Monday 25 November 2013

Early Literacy

How do you prepare the child for early literacy in a Montessori prepared environment?

"The only language men ever speak perfectly is the one they learn in babyhood, when no one can teach them anything!"
Maria Montessori

Literacy is defined as the ability to read and write - the ability to read and write a particular language or two or even more.  Preparing a child for early literacy simply means to facilitate the environment with language-based activities which can lead him/her to the gradual process recognition of letter, their formation, forming of simple words and construction of sentences.

"There are three major aspects of literacy; 1) the complex interrelationship of listening, talking, reading and writing.  2) the roots of literacy located in a general symbolizing development in infancy, and 3) the function fhte symbolizing power in the creation of meanings."  
Language and Literacy in the Early Years by Marian R. Whitehead

Language is a system of communication which is composed of set of rules called 'grammar'.  Language, at initial stages, is not learned by reading, writing or through grammar.  It is absorbed by listening to sounds and voices in the immediate surroundings.

"Listening, talking reading and writing are the four modes of language".
Language and Literacy in the Early Years by Marian R. Whitehead

So, for preparing the child for early literacy is the teacher/facilitator's ability to create an environment and design the syllabus for initiating the process of, 
- recognition of the beginning sound of the words spoken
- absorbing the vocabulary, formation of sentences and accent from the surroundings
- developing an ability to differentiate among words as names and actions
- listening to stories and nursery rhymes for the development of cognitive faculty
- learning to express his/her own feelings and share his/her ideas and experiences
- developing and refining the fine motor skills as a requisite for pre-writing faculty

Any flaw in form of lacking any of the above processes may cause troubles in streamlining child's further progress in the area of literacy.  I would propose for myself to maintain a record of those children who are  passing through the stage of preparation for Early Literacy.

"Writing and reading require instruction of some sort and require some degree of effort by the child.  She must exert herself on the components of our language to build it for herself.  She must mount each of these steps:

Step 1: Spoken Language: create an internal dictionary and practice using the words in it
Step 2: Phonetic Awareness: learn the sounds within words and the sound/symbols of our alphabet
Step 3: Creating Words (Writing): learn to put those sounds/symbols together to make words 
Step 4: Reading: Learn to decode those sounds/symbols to decipher words."
Literacy Overview: Language Development in Young Child

Aims and Objectives

Aim: Preparing children for early literacy through language material

Objectives:
- to develop listening skills
- to build vocabulary and language skills
- to refine pronunciation 
- to develop interest in books
- to develop memory skills
- to develop and refine fine motor skills

Indirect Objectives:
- Literacy is associated to all other areas of learning; namely, biology, zoology, astrology, botany, history, geography, geology, geometry, etc.  It is literacy which enables a child to comprehend the concepts and ideas beyond their imagination and helps understanding the world and the relation between it's elements.  I remember the saying of one of my mentor, "All English is hidden in letters A to Z, all Urdu is hidden in letters Alif to Ya and all Mathematics is hidden in number 1 to 9."  So, preparing a child for literacy is to give him/her a confidence to explore the world on his/her own and develop feelings of ownership to the world.


Literacy in Pakistan

As the question is being asked in English, I presume that it requires to respond in English and that the term 'literacy' has also been used for English language only.

Urdu is the national language of Pakistan, as well as the main source of communication among its citizens and the neighboring countries.  Despite of parents' top most concern of sending their children to school for learning English as a language and of the fact that most subjects from pre-school to higher level are taught in English; English still stands at the third place following the native languages after Urdu.  The reason for that is quite obvious, English is being taught mostly by grammar and is not spoken at homes and on streets.  Therefore, the children by the age of 2.5 are well-acquainted with either Urdu or their native language and take time in learning English and that is if they are admitted to a pre-school system at an early age.

The current educational system and the general attitude towards English that is it the only way towards progress, prosperity and honour, both have coordinated to crush creativity and learning behaviour in children.  That has resulted in lacking reading, writing and speaking skills in both languages.


Planning

Language Skills:
Language skills are the base of literacy.  Children absorb words and sentences form their environment.  They even reflect accent, expressions and delivery of the adults in their immediate surroundings.  It is the job of facilitator to constantly replenish the environment with felicitous methods and fresh ideas.

The first interaction between the child and the facilitator is always verbal on mostly one-on-one basis, therefore, the facilitator must be careful about his/her facial expressions, body language, the voice tone and the choice of words.  A handshake with a smile on face followed by a gentle greeting and an offer to visit any of the attractions in the environment is a good stimulation for a child decide to stay there.  The process of listening and absorbing words, sentences, grammar and accent begins from here.  The congeniality usually leads to little question, usually, 'what is this?' and the facilitator keeps replying by naming the objects, 'This is a horse, this is magnifying glass, this is globe', etc.  'Responding to children's queries at right moments helps building a strong relation with them.

