Album Pages are Incomplete

   At all ages provide appropriate activities according to the ideas presented in the environment as the children’s interests are piqued. 

Plant those seeds of interest and they will sprout when properly fertilized. 

As much as possible follow the children’s interests in developing follow-up activities (without becoming "cheap" - provide high quality experiences - and invite the children to utilize basic supplies to create their own follow-ups). 

No album page or lesson plan or curriculum can plan for every interest! 


(and no album page or lesson plan or curriculum SHOULD!)

Spiritual Preparation of the Adult: Ownership of the Environment

This Montessori Nugget applies to all environments - not just Montessori ones.

Who owns the environment?

Adults? Children? Parents? Teachers? Do any of us? Do any of us truly own the environment?

The adult prepares the environment, but does so while considering the needs and characteristics of the children who will be present. The adult also looks at the bigger situation: is this is a school environment, a part-time co-op, a homeschool, an after-school, an impoverished area, an affluent area. All of these considerations and so many more dictate that the adult is not going to come in and set something up in a vacuum.

The children utilize the environment, take into themselves and construct themselves through their experiences.

This whole concept is a tough one for us adults, and there will be many more Montessori Nuggets on the subject.

For our Montessori environments:

Trust the materials described in the albums - go deep with them. There is a LOT that can be culled from just the basic materials. Then, if a child has found a true deep interest that even the depths of the material can't provide, then look at your situation, clarify the needs and fulfill them with appropriate further basic material. 


Anything beyond basic: let the child create - it's his interest, let him own it. 


You the adult provide the keys; you provide the environment; you provide a structure within which the child knows and can fulfill the requirements. Fully formed people at every plane are able to take responsibility for themselves through having access to the right tools. Provide those tools and disengage your own emotions, except to be proud of the wonderful creation in front of you :) 

History Timelines

When it comes to extra timelines needed to fulfill interests OR other educational requirements:

          Equal weight has to be given to allow the children to explore freely whatever they wish to explore and to develop the sense of responsibility to society.  Cosmic education was first fully developed in 1944 by Dr. Montessori and her son Mario while they were living in India.  When they arrived back in Europe in 1945, they began to present this idea in training courses.  In one lecture, Mario said, “Regarding the memorization of historical elements, a sort of game has been devised.  The teacher has to first give the lesson, then by way of testing the memory, cards and charts are prepared.”

Geography Puzzle Maps in Elementary

Especially for homeschoolers, there are certain materials that always provoke questions: are they useful or not and at which ages?

The puzzle maps are one such material. Large puzzles of the world and each continent, with each continent or country its own pieces (and knobs placed at the capitals as much as possible).

The official AMI statement is that elementary children are too old for this material, even if they are all new to Montessori. Experiences by so many parents and teachers show that they most certainly CAN be useful, although they are likely to be used in different ways than primary.

In any area, the main points to consider when choosing a material that is "out of age range" are the following:

• is this material FEEDING a child's needs?
• is it useful?
• how long will it be useful for?
• Do you have money and space for it? Or do you need an alternative?
• Is the child just going to hide behind this work? (it is ok for a 4 year old to spend 3 hours with the Africa map, just reconstructing it; but it is not ok for a typically developing 8 year old to do so - the 8 year old should be labeling the countries, listing the capitals, creating a booklet or chart of information, creating a new control map, etc - anything that is an extension and using his imagination to come up with new extensions). 
• is there a more appropriate material for the proper age range? if so, hone in on that material instead. 

For the Geography Puzzle Maps: 

• Elementary children should not be working them "just as puzzles" if they work with them. 
• The outlines are not the most accurate. They are fine for the primary age as a sensorial impression. This is a good conversation starter at elementary and gets the children analyzing. 
• The ideal piece of material are pin maps, but if you have puzzle maps it makes sense to use them for as long as possible. The elementary children can ultimately create pin-maps themselves out of cardboard and pins - or skip the pins and just create their own maps. 

Think through each material carefully and make the decision that is right for YOUR situation. 

Environment Not Working

Always keep in mind the psychological characteristics of the children and teach to them. 


