure of language,
modifying and discarding old theories as he goes” (Slobin, 40). Montessori credited children for being
capable of using their senses at a very early age. Noam Chomsky, a behaviorist, agreed with Montessori that
language is not learned.
It seems plain that language acquisition
is based on the child’s discover of what from a formal point of view is a deep
and abstract theory—a generative grammar of his language…One the basis of the
best information now available, it seems reasonable to suppose that a child
cannot help construct a particular kind of transformational grammar to account
for the data presented to him, any more than he can control his perception of
solid objects or his attention to line and angle. Thus, it may well be that the general features of language
structure reflect, not so much the course of one’s experience, but rather the
general character of one’s capacity to acquire knowledge-in the traditional
sense, one’s innate ideas and innate principles (1965, 59).
Continued support by current
research is Montessori language curriculum idea of language “explosions.” These stages appear to be the best
descriptions of child language development specifically in regards to
vocabulary (120). Similar to the
findings and opinions of current research, Montessori considered writing and
reading as integrated, especially related to the child’s oral language.
Misunderstandings
of Montessori Language Curriculum
Contrary to common belief, Montessori’s
ideas on reading are more similar to what is currently called a While Language
approach than a phonic approach.
Perhaps this misconception comes from the material, especially the
sandpaper letters. In any case,
many contemporary ideas, such as the linking of reading with (prior) writing,
the focus on use of writing to communicate, and the labeling of objects in the
environment, have been a part of the Montessori language curriculum since its
inception (129).
Debates continue surrounding
what is the best instructional method for reading. New issues added to the old debate of phonics vs. sight
words are terms like skill tactics vs. ideational tactics, whole language,
language experience, and emergent literacy. Most programs today incorporate at least two of the
discovery teaching, direct or indirect teaching strategies. A useful area to look at is asking what
type of direct teaching is going on this the environment. For example, when a lesson is being
facilitated on sound/letter matching, is the lesson administered with dittoed
worksheet or with a manipulative?
“The worksheet-oriented approach, instructionally similar to primary
grade work, rather than preschool, is in fact the most common type of reading
instruction in American Kindergartens today” (121). With this particular approach the emphasis on letter naming
and letter/sound matching.
Montessori language curriculum, with the assistance of sandpaper
letters, presents letter/sound matching but attempts to avoid letter
naming. The next step is offering
the child the chance to work further with the letter to explore and play.
Sandpaper letters are used as
a solid foundation for letter/sound introduction and can be linked to many
other areas and extensions.
Another important part of the language area is the movable
alphabet. “These set of letters
allow the young child to write—to use the letter shapes to communicate—at the time
when the physical act of drawing the letters may be so difficult and tedious
that she would not undertake it otherwise” (122). The moveable alphabet is an example of Montessori’s
principle of isolation of difficulty.
A common criticism and
misconception of Montessori language curriculum is that children are forced to
work with language. Criticisms
such as this need a clear response: nothing is forced on Montessori educated
children. Force is the opposite of
Montessori core philosophy of “Follow the Child.” A well working, joyful Montessori classroom does not include
long hours of language lessons, patterned language drill or fixed assignments
in pre-reading workbooks. Rather,
Montessori language is modeled, shown a lesson and extension opportunities to
the child in-group and individual presentations of short duration. The child always has the option to
choose not to do the work shown (124).
The
Rational Behind Montessori Language Curriculum, Methods and Materials
Language competency,
described by Rosemary Williams (1975), is acquired first through the building
of attitude, not skills. “If the
child sees the uses of labels, the utility of written instruction and directions,
the joy of reading, then the teaching of skills necessary for reading and
writing will be a matter of feeding the child’s interest, not a battle of
wills” (122). The most important
reminder for awareness and practice for educators and caregivers are allowing
the child to move at his/her own pace during this birth-six years language
immersion time. Also, recognizing
that sometimes hidden, or out-right expectations are held in the language area
that may not be present when dealing with other areas in the classroom. The same practice and patience is
required in all areas at an equal level.
With that idea in mind, we as educators and caregivers receive the honor
of holding patience in the process of language development. Similar to learning to rollover, crawl,
walk, swim, ride a bike: language is a process and we all experience it.
The birth-six year child is
“riding the crest of a wave of development in spoken language” all areas of the
Montessori language curriculum are designed to honor the child’s interest in
language, communication and amazing capacity for learning from his/her environment.
Montessori teachers must be
aware to offer a full range of language experiences to the students. All forms of self-expression such as:
interpretive reading, finger plays/puppets, songs, calendar, oral story
telling, poetry, games, etc. are all suggested as wonderful ways a child can
process and use language they are exposed to in life. “All are essential for the child’s preparation for language
learning, reading and writing” (126).
These partnered with Montessori language materials become important
components in assisting in creating a well-rounded child experience.
Reading and writing are
offered and taught together and incorporated throughout the child’s experience
in the classroom in all areas: Math, Sensorial, Practical Life, Geography/Cultural,
Botany, Zoology, Art, Music, Movement.
“Since reading and writing are taught in parallel, which does a child
learn to do first? Again, the
individual child will choose” (126).
Work Cited
Chattin-McNichols, The
Montessori Controversy
Chomksy, N. Aspects of the
Theory of Syntax
Greenberg, Polly “Ideas That
Work With Young Children”
Pape, Bee “Before Number”
Schneider, Mary “Encouraging
Development of Mathematical Skills Early Childhood Years”
Slobin, D. “Universals of
Grammatical Development in Children” in Advances in Psycholinguistics
Standing, E.M. Maria Montessori: Her Life and Work
Unglaub, Kathye W. “What
Counts in Learning to Count?”
Class Notes:
Educator/Montessori Math Curriculum Instructor Betsy Martin July 2004