Preschoolers in Pakistan come from a non-English background, bearing that in my mind, the first thing that should be focused on before expecting them to respond in English is to build their vocabulary and enrich it with adjectives and prepositional phrases.  Flash cards, book corner and outdoor activity time provide children with plenty of opportunities to learn new words and understand their link to the environment.  For example, while presenting them the flash cards of sea animals and using the method of three period lessons, the child can learn the name of those animals and can visualize the difference between their physical structures.  Children pick new words and repeat them.  

Listening Skills:
The child does not start reading but from the moment when his/her parents or grandparents read stories, which are mostly fictional or when they share their experiences.  So, when the child enters the Montessori environment, he/she is often familiar with imagining characters and events.  What makes the Montessori environment different from home in regards to 'reading' is the book corner, where books are kept to serve certain purposes, such as, to invigorate child's interest in listening to stories, to introduce new thoughts, to build new vocabulary, to develop cognitive thinking, etc. 

'Listening is imperative for speaking just as reading is indispensable for writing.'  If I prepare the environment for supporting literacy on the basis of this principal of mine, the book corner will always be the first place to occupy my attention.  Dr. Suess's 'The Cat in The Hat', 'One Fist Two Fish Red Fish Blue Fish', 'If I ran the Zoo' and 'Yertle the Turltle' will be my first choice as these books attract children because of their colourful pictures, rhyming in short sentences and strange characters.  Then the books about animals, places, juvenile picture dictionary, space, solar-system, pop-up books, literature books of Tom Sawyer, Robinson Crusoe and Gulliver's Travel and many more - the purpose of a vast collection of books is to develop the child's listening skills and to refine his/her visualization of the text and pictures.

Literature:
While choosing the juvenile literature, this is important to select the books which enhance child's imagination of places and characters in the novel.  For example, the novel of Robinson Crusoe tells the story of a man who accidentally landed on an island and learned to survived on his own for many years.  The traveling of Ibn-Batuta describes his means of transportation from Morocco to China.  Dr. Suess's books although contain concepts and characters that are beyond children's imagination, but children are yield to listening as they stories are described in short sentences, easy words and in rhyming.  Most children enjoy rhyming rather than asking why Thing A and Thing B do things opposite the words said to them or how it is possible for the Little Who community to live on a speck and how a tiny speck serve as a planet to them.

Children's movies and educational videos also has strong influence on children's cognitive and intellectual development and to refine their senses.  The ones I chose for my daughter when she was only six months old were Barney, Lamb Chop, Between the Loins and Sesame Street.

The facilitator should avoid to prolong explanation to keep children from losing interest in books and listening to stories.  However, he/she should describe the things/objects in a novel or a story in context to geography, biology, history, mathematics and other areas of knowledge.

Phonics
I have developed a philosophy of my own for teaching phonics.  It is that the world began with objects, those objects were given names, those names had the beginning sound, later on the middle and ending sounds were also being recognized as the part of the pronunciation, then letters were developed to give those a name.  So, I introduce sound through objects, starting with the beginning sound.  For example, show the child a real object or it's miniature or the picture and say the beginning sound, 'cu cu cup - this is a cup or f, f, flower - this is a flower'. Sometimes the words and sentences are spoken so speedily that the children cannot distinguish among their sound and repeat them all wrong.  Like one of my nephews, when he was three plus called Pepsi - tepsi and Taxi - tapsi.  So, what I do is to focus on the beginning sound of the objects way before introducing letters/alphabets to the children.  
I consider this the first and the most important step towards literacy.

Some early childhood educational institutions usually introduce letters by sound instead of the names given to them.  That confuses the child.  Most children have a hard time for years to figure out the beginning sound of 'c' as 's' and they pronounce cycle, celebrate, certain with a 'k' sound.  A four year old girl, Rahmah, read 'saw' with sound - sa e wa - and failed to pronounce it as 'saw'.  Another child in Fourth Grade, Hassan, still pronounces all words beginning with 'c' as 'k'.
Similarly, children have problem while reading words merely through phonics - cat, pan, bag, wax, was, car, far - food, foot - ink, ice, island - gum, gem, etc.

Memory
Developing memory skills is also the part of Literacy curriculum which the facilitator must focus on.  The simple procedure for that is to recall child's recent memory rather than reminding him/her what happened a day or a week ago.  Three period lessons is the best strategy to start with and that can be applied not only during proper three-period lesson presentations but also when the child is busy at the farm table or colour table or nature table, or even having fun with 'I Spy Box'.  The technique is to not to let the child feel that he/she is going through a process of learning.

Outdoor activities and circle time discussions do help in sharpening memory.  A couple of children recall the incidents related to the topic or activity and share it with their fellows, that encourages other children to share their personal experiences.  This practice aids children in developing sequences and link of events for writing debates, speeches, essays and stories.

Grammar
Grammar is a quintessential part of the early childhood curriculum and must be acknowledged in its due regards.  As it has been mentioned earlier that listening is the key to speaking, the child repeats what he/she hears and listens to.  The facilitators and adults in a Montessori should communicate with children in short sentences, should use easy-to-understand vocabulary along with verbal expressions at a steady pace.  they should try to speak clear and in a moderate voice during presentations and class discussions.  The facilitator can bring out their own planning to introduce grammar conveniently.  For ESL children,few words and phrases can be selected on weekly basis and reinforce them throughout the week through different activities.  Children at this age have no idea of tenses, the action word they learn, they speak it for all tenses.  Instead of telling them that they are incorrect, just repeat the sentence in correct tense few times.  