Anytime there are bored or frustrated children in a Montessori environment, the adult must ask, 

“Where are the needs of their psychological characteristics not being met? What should be done differently within the environment to change their attitudes?” 

It is the adult’s role to find those solutions.

Living History

From AMI History album: 

          There is a story that comes from Leicester in England, the name of which is derived from the Latin castra, meaning “camp”.  There is a museum in this area with lots of things that have been dug up from the Roman times onward.  There was a little account in the newspaper told by the curator of the museum:


       Every day before he goes to work, he goes down to the basement and picks up a brick and holds it.  That brick takes him back to the time of the Romans being in the city of Leicester because in the brick is the little print of a child’s foot and lines that must have been drawn with a stick, a child of about two years old.  He was probably amongst workmen making bricks and came upon the brick before it was dried.  He probably took a stick, as tiny children do, and began to draw lines on it.  Some adult must have come along and shooed him off, and he went running, leaving his foot imprint on the brick.

         It is stories like this that make history come alive; this little boy playing at the time of the Romans.  Now that brick is there in the museum, a display-piece of the lives and times of these people.  

History needs to be made visible.  

It is not a record to be memorized.  

It is a life to be lived and to be studied.

Adolescence - Third Plane of Development

There are many questions about how to apply the Montessori method to the third plane of development.

There are no solid answers, since every child is unique as is every situation.

Some universal and general principles to consider:

• the Montessori approach is about respect for life, meeting the needs and tendencies as differently expressed at every stage of life, and a balance of freedom and responsibility
• at every age, we want connection with real life, a building upon the past plane and a foundation for the next - while fulfilling needs and tendencies NOW, at THIS age. 
• preparation for adolescence (in the primary and elementary years) will include fulfilling both the first plane and second plane of development as much as possible; providing skills and intellectual knowledge at the times appropriate for maximize the child's potentials. Art skills, language skills, history studies, cosmic education. 
• The adolescent is looking for his place in the grand scheme of things; has ideas that are grand; yet has crazy things going on with bodily development, so less mental capacity for continued learning at the same rate as elementary. 

Please contribute your ideas! 

If you have children ages 10 and up right NOW - we have an Adolescent Montessori discussion group starting at Keys of the Universe on June 21 - it is not too late to join. 

Later, we will add a discussion group for the general public. See this Montessori Trail post for more information. 

Spiritual Preparation of the Adult: Who Owns the Learning?

Who owns the learning that takes place in the environment?

We want the children to be responsible, to want to be responsible, for something which we put our heart into for their sakes - the environment and the learning that takes place within it.

It can be so hard to avoid turning into a dictator, even a loving, well-meaning one. When we see our children delve into an interest, most of us want to immediately own that interest, direct that interest, provide requirements for that interest. "Oh, my son, I see your passion for Ancient Egypt! I have this book I want you to read through, it has all sorts of Egyptian activities we can do together! We'll do these particular ones here and we'll have so much fun!"

That can turn out great - but it also takes away ownership of the interest from the child. What if the child really just wanted to study a particular area of the culture and create a timeline; but just wasn't yet interested in the art projects and activities? What if he would have gotten to it later in his journey of exploration and been thoroughly fascinated then?

There are times we provide requirements, and give new presentations regardless of interest (this is how a child discovers new interests), but if the passion is already there, we can strew materials, drop hints, provide ideas, and even minimal requirements, but the child should truly own this passion.

It is a tough balance. And there will be more Montessori Nuggets on this subject.

In the example above, we can make a discovery of the said book, "Look what I have found! I thought this might be of interest to you. I'd love to do some of the activities in it together if you'd like. Just let me know!" And let it go.

If it comes down an education requirement, then it should be discussed ahead of time as part of a work-plan, or just done as a group separate from the child's actual exploration and research.


It is the child's passion - let him own it. 

Montessori and the Special Child

Montessori and the Special Child by R.C. Orems is the first comprehensive guide to utilizing the Montessori Method with special needs children, written for the use of parents and anyone interested in this field.

Recall that Dr. Montessori started with special needs children; then worked with typically functioning children living in the inner-city slums.

Interesting that so many still think of Montessori as an upper-middle-class private school phenomenon.

