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!