Language Material


Pink Series, Blue Series and Green Box are the three material for developing reading in three levels in a Montessori system. 

Pink series is a set of 5 boxes and five books which consist of the words mostly in a consonant-vowel-consonant pattern.  It is an introduction to words and sentences with easy three letter phonic words, such as, cup, bus, mat, bat, kid, lid, mop, top, etc.  The sight words such as 'an' , 'the' , 'is' , 'you' are also introduced at this level to form sentences.

Blue series is a set of 5 boxes and five books which mostly comprised of four, five or six letter words with blends, such as, fr, cr, cl, br, ck, nk, ng, etc.  More sight words, such as, have, were, was, are, are introduced to form sentences.

Theme box is a set of objects that represent a specific topic, such as, farm animals, grocery, sports, etc.

Teacher/facilitators make their own vocabulary cards for grammar, all colour coded, to distinguish among noun, verb, adjective, preposition and conjunction, for singular and plural activity and other language-based games. 



Writing 

Learning to draw strokes to develop and refine pre-writing skills are an essential part of early literacy.  The child begins with scribbling on the scribbling board, slate or papers.  

Pincer grip, flexibility of wrist and hand, eye-hand coordination and visual discrimination are the basic skills which need to be refined before giving the child any writing task.  Sandpaper letters and Inset for Design serve to attain these requirements.  

Sandpaper letters is the material which builds muscular impression of letters for writing by tracing them with index and middle finger.  Inset for Design is the material which is designed aids the flexibility of wrist and hand and firm pincer grip.  The child traces around the shapes - triangle, rectangle, square, circle, trapezium, pentagon, oval, ellipse, curve-linear triangle and quaterfoil -  and learns to draw the strokes that are necessary for writing letters.

Large Movable Alphabets is a material which consists of a wooden box with compartments for 3-d letters, consonants in red and vowels in blue.  This is the best material for initiating the process of visualizing the shapes of letters and to put them together to make words even before the child learns how to write them.  The material contains more than one piece of each letter, so even if the child does not identify them by their name or sound, he/she can explore the material by matching them, putting them in line, finding similarities between b and d, p and q and n and u.  At this point, the child can gradually grasp the sequence of letters, their sounds and making of three letter phonic words.

There are many exercises in the area of 'Activities of Everyday Living' and 'Sensorial' which help refining child's fine motor skills for writing, such as, cutting with a scissor, threading and sewing, dressing frames, knobbed cylinders, broad stairs, etc.

The child who passes through these initial undertakings would certainly develop skills that will help him/her reading and writing independently.






















Friday 22 November 2013

Early Literacy in Montessori

Mention three objectives of introducing early literacy in a Montessori.
     1) to develop language skills and build vocabulary
     2) to introduce phonics
     3) to develop writing skills

Name the materials for early literacy in a Montessori environment.
     1) Pink Series
     2) Blue Series

What is the pre-requisite for Blue series?
     The child has developed the ability to read words, phrases and sentences in the Pink series.

Mention the elements of Blue series for expanding vocabulary and reading skills.
     1) double blends (og, um, an, at, in, ut, etc.)
     2) triple blends (est, ulb, lam, usk, esk, ond, ilk, ent, etc)
     3) double consonants (ll, ss, ck, nt, ng, etc)
     4) consonant digraphs (ng, nk, sh, ch, th) - Blue Box 4
     5) consonant trigraph (tch, sph)
     6) 'schwa' vowel

What are graphemes and phonemes divided into?
    Graphemes are divided into 21 consonants and 5 vowels while phonemes are divided into 24 consonants
    and 20 vowels.

Define schwa vowel with examples.
     Schwa vowel is the part of phonemes and is referred to the vowel sound that is not pronounced.  For example, lemon, air, mosque, fatigue, eight, etc.

Mention the three attributes/skills needed for developing writing.
     1) Pincer Grip
     2) Flexibility of wrist and hand
     3) Eye-hand coordination
     4) Visual discrimination

Name the two elements for writing in a Montessori system of education.
     1) Motor Mechanism (Insets for Design and Sandpaper Letters)
     2) The Intellect (Large Movable Alphabets)

Mention three direct objectives of 'Inset for Design' and 'Sandpaper Letters'.
Insets for Design
     1) develop kinaesthetic sense of the geometric shapes for writing purpose (circle, ellipse, oval, curve-linear, triangle, quaterfoil, pentagon, triangle, square, rectangle, parallelogram)
     2) develop control of writing strokes
     3) develop eye-hand coordination
Sandpaper Letters
     1) develop control of fingers for writing letters
     2) facilitate lightness of touch
     3) develop kinaesthetic memory and visualize the formation of letter


Thursday 21 November 2013

Creativity in Montessori

What are the two main areas/categories of creativity in a Montessori environment?
     Visual Arts (Arts and Crafts) and Performing Arts (Music and Movement)