The link is to a downloadable pdf file of the book as it is available on US Archive's website.

Art Presentations in Elementary (and all ages)

Provide art experiences in the basic skills at primary and early elementary. Nothing fancy, but use *real* materials: real watercolors with good brushes to make small designs on small watercolor paper; rubbings; outlining, etc. (in primary, some albums have art in the Exercises of Practical Life and some have it in "Culture").

"The best for the youngest." Give the children the best materials possible and show them how to utilize and care for the materials during this time of formation.

By providing basic skills and assuring they are well learned, with good materials, they can then apply those skills to their later studies, interests and passions.

When studying an ancient civilization or another modern culture, or finding patterns in geometry or mathematics, or just illustrating a work in language, they will have the skills they need to reproduce anything they see.

There is no need to present every art form, if you have provided the very basics.

So we might not have a presentation on mosaics, or on pottery, but they can re-create these things because of the experiences they have had utilizing non-drying clay, cutting and gluing. They can learn from a crafter or a book or a video the additional skills they desire to reproduce an art form for which they might not yet have the skills.

If they have basic folding skills (folding napkins in primary, leading to folding paper - very, very basic), we won't have to present origami to them before they read Sadako and the Thousand Paper Cranes and teach themselves how to make cranes.

And they can create pyramids from paper folding when studying Egypt.

Basic plant skills or other basic art skills: they can re-create their version of the Hanging Gardens when learning about the 7 Wonders of the Ancient World.

They can study artists and art periods under the guise of history, creating timelines, and creating in the style of various artists.

They will extend their art skills in day to day life and studies, without art skills being a separate study.

And they will be able to express themselves when words are not enough - now or in the future, as they prepare for adolescence.


How many pyramid paper patterns can be designed?

Let the children discover this! You've given them the tools: how to fold paper, all the sensorial materials; you've given them the structure, now let them explore! :)

Fractions Material in Montessori

In Montessori, we have several sets of fractions materials:

The earliest material we give the children consist of circles cut from 1-whole through 10-tenths. They can use these primary as well as elementary for sensorial purposes (experiencing equivalencies) and design work purposes (tracing and creating figures).

In primary, they can begin simple operations - no changing of the denominator or going over 1-whole. They can experience all 4 basic operations in this manner. 


In elementary, they continue (sometimes begin) this work with operations and go much further with it, dividing and multiplying fractions by fractions, converting into decimal fractions, and going far beyond simple operations through the use of a plastic material of multiples of each fraction circles (lots of unit-wholes, halves, thirds, etc. through lots and lots of tenths). There is so much they can do with this portion alone, without even going into different denominators.

Why did the Montessoris only go to 10 with this material? Probably because it is the basis of our number system, and because it directly leads into the use of decimal fractions with the yellow board and all those little colored cubes. 

The fact is, there is even more fraction material in the traditional albums:

• Metal squares cut into further squares and triangles, with total pieces in some squares totalling more than 10 (here the children sensorially experience division of more than 10) - while not specifically a fraction work (it is used in geometry), the material still provides a fraction experience. 
• Fraction skittles for use in dividing by fractions
• Clear plastic overlays to help the children abstract beyond denominations of 10; you provide 2 rectangles with lines cutting into 3 and into 4, along with blank transparencies for them to make their own divisions for their own purposes. 
• And as previously mentioned, the decimal fraction material with the yellow board and cubes to represent each decimal place - along with the decimal checkerboard for continuing one's work from the multiplication checkerboard. 

Use caution when utilizing other fraction materials. Consider if it is truly useful or a distraction from the foundation they are building now (going ahead too soon; not fast enough; getting off the path of delving deep); be sure it does not cause them to become too dependent upon the materials such that they later cannot get away from them. 

Many children develop an intense interest in fractions at age 5 or 6; they work with it a LOT (hence the fractions are found in the primary class), and then they step away for a time; and when they come back, they are ready for more. They were building a foundation that, if not filled with distractions, is truly full and strong. 

