Developing Concentration

"The first essential for the child's development is concentration.  The child who concentrates is immensely happy."  ~ Maria Montessori 

The Button Frame

Concentration is essential to learning and learning cannot happen without concentration.  How does the Montessori Method develop concentration in children?  

Making Patterns - An Extension with the Pink Tower
 and Brown Stair

Numbers 11 - 19

Firstly, their must be interest.  Montessori environments (classrooms) are beautiful, child-centered spaces.  The Montessori materials are attractive to the children and invite repetition.  This repetition leads to concentration.

The Number Rods

Puzzle Map of Asia

Language Work - The Blue Boxes
(reading and writing phonetic words of four letters or greater)

In a Montessori environment, the children are given the time and opportunity to work with the materials.  The uninterrupted three-hour work period provides children with time. 

The Cylinder Blocks

The adults (teacher guides) in the environment are careful not to interrupt and break the children's concentration unless absolutely necessary.  This is vital to the development of deep concentration.

Language Work - The Pink Boxes
(reading words of two and three letters)

Language Work - The Blue Boxes
(reading and interpreting sentences)

Spelling words with the Moveable Alphabet

The Bead Stair (numbers 1 to 10)

The Golden Beads - The Decimal System

The Subtraction Finger Chart
(memorization of subtraction facts)

Whether a child is buttoning buttons, learning multiplication facts, using a dustpan, raking leaves or tracing the Sandpaper Letters, all work is meaningful.  As the child's ability to concentrate improves, so too does their self-control and self-regulation.  Concentration is essential in schooling and in life.

Let's Celebrate! ~ Celebrations in the Montessori Classroom

There are many different opinions on whether or not to celebrate holidays in the Montessori classroom.  Some schools choose not to celebrate anything except the birthdays of their students.  Whether we choose to celebrate holidays in the classroom or not, they still exist in the world.  In my nearly 30 years of teaching, I have always celebrated holidays with the children in my classrooms and at our little yellow school.   The holidays we have celebrated are inclusive of the cultures and religions of the children and families in our school community.   

At our little yellow school, the celebration of a holiday is not highlighted on one day with no connection to anything else.  Rather, activities are introduced gradually across the curriculum in the weeks leading up to the celebration.  The following are some examples.

The Practical Life shelves reflect the colours and theme of the celebration.

Valentine Tonging Work

Lunar New Year Tonging with Chopsticks

Spooning Pumpkin Seed 'Ghosts"

Opening Easter Eggs with Surprises!

Preparing Pumpkin Seeds for Roasting

Peg Christmas Tree

The Language Shelves and Circle Time incorporate stories, poems and songs.

Melting Like a Menorah Candle

A Halloween Rhyme

Learning About Diwali

 

A Valentine Book

Playing Tombola (An Italian Christmas Eve Tradition)

Spinning a Dreidel

Decorating the Christmas Tree

Arithmetic activities incorporate seasonal items such as seasonal counters.

Halloween Ghost Counters

Valentine Heart Estimating Activity

Art activities change to reflect the holiday.

Valentine Hearts

Lunar New Year Tigers

 

Reindeer Craft

Diwali Lamps

The Culture Shelves have items and photos associated with the holiday.

Lunar New Year Items

Hanukkah Items

A Visit from Santa Claus

A Visit from St. Nicholas on December 6 (Treats left in our shoes!)

The loveliest thing about introducing holidays and celebrations gradually is that it does not interfere with classroom routines.  Children thrive on the routine and the predictability of their school days.  By incorporating the holiday into the classroom routine, the children are able to learn about the holiday at their own pace while expanding their minds, their worlds, but most of all their hearts.  

"As different as we are from one another, as unique as each one of us is, we are much more the same than we are different.  That may be the most essential message of all, as we help our children grow toward being caring, compassionate, and charitable adults."

~ Mr. Fred Rogers (Mr. Rogers Neighborhood)

Math Materials ~ The Small Bead Frame ~ Operations ~ Multiplication

 *The third of three blog posts about the Montessori Small Bead Frame.

The Small Bead Frame is an arithmetic material which helps a child move toward an abstract understanding of mathematical operations.  Addition, subtraction and multiplication equations are solved using this material.  

The Small Bead Frame

The Small Bead Frame is introduced at either the end of the Montessori casa program (ages 3 to 6 years) or at the beginning of the Montessori lower elementary program (ages 6 to 9 years).  Work with the Golden Beads Decimal System material

 

The Golden Bead Decimal Material

and the Stamp Game precedes this work.

Solving an Addition Equation with the Stamp Game

How is the Small Bead Frame used to solve multiplication equations? 

Before I get to how this material is used for multiplication, it is important to discuss the language used.  It differs slightly from more traditional methods.  The language is the key.  Instead of saying multiplication is two times four, we would say that multiplication is a number taken many times.  In this way, we would say two taken four times.

Multiplication - Static

Let's solve a static (no exchanging) multiplication equation.  

2,324

x     2

Begin by sliding the quantities of the multiplicand by the multiplier.  Slide four unit beads to the right one time and then two times.  How many units do we have in total?  Write 8 on the Small Bead Frame paper. 

Sliding four beads to the right once and then twice.

Four taken two times equals eight.  

Do the same for the tens, hundreds and thousands.

The product of the equation - 4,648 - is on the right.

The product is 4,648.

Multiplication ~ Dynamic

Let's solve a dynamic multiplication equation.  Dynamic multiplication equations involve exchanging.

2,394

x     2

Begin by sliding the quantities of the multiplicand by the multiplier.  Slide 4 unit beads to the right one time and then two times.  How many units do we have in total?  Write 8 on the Small Bead Frame paper.

Four taken two times equals eight.

Continue with the tens.  Slide 9 ten beads to the right one time.  

Nine beads taken one time.

Slide 9 ten beads to the right a second time.  There are not enough beads.  Slide the final bead over.  That makes 10 beads.  10 ten beads make one hundred. 

Ten ten beads make one hundred.

Exchange the 10 ten beads by sliding 1 hundred bead to the right.  Slide all 10 ten beads to the left.

Exchange the ten ten beads for one hundred.  Slide one red
hundred bead to the right.  Slide the ten ten beads to the left.

Continue sliding the ten beads to the right until you have slid 9 over in total don't forget one was already slid over before exchanging).  How many tens do we have in total?  Write 8 on the Small Bead Frame paper.

Nine tens taken two times. 

Continue with the hundreds and thousands.  Slide 3 hundred beads over one time and then two times.  How many hundreds do we have in total?  Write 7 on your Small Bead Frame paper.  Slide 2 thousand beads over one time and then two times.  How many thousands do we have in total?  Write 4 on your Small Bead Frame paper.

The product is 4,788 (on the right).

The product is 4,788.

Note:  This material is introduced to children at 5 1/2 + in a Montessori program (SK - grade 1).  Numbers to the thousands are introduced to children in grade 4 of the Ontario Math Curriculum.  Multiplication of the times tables up to 7 is expected by the end of grade 3 of the Ontario Math Curriculum.