What are the three preliminary stages of creativity (artistic development)?
     1) The Scribbling Stage (1 - 4 years)
     2) The Pre-Schematic Stage (4 - 7 years)
     3) The Schematic Stage (7 - 9 years)

Mention some themed role-play in performing arts.
     Hospital, Supermarket, Post Office, Library, Boat, Bus Stop

Mention some themed role-play of home-corner.
     Kitchen, Telephone, Ironing Board and Iron, Dolls

What is pattern of images called according to Mandler?
     Image Scheme

What is pattern of actions called according to Bruce and Meggit?
     Action Scheme

Mention three Do's and Don'ts for supporting creativity in a Montessori environment.
     1) Make sure all art material is safe and accessible for the child
     2) Make sure the material is open-ended
     3) Make sure that the due freedom of choice is granted to the child
     4) Don't plan too many perspectives
     5) Don't follow a rigid time table or time limit
     6) Don't criticize or correct the child

Enlist at least four characteristics of a prepared Montessori environment for supporting creativity.
     1) Order (external) (and beauty)
     2) Safety
     3) Child-sized
     4) Isolation of skills

Which material is designed to develop creative and writing skills?
     Insets for Design

List down briefly Maria Montessori's views about creativity in a Montessori environment.
    - Beauty is not a Divine inspiration.  It is found in nature and provides the greatest source for stimulating
       the child towards creativity.
    - The child should be surrounded by real objects and famous art work in the art area
    - The child's art work should not be hanged for display or competition
    - Creativity is directly linked with problem solving skills.
    - Creativity encompasses all areas of development (intellectual, artistic, emotional, physical, cognitive)
    - Fantasy should not be the part of Montessori environment.
    - Strong imagination is developed through child's first hand experience of the world in his/her surroundings.

How is Piaget's theory of assimilation and accommodation (cognitive development) is related to creativity?
     Assimilation is the process of receiving information from the world and Accommodation is the internal process of accommodating/adjusting the information for necessary adaptation.  The child in a the Montessori prepared environment absorbs (assimilates) literal, practical and linguistic data and is given freedom and has been provided with a huge variety of material to apply (accommodate) it in his/her own unique way particularly in the art area.









Wednesday 13 November 2013

Early Numeracy and Arithmetic - Math Material



"The chief forms of beauty are order and symmetry and definiteness, which the mathematical sciences demonstrate in a special degree."
Aristotle


Outline first five activities and explain the reason for the sequence in which they are presented.

1 - Large Number Rods (fixed quantity)
2 - Sandpaper Numerals (fixed symbols)
3 - Large Number Rods and Cards (fixed quantity and loose symbols)
4 - Spindle Box (fixed symbols and loose quantity)
5 - Cards and Counters (loose quantity and loose symbols)
are the five activities in the sequence of their presentations.

The sequence of these introductory activities for numbers 1 to 10 starts with, 
1- oral counting of numerals 1 to 10 and visualizing the length on large number rods, 
2- recognizing the numerals 1 to 10 on sandpaper numerals
3- corresponding loose symbols to fixed quantity on large number rods and cards
4- corresponding loose quantity to fixed symbols on spindle box
5- corresponding loose quantity to loose symbols on cards and counters

Large number rods activity is an introduction of numbers 1 to 10 in form of fixed quantities.  It helps in visualizing the variation in length and colour coded segments of equal length.  The child develops a sense of order of numbers from shortest to largest or from largest to shortest.  While counting the segments orally, he/she understands that one is the smallest number, 2 is greater than 1 and 10 is the largest number.  The control of error is there to put rods in sequence to build a stair.  

Sandpaper numerals are the introduction of oral numbers 1 to 10 in their particular formation.  Through large number rods, the child has already developed the sense that the numerals will begin with 1 as first and the smallest number and ten will come in the last.  Through this activity, the child learns the recognition of numerals and is prepared for writing by tracing them with the index and middle finger.

After the first two activities, the child is able to recognize the numerals and understands their sequence from smaller to greater.  

The third activity, Larges number rods and cards, reinforces the concepts of numerals by their correspondence to the correct number rod, randomly and then in sequence.  In large number rods with cards, the child places the cards (symbol) to the rods (fixed quantity).

Spindle box consists of a wooden box with numerals 0 to 9 written on the back (fixed symbols) and 45 spindles (loose quantity).  The child compares the loose quantity which is spindle with fixed symbols which is numerals.  In addition to pairing numerals with spindles, it introduces the concept of zero for nothing or empty.

Cards and Counters in sequence to learning numerals, reinforces the child’s ability to recognize, count and compare the loose quantities with loose numerals.  This activity can be an introduction to the concepts of ‘more and less’ and ‘even and odd’.

Outline the sequence of exercises and pre-requisite in golden bead material.

