Rationale
Children come into contact with numbers early on in life, as our world is dependent upon mathematics, from counting pennies to baking cookies. Therefore the practical purpose of helping children to develop mathematics skill is to aid the child in acquiring tools that allow him/her to function and to interact with others.In a true Montessori classroom, mathematics curriculum is reality based, concrete materials are used to present abstract mathematical concepts. The teacher creatively uses appropriate and beautiful didactic materials to lure the children to understand mathematics, the logical thinking, not just in computing.
Mathematical ideas are first introduced to a young child through the use of materials in the practical life area in a Montessori prepared environment. These activities develop coordination between the brain and the senses. Sensorial exercises develop concrete manipulative experiences in discovering perceptual and spatial relationships.
Pre-math activities are present in all the areas of a Montessori classroom. A child is most “sensitive” from 3 to 5 ½ years of age. At this time it is easier for him/her to be introduced to concepts of numeration, the decimal place value system and linear counting.
The role of the mother/teacher is to prepare her/himself with the working knowledge of Mathematical skills and to set-up the environment with the appropriate materials necessary for the child to experience yet another dimension of the world he/she lives in.
Montessori Mathematics Curriculum Outline
Part 1 - Preparation for mathematics
a) One-to-One Correspondence
b) Books - Counting
c) Songs – 3 Little Speckled Frogs
d) Sorting/Classification
e)Sequence/Patterns – Do As I Do
f)Sequence/Seriation – Bead After Bead
Part 2 - Numeration Sets
Children are typically introduced to numbers at age 3: learning the numbers and number symbols one to ten: the red and blue rods, sand-paper numerals, association of number rods and numerals, spindle boxes, cards and counters, counting, sight recognition, concept of odd and even.
i) Number Rods
a) Introduction – First Period of 3-Period Lesson
b) Introduction – Second Period of 3-Period Lesson
c) Memory – Order to Order
d) Memory – Order to Mixed-Order
e) Memory – Concept of Larger and Smaller
f) Memory – Concept of One More and One Less
g) Memory – Concept of Two More and Two Less
h) Memory – Concept of Greater Than and Less Than
i) Addition – The Making of 10
j) Addition – The Making of ?
k) Subtraction
l) Counting Backward
ii)Numeration Sets - Sandpaper Numerals (0-9)
a)Introduction
b)Write – Sand
c) Association to Numeral Cards
d) Memory – Go Fetch
e) Memory – Surprise and Go Fetch
iii) Numeration Sets - Number Rods and Numerals
a) Introduction- Association with Numerals-Both Numerals and Rods in Order
b) Numerals in Order and Rods in Mixed-Order
c) Numerals in Mixed-Order and Rods in Order
d) Go Fetch Symbol and Quantity
e) Memory – Order to Order
f) Memory – Numerals in Mixed-Order and Rods in Order
g) Memory – Numerals and Rods in Mixed-Order
h) Addition – The Making of 10
i) Addition – The Making of ?
j) Subtraction
iv) Numeration Sets - Spindle Rods
a) Introduction
b) Different Objects
c) Number Jumping Game
v) Numeration Sets - Numerals and Counters
a) Introduction – Numeral Cards
b) Introduction – Cut-out Numerals
c) Association – Numeral Cards and Cut-out Numerals
d) Even and Odd
e) Pick-up Even and Odd
f) Quantity – Even or Odd?
g) Symbol – Even or Odd?
h) Memory Game
Part 3 - Linear Counting
Children learn the number facts to ten (what numbers make ten, basic addition up to ten); learning the teens (11 = one ten + one unit), counting by tens (34 = three tens + four units) to one hundred.
Skip counting with the chains of the squares of the numbers from zero to ten: i.e., counting to 25 by 5’s, to 36 by 6’s, etc. (Age 5-6) Developing first understanding of the concept of the “square” of a number.
Skip counting with the chains of the cubes of the numbers zero to ten: i.e., counting to 1,000 by ones or tens. Developing the first understanding of the concept of a “cube” of a number.
i) Short Bead Bars
a) Introduction – 1 to 9 Short Bead Bars
b) Bead Design Cardsii) Snake Game – Search for Ten
a) Snake Building – Even Number that Equals 10
b) Snake Building – Random
iii) Teen Boards
a) Introduction – Quantity
b) Introduction – Symbols (Order)
c) Introduction – Symbols (Mixed-Order)
d) Quantity and Symbol – Order
e) Quantity and Symbol – Mixed-Order
f) Random Numeral – Go Fetch Quantity
g) Random Quantity – Go Fetch Numeral
h) Making Numeral and Quantity Pictures
iv)Number Rods – Teen Presentation
a) Introduction – Number Rods (Only)
b) Introduction – Number Rods and Numeral Cardsv)Ten Boards
a) Introduction – Quantity
b) Introduction – Symbols
c) Introduction – Quantity and Symbols (10-90 with Ten Bars
d) Introduction – Quantity and Symbols (10-99 with Unit Beads)
e) Making Numeral and Quantity Pictures
vi) 100 Chain and Labels
a) Introduction – 100 Chain and Labels
vii) 1000 Chain and Labels
a) Introduction – 1000 Chain and Labels
b) Compare 100 Chain to 1000 Chain
viii) 100 Board and Numerals
a) Introduction – Order
b) Introduction – Mixed-Order
c) Go Fetch – Mixed-Order
ix) Squaring Chains – 1-10
a) Introduction – Comparison to Squared Chain/Use of Labels
b) Go Fetch
x) Cubing Chains – 1-10
a)Introduction – One through Ten
b) Complete Layout
Part 4 - Base 10–Decimal System
Introduction to the decimal system typically begins at age 3 or 4. Units, tens, hundreds, thousands are represented by specially prepared concrete learning materials that show the decimal hierarchy in three dimensional form: units = single beads, tens = a bar of 10 units, hundreds = 10 ten bars fastened together into a square, thousands = a cube ten units long ten units wide and ten units high.
The children learn to first recognize the quantities, then to form numbers with the bead or cube materials through 9,999 and to read them back, to read and write numerals up to 9,999, and to exchange equivalent quantities of units for tens, tens for hundreds, etc.
i)Decimal System-Quantity (Golden Beads)
a) Introduction – Unit, Ten Bar, Hundred Square and Thousand Cube
b) Hide and Go Seek
c) Relationship of Materials
d) Complete Layout
e) Go Fetch
ii) Base 10 – Decimal System - Symbol
a) Introduction – 1-10-100-1000
b) Complete Layout
c) Go Fetchiii) Base 10 – Decimal System – Quantity and Symbol
a) Introduction
b) Birds Eye View Layout
c) Crisis of Ten
d) Go Fetch – Symbol
e) Go Fetch – Quantity
iv) Formation of Numerals
a) Introduction
