Making Real Connections with Math in a Montessori Classroom With: Margaret Combs and Gwen Harris
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Making Real Connections with Math
in a Montessori Classroom
With: Margaret Combs
and
Gwen Harris
Concern for the Whole Child
Physical Development
Social and Emotional development
Cognitive Development
Skill Focus:
Early Literacy
Logical Thinking
Problem Solving
Social Understanding
Physical Coordination
Creativity
Positive Character Traits
Our End Goal?
Understand who they are
Know what they want to do with their lives
Possess skills that develop their whole self
Life-long lovers of learning
Global citizens
Make positive contributions
Be prepared for life’s experiences
Developing into an Adult
Adult Work VS. a Child’s Work “An adult has [their] own task to perform, that of building up a transcendent
environment. [They] must use [their] intelligence and external efforts for
productive work, which is as a rule both social and collective” (Montessori, The
Secret of Childhood).
MINIMUM EFFORT-------MAXIMUM PRODUCTIVITY
“[A child’s work is] that of producing a[n adult]. It is solely from a child that a[n
adult] is formed. An adult cannot take place in this labor” (Montessori, The
Secret of Childhood).
MAXIMUM EFFORT
Montessori approached math from an entirely unique perspective!
The mathematical mind is not built on abstract concepts or rote
memorization but on concrete experiences that are tangible and
real.
THE MATHEMATICAL MIND
TENDS TO ESTIMATE
NEEDS TO QUANTIFY
SEES SIMILARITIES
SEES DIFFERENCES
SEES PATTERNS
MAKES ORDER AND SEQUENCE
First Plane of Development (0-6)
Development of the Absorbent Mind
Intense Concentration
Language Order
Self-Construction
Physical and Biological independence
Maria Montessori said that a
mathematical mind was “a
sort of mind which is built up
with exactity.” The
mathematical mind tends to
estimate, needs to quantify, to
see identity, similarity,
difference, and patterns, to
make order and sequence and
to control error.
The First Plane of Development
Human tendency to make order
Classification of experiences with the world
Montessori materials, especially in sensorial,
help the child construct precise order
Practical Life
Nurtures the Mathematical Mind through
precision and order
Development of fine motor skill and control
to manipulate concrete materials
Development of concentration, order,
independence
Development of sequence and progression
Development of work cycle
Sensorial Sensorial materials aid in the development of the
mathematical mind
Material is presented with exactness and precision
Materials present ‘materialized abstractions’
Allows the child to sort, sequence, classify and
compare
Materials develop skills of acute observation
Isolation of difficulty allows focus on one quality at
a time
Math
Materials move from sensorial quality to
mathematical quantity
Material begins with concrete quantity and
moves to abstract symbol
Progression of material moves from concrete
concept to abstract concept
Why do I have to do this math anyway?
To become a good thinker and problem solver in life
To open future doors in your life
To understand the magic behind inventions
To build small skills into greater learning
To understand nature
To be able to answer questions
To build up logical reasoning
To stretch your mind!
Second Plane of Development (6-12)
SENSITIVITIES:
Need to go beyond the narrow circle
of family and friends
Great intellectual development
Building up the sense of morality
CURRICULUM:
Expands to the universe
Provides bits of knowledge that cause a child to ask
why and to pursue knowledge by themselves
Provides opportunities to learn about and practice morality
Third Plane of development (12-18)
This is a second period of great physical and psychic development.
It is a period of intense activity and creativity.
“Second Birth”
EDUCATIONAL IMPLICATIONS
The students at this stage must be allowed to further connect their
knowledge that they have gained concretely and apply it abstractly to
real-world problem solving.
Why Use Didactic Materials to Teach
Mathematics?
As children use the materials to solve mathematical equations and
problems they not only find a solution to the equation or problem, but
they develop their mathematical mind!
It is not just about how to solve a problem, but it is about thinking
and problem solving.
“This system is which a child is constantly
moving objects with his hand and actively
exercising his senses, also takes into account a
child’s special aptitude for mathematics”
Maria Montessori, Discovery of the Child
3-Dimensional / Multi-Sensory The more senses we use to take in experiences, the richer the learning.
Movement and Cognition
We learn better and remember better when movement is connected to
cognition!
It is through manipulating/moving the didactic Montessori materials that
the child is allowed to DISCOVER learning not just memorize and
regurgitate information. Our goal is for the child to truly understand the
answer they have found.
Teacher Control VS. Student Choice
The more control we give to the child, the more they will learn through
their own discoveries with the materials.
Allow children to decide if they want to work alone or if they want to
work together, with a partner, or with a group of people.
Allow students to find their own mistakes.
The Control of Error is never the ‘correct answer.’ Rather, it is the
logical process, the “realization that an activity was not correctly
done. The realization of an incorrect activity lead to perfection”
Maria Montessori
The Control of Error follows the same path of abstraction as the
material. It moves from the mechanical (e.g. the knob cylinders)
to the internal, conscious awareness. When the child is allowed
to make mistakes, he makes connections and independent
discoveries.
Geometric and Algebraic Relationships The Montessori materials allow us to connect geometric representations to
algebraic functions.
Examples: Decanomial -----Table of Pythagoras
Trinomial Cube ----- Formula
Growing the Brain
USE IT or LOSE IT!
Using the Whole Brain
Simultaneous use creates higher learning
Standards / Core Curriculum
3-6 CURRICULUM NUMERATION
6-9 CURRICULUM ADDITION, SUBTRACTION,
MULTIPLICATION, DIVISION
WITH WHOLE NUMBERS
9-12 CURRICULUM ADDITION, SUBTRACTION,
MULTIPLICATION, DIVISION
WITH FRACTIONS & DECIMALS
Let the children
make the connections
with the world!
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