1 - Teaching the names of the quantities
      Golden beads for one unit, one ten, one hundred and one thousand
      Three-period lesson

2 - counting through quantities
      Golden beads for 9 units, 9 tens, 9 hundreds and 1 thousand
      Starting from units, counting down to 9 and adding one more to start the column of 10.
      Starting with tens, counting down to 9 tens (90) and adding one more ten to start the 
      coloumn of 100.
      Starting with hundreds, counting down to 9 hundreds and adding one more hundred to start 
      the column of 1000.

3 - Bead practice
      The bank of golden beads

4 - Naming the symbols - Large Number Cards 
      A set of cards showing 1 unit, 1 ten, 1 hundred and 1 thousand
      Three period lesson
      
5 - Counting through with symbols
      Set of Large Number Cards - all quantities 1 to 9 - new column starts at 10

6 - Practice with the symbols
      Set of Large Number Cards - overlapping cards to make large figures
      Reinforcement of Ex # 4 and 5

7 - Combining quantity (beads) with symbols (LNC)
      Set of Large Number Cards and quantity of Golden Beads (the bank)
      Collect beads and then corresponding LNC
      Reinforcement of Ex # 3 and 6

8 - Combining quantity and symbols in sequence - Bird's Eye View
      Golden Beads - all quantities in 45 pieces and set of LNC
      Stacking up number cards in hierarchical order and then the corresponding beads
      Reinforcement of Ex # 2 and 5

9 - Changing unlimited quantities and carrying over
      A bead bank, set of Large Number Cards
      Introducing the idea of carrying over when beads are add up to 10 or higher number.

Pre-requisite for golden bead material, 
- The child can count and can recognize numbers 1 to 10.
- He/she has the ability of corresponding between symbols and quantities.


List down the exercises for early addition and early subtraction.

Early Addition Activities
1 - Snake Game (Initial and Complex)
     2 sets of short bead stairs, box of 10 x 10 golden beads, bead marker
     Reinforcement of the concept of conservation and reversibility
     Introducing adding numbers to 10
     
     5 sets of short bead stai, box of 25 x 10 golden beads, 1 black and 1 white stair, marker
     Introducing carrying a number over


2 - Addition with Small Number Rods
     2 sets of small number rods
     Practicing addition
     
3 - Addition with the Short Bead Stair
     Short bead stair, marker, exercise cards/sheet, pen/pencil
     recording addition and writing answers

4 - Addition Strip Board
     Strip board, 2 sets of number cards, stage 3 card, pen/pencil
     Counting up to 18

Early Subtraction Activities 
1 - Subtraction with Short Bead Stair
      Short bead stair, marker, exercise cards
      recording subtraction

2 - Subtraction Strip Board
      Subtraction strip board, a blank strip, set of number strips 1 to 9, exercise card, pencil
      Subtraction up to 18


Outline Seguin Board exercises in sequence.

1 - Seguin Board A - Exercise 1 - naming quantities 11 - 19
      Golden beads - 9 tens, short bead stair
      The child builds short bead stair, take 1 ten and unit from short bead stair
       Three period lesson

2 - Seguin Board A - Exercise 2 - naming symbols 11 - 19
      Seguin Board A with numeral cards
      Introducing written symbols from 11 - 19
      Combining quantity and symbols  
      
3 - Seguin Board A - Exercise 3 - combining quantities and symbols 11 - 19
      Seguin Board A and numeral cards, box of 9 tens, box of short bead stair
      Building numbers with beads and then on board.
      
      
4 - Seguin Board B - Exercise 1 - naming quantities 10 - 90 
     Golden beads - 45 x 10s
      Introducing numbers 10 - 90 - ten, twenty, thirty, forty, fifty, sixty, seventy, eighty, ninety
      Three period lesson
      
5 - Seguin Board B - Exercise 2 - naming symbols 10 - 90
      Seguin Board B
      Introducing written symbols from 10 - 90

6 - Seguin Board B - Exercise 3 - combining quantities and symbols 10 - 90
      Seguin Board B, Golden Beads 45 x tens
      Reinforcement of numerals 20 to 90
   
7 - Seguin Board B - Exercise 4 - combining quantities and symbols 10 - 99
      Seguin Board B, Golden Beads 9 x tens and 9 x units
      Using quantities and symbols to experience numbers 10 - 99
























Tuesday 12 November 2013

Early Numeracy and Arithmetic - MCI (London)

How do you prepare the child for early numeracy in a Montessori prepared environment?

Numbers are abstract. They do not exist in physical form.  They symbolize the quantity, size, weight, distance, speed, temperature, clock time and calendar.  We think of numbers when we want to know about mathematical properties of objects.  The language we have developed for basic mathematical queries is how many, how much, how big, how deep, how hot, how fast, how far, what time, at what time, how early, etc.


Numbers are represented by numerals.  Numerals could be words, letters, symbols, figures or anything that expresses numbers.  For example, one, two (in words), 3, 100 (in digits), iii, xv (in Roman), 1/2, 3/4 (in fractions), 3x, 5a (in Algebra), 3+6 = 9, an abacus, tally marks, ten fingers, ten toes, even the round or oval shape for zero, which is an Arabic invention to stand for 'nothing' and is not a natural number, are all numerals.

Arithmetic is a branch of mathematics which provides acquiescence to basic mathematical skills, such as, counting, addition, subtraction, multiplication, division, fraction, estimation and patterns.  It streamlines a mind for dexterity in further branches of mathematics in higher levels, like geometry, Algebra, trigonometry, mensuration, calculus, statistic, etc.

Arithmetic could be as simple as counting the objects from 1 to 5 and say how many they are.  It could be a complex activity like comparing among objects, such as, more than, fewer than, how deep, how high, how hot or how cold, etc.  It can also be a complicated transaction, such as, to calculate the volume of water in a tank or to change a fraction into a decimal figure or express as a percentage.

 Aims and Objectives

Aim: Introducing early numeracy to children in a convenient orderly manner through Montessori material during the three-year Montessori period.

Objectives:
The objectives should be to help the child,
1- understand one on one correspondence between numbers/numerals and objects (preparing mind for problem solving skills)
Knobbed Cylinders, Cards and Counters, Large Number Rods, Spindle Box, etc.

2 - learn the language pertaining to Math, for example, more, less, heavy, light, right, left, deep, long, tall, short, large, small, add, take away, half, quarter, measure, etc. (language skills)
      Pink Tower, Broad Stairs, Short Bead Stairs, Seguin Board, etc.

3 - do counting (development from concrete to abstract)
     Short Bead Stairs, Seguin Board, Large Number Cards, etc.

4 - identify geometrical shapes and learn their dimensions (preparation for geometry)
      Geometric Cabinet, Constructive Triangles, Geometric Solids, etc.

5 - distinguish the objects by their properties (preparing mind for problem solving skills)
     The entire Sensorial material

6 - learn the concept of more and less (preparation for addition and subtraction)
      Golden Bead Material, material in the area of Activities of Everyday Living

7 - do matching and grouping (problem solving skills)
      Puzzles, Geometric Cabinet, Binomial Cubes, Trinomial Cubes, etc.

8 - learn cardinal (quantity), ordinal (position) and nominal (number tags/codes) numbers/numerals
   
9 - identify numerals (visualization)
      Sandpaper numerals, Spindle Box, Large Number Cards, etc.

10 - draw basic strokes for writing numerals (develop writing skills)
        Painting, Scribbling on writing board, tracing around geometric trays, Sandpaper Numerals, etc.

Aim: Pre-requisite for the above mentioned aim of this area
         Preparing child for early numeracy and arithmetic

Objectives:
To obtain the above mentioned objectives, it is necessary to...
1 - to develop child's interest for counting orally through poems and nursery rhymes
2 - to develop the basic principles of conservation, reversibility and one-on-one correspondence
3 - to initiate the process of counting from body parts
4 - to develop and refine fine motor skills as a requisite for pre-writing faculty
5 - to develop the recognition of numerals through finger tracing and scribbling on a slate

Objective # 2
Conservation: It is an ability to conserve actions, order of actions, mathematical properties and concepts - the two equals remain equal unless a change occurs in their physical or spiritual manner.  The child constantly absorbs millions of impressions since his/her birth and moderately discovers the relation, pattern and order among the objects in his/her surroundings.


Reversibility: It is an ability to understand that the possibility remains for an action to be undone or re-done.
Jean Piaget developed the theory of cognitive learning and set conservation and reversibility as it's two principles as a sign of normal intellectual progress of a child.
For example, an infant conserves the idea of flipping on his/her shoulder to reach an object, later on, he/she figures out the reverse action of rolling back.  Similarly, in his/her infancy, the child opens his/her mouth for the spoon and sucks and swallows the food, later, he/she learns to spit out the food after having enough meal.  So, in simple words, flipping and sucking food is conservation while rolling back and spitting out is reversibility.  

One-on-One Correspondence: This is an ability of pairing objects to their corresponding numbers and/or for completing a set.
In a Montessori environment, for example, a child removes the cylinders which is conservation, he/she puts them back in the holes which is reversibility while trying to put them back in their respective holes (through control of error) is one-on-one correspondence.  

Numeracy in Pakistan
Pakistani culture is comparatively more privileged with cultivating numerical skills in children's absorbing mind.  The calendar is used frequently for cultural purposes than just for learning months and days.
Both, Gregorian and Lunar (Hijri) calendars are the part of people's daily life in Pakistan.  Children's date of birth is marked and remembered in both calendars.  Since their birth, children get to hear the conversation concerning the lunar dates for celebrating their birthdays, national days and Islamic festivals; 1st of Muharram (the beginning of Islamic year), 10th of Muharram (martyrdom of the grandson of the Prophet Muhammad (pbuh), 12th of Rabi-ul-Awwal (birth of Prophet Muhammad pbuh), 27th of Rajab (Prophet Muhammad pbuh's ascention to the heavens), 14th of Sha'aban (the Night of Destiny), 1st of Ramadan (beginning of the fasting month), 21st/23rd/25th/27th/29th of Ramadan (the Night of Power), 1st of Shawwal (Eid-ul-Fitr), 9th of Dhul-Hijjah (Hajj/pilgrimage to Makkah) and 10th of Dhul-Hijjah (Eid-ul-Adha).  On Gregorian calendar, 23rd March, 14th August, 9th November, 25th December are the most significant national celebrations.

On the Independence Day, 14th of August, children draw or make national flags, focusing on it's rectangular shape, the crescent and a five-cornered star in the middle and it's green and white colour.  The national flower of Pakistan, jasmine, has five petals.  There are four main provinces of Pakistan.  The five main rivers of Pakistan merge at a point to flow into River Indus.

Pakistani wedding ceremonies provide plenty of opportunities for children to learn numerical skills.  children love to decorate, count and hold the clay bowls of different sizes full of 'mehndi' for pre-nuptial ceremonies.  Girls love counting their bangles and make sure there are dozen in each hand and they match with their dresses which are in green, yellow and orange combination.

Children hear 'Adhan' (call for prayer from mosques) five times a day and gradually learn the times of the day and clock timings through adhan.  During the month of Ramadan, 29 or 30 days of fasting, children hear the conversation regarding 'sehri' (waking up and eating before dawn) and 'iftar' (breaking fast at sunset) and the countdown for fasting days.  On Eid day, they count 'eidi' (money given to them by elders) and plan how many things they can buy with this amount.  Most children are aware of the significance of Friday because of the Friday congregational prayer and they know it is offered at Zuhr (noon).

Satisfying Parents' Concerns
While preparing the curriculum for numeracy, the milieu in reference to children's social and cultural background cannot be disregarded.  Generally, in Pakistan, parents from all ethnic backgrounds and sects expect and admire the result-oriented system of education.  They do appreciate the inclusion of new techniques and modern approach in teaching but do not withdraw from their demand of traditional mode of repercussion.  As far as the freedom of choice and freedom of movement is concerned, parents will acquiesce with these terms but with ambiguities and lack of trust unless the daily progress of their child accords their anticipation.  

Vertical grouping is also unacceptable for parents as they don't allow their child to sit with the children or older or younger age and learning from each other.  Considering this a waste of time and money, they expect teachers to be there to educate and train their child.   

Trying not to be heedless of parents' expectations and avoiding raising contentions regarding the advantages and disadvantages of Montessori system of education should be top priority of an educationist in Pakistan.  I affirm that parents wouldn't mind at all the shelves full of Montessori material and will only value it as an additional  source to the traditional methodology.

During the last two decades, the early childhood period in Pakistan has started to be from age 2.5 till 4.5.  A 5 year old must be ready for 1st Grade, otherwise, the child is considered to be left behind.  The child has to pass an entry test for an admission in 1st Grade.  So, by the age of 5, the child must know to read and write Urdu and English alphabets properly on and between lines, reading and writing counting 1 to 100, single digit addition, table of 2 and to write sentences in Urdu and English.  The child must recognize all the colours and most shapes, should know how to spell the name of birds, farm animals, wild animals, colours, shapes, etc.  This is the least to be mentioned.  This is the ground reality of the system here in Pakistan and at least I wouldn't consider myself 'proficient' if I fail to present an environment fulfilling the requirements from both sides - the parents of children and the Montessori philosophy.

The pre-school educational system should make parents realize why they want to put their child into a Montessori environment.  They should be explained in brief the importance of three-year Montessori period and of child working on his/her own instincts for a while before jumping to the conclusions.  Parents need to forebear with child's moods and should institute a learning environment at home for a stead progress.  They need to stand parallel to teachers/facilitators for building a concrete foundation for their child's learning.  

Planning

"It is certain that mathematics organizes the abstract path of the mind, so we must offer it at an early age, in a clear and very accessible manner, as a stimulus to the child whose mind is yet to be organized."
                                                                           Maria Montessori - The Discovery of the Child

Montessori classroom provides a comprehensive learning environment which is composed of five basic areas namely; 1) Activities of Everyday Living  2) Sensorial  3) Early Literacy  4) Early Numeracy and Arithmetic and 5) Knowledge and Understanding of the World.  The entire Montessori environment is actually lubricated with mathematical concepts as all theses areas incorporate to impart the knowledge of basic mathematical features in some way.  The mathematical characteristics are present in a Montessori environment concurrently.  The flash cards in the language area are rectangular and their corners are curved, not pointy.  The globe in the cultural area is sphere in shape.  The pouring and transferring exercises develop equilibrium sense for measurement.  Thus, the teacher/facilitator must be mindful of highlighting mathematical characteristics in each of these areas while preparing the classroom and the lesson plan as well.  An integrated curriculum would serve the best to develop connection among all five areas in a Montessori environment.

The area of 'Activities of Everyday Living' provides numerous activities to develop mathematical skills indirectly.  During presentations, this area can be used to encourage counting objects, such as, large beads and sorting them by colour before threading.  The child can be encouraged to count buttons, hooks and bows on dressing frames along with emphasizing on the sequence of work from top to bottom  and one-on-one correspondence.  The pouring and transferring exercises help the child visualizing the amount poured or transferred  into containers and the child develops the concept of 'conservation and reversibility'.

The sensorial activities are designed to focus on sharpening five basic sense and six sub-senses and to refine the concepts of 'conservation and reversibility' and one-on-one correspondence in different ways.  This area mainly consists of the material based on geometrical shapes and colours, which helps refining stereognostic and other senses and numerating flat surfaces, edges and corners of solid geometrical shapes.


Solid shapes of sphere, oval and ovoid can be used to introduce the concept of 'zero' as they have no edges and corners.  'Zero' is usually written in round or oval.

The area of 'Early Literacy' is enormously enriched with numerical skills and is an effective source of building vocabulary pertaining to numeracy.  The words in stories present the concept of time and distance which helps the child to form images of the events taking place from the very beginning.  The story usually begins with,
'Once upon a time, in a far away land.....'
'Long time ago.....'
'It was calm and cloudy.....'
'It was a stormy night....'

Children hear the words that show quantity, such as,
'Oncce there was a king who had four sons.....'
'Once there were two boys who were very good friends...'
'Once there was a little girl who had seven dolls....'
'The old man had not eaten anything for three days....'
'The young prince enjoyed the pleasant sight of hundreds of colourful flowers....'

Children take interest in counting body parts of animals; the cat has four legs, two ears and a tail, birds have two wings, snakes have no legs and arms.

Children don't just listen to the story but they do concentrate on the number of people, animals or objects.  Try telling a story of two kittens, mentioning the activities of one kitten for couple of minutes and the child will inquire about what happened to the other one.


Lubricating Little Minds for Numeracy
Montessori environment is not a place for imposing lessons.  The child either learns by presentations offered by the facilitator or whenever he/she is fascinated with the material.  That is why the area of Early Numeracy and Arithmetic in a Montessori environment should be well-equipped with the material sufficient for developing mathematical agility.  The facilitator must be attentive to serve the child in either case.

Beside the preparation of spider chart and the weekly lesson plan, I personally would prefer to maintain a record of the material that the child has been through and of the ones which he/she needs to be attracted to.  As we know that each material is designed with a specific purpose, the child's avoidance to any of the material can't be neglected.  A good facilitator must investigate the reasons of that avoidance and make sure that the child must somehow be introduced to all materials during his/her Montessori period.

To implement lesson plans according to the sequence of the material for Numeracy and Arithmetic and it's presentation as it is being taught during Montessori training is hypothetical.  We know that children are unpredictable and they don't always end up according to our expectations.  Therefore, a multiple planning with appropriate techniques and precise vocabulary and language must be contemplated.  Besides waiting for children to get attracted to the material or offering presentations on sandpaper numerals, number rods, spindle box, cards and counters, short bead stairs, Seguin Board and Golden Beads material - to initiate the process of counting and developing interest in numeracy, I would rather moisten their minds with some old-fashioned techniques.

For example, singing nursery rhymes and poems is the most entertaining part of the curriculum.  This is one activity which substantiate child's vocal, physical, educational, psychological and cognitive development at the same time.  Some of the rhymes are a reinforcement for counting straight and backwards.

'One two, buckle my shoe...'
'This old man, he plays one, he plays one...'
'One two three four five, once I caught a fish alive...'
'Five little ducks went out one day...'
'Five little monkeys were jumping on the bed...'
'the ants go marching one by one hoorah, hoorah.....'

Counting body parts has also proved to be one of the best techniques for learning counting.  Most children love counting ten fingers and ten toes and then count them together from 1 to 20.

One of the practice that I learned at home in my childhood and have tried on many children is to count on finger cubes.  It is very simple and very effective too.  The child learns to count in order, starting from right hand pinky towards thumb from 1 to 15 (every time starting from the top cube) and then from left hand pinky from 16 to 30.  It builds a memory of correspondence between numbers and finger cubes.  The child in few weeks identifies the cubes by their numbers and can do addition and subtraction later on.

Counting steps on a marked distance is also fun.  Children count their steps moving forward on the marks and them coming back either straight or backward.

Another old time approach for learning numbers and writing is to let the child scribble on a slate.  The child learns to draw strokes through scribbling and finally starts forming shapes and numerals.

Children in my time were more interested in collecting their favourite objects as their precious possessions, such as, dolls, coins, rocks and pebbles of specific shapes and colours, seashells, pieces of broken colourful bangles, their art work, etc.

The question 'how to prepare a child for numeracy' requires an explanation on a facilitator's understanding of the area of early numeracy and arithmetic, his/her preparation for numeracy and arithmetic for early stages and planning and methodology for developing the child's interest for learning mathematical faculty.  It is understood that once the child's interest is developed, nothing can resist his/her curiosity from putting hands on material and absorb the concepts behind each activity.

http://www.amontessorimusingplace.org/2010/10/childs-mathematical-mind-part-1.html
http://www.infomontessori.com/mathematics/introduction.htm
http://montessoricompass.com/mathematics
http://tothelesson.blogspot.com/2011/04/mathematical-mind.html
http://www.studymode.com/essays/Montessori-1226629.html
http://www.montessorianswers.com/myth-fantasy.html
http://www.simplypsychology.org/piaget.html