Trust the materials described in the albums - go deep with them. There is a LOT that can be culled from just the basic materials. Then, if a child has found a true deep interest that even the depths of the material can't provide, then look at your situation, clarify the needs and fulfill them with appropriate further basic material. Anything beyond basic: let the child create - it's his interest, let him own it. 

Remedial Mathematics and Remedial Language

Montessori remediation is a bridge. 

In our society, we think of remediation in a negative light. The child is deficient in some way, his previous experience was impoverished, whatever conclusion one reaches - it is always negative.



In Montessori, it is a simply a bridge to assist the children getting from where they are now to where they need to be at a particular plane of development.

Children new to Montessori at elementary and in need of reading and math skills? They need some mathematics and language skills to entirely gain from cosmic education, but they should still participate in all other aspects of the environment, including the Great Lessons. They should NOT be held back from any other area just because math, reading and writing skills aren't where they could be.

Many times those other experiences are exactly the path they need back into mathematics and language arts.

Give them cosmic education. We fill their other needs so that they are not paralyzed, and we provide experiences that provide an impetus for utilizing those mathematics and language skills.

Meet them where they are.

Follow the child.

Know where the child is and should be (plane of development characteristics, human needs and tendencies - other theoretical aspects) - so that you can follow the child appropriately.

Montessori remediation is a bridge.



Remediation album pages are found at the end of the appropriate albums so that the teachers and parents don't START there; but if you find a child isn't able to keep up with the early mathematics work or is not reading or is not writing well, then you refer to the remedial mathematics or the remedial language sections for JUST and ONLY what the child needs. BUT KEEP COSMIC EDUCATION GOING.
(so many teachers keep the child separated, so this last line cannot be over-emphasized!).

Remediation = Bridge.

Cosmic education - happens for the 2nd plane child no matter what.

:)

Grammar Materials - By Maria Montessori

From Volume 2 of The Advanced Montessori Method: The Montessori Elementary Material:

The study of grammar has finally been arranged in a methodical series of exercises and the material has been prepared after careful and rigid experiment.

Those who read this method will get a clear idea of the teacher's task.

• She has a material ready for use. 

• She need not bother to compose a single sentence nor to consult a single program. 

• The objects at her disposal contain all that is necessary. 

• She need know simply where they are and how they are to be used. 

The lessons which she must give are so simple, and require so few words, that they become lessons rather of gestures and action than of words. 

She goes on to describe the joyful experience that grammar exercises become.

Embellishment - or Doodling?

When most of us went to school, if we drew on our mathematics or language or social studies work, we were punished for doodling.

But in Montessori, we encourage children to make their work in any subject a personalized work of art. When they have done real work that they care about, they want to take their paper representation of that work and embellish it.

Embellish as a Montessori term: encouraged doodling ;)

So your stamp game paper for primary?
There are 7 rows. Enough space for 2 problems (if doing using just 2 terms within a problem), and a row in between. The division paper is longer and turned horizontally, so there are 3 rows - enough for two problems written straight across with a doodle-row in between.
That extra row: is designed for embellishment ;)

Short and large bead frame paper? Embellish around the edges and in between problems to keep them separate.

The graph paper used in elementary for so many subjects? Yep! Embellish with borders and separators.

Think of all the art and geometry a child is getting just embellishing all those squares, let alone the unlined paper he also uses. Repeating shapes; something new in each square; alternating designs; varying the colors.

Children in Montessori classrooms leave behind veritable works of art when they leave a classroom, because they do SO much of it.

Art is an external expression of the inner soul. Let's encourage it, entice it, and build on those skills NOW at primary and elementary, so that the child has plenty of strong outlets in the hormonal and emotional adolescent years, when they CRAVE artistic expression of their very souls.

Montessori Colors - Art

So why is the pink tower pink and the brown stair brown and the red rods red and the number rods red and blue and the metal insets pink and blue - and all those other colors? I don't know why each one was initially chosen. 

Do they matter?

YES!

Can you change them up a bit - well, yes. But why re-think the wheel? There are SO many benefits to the colors as they are. Perhaps Dr. Montessori couldn't define why she made all choices; but she was a careful observer and the colors she chose that she never changed - she didn't change because they WORKED. She only changed if something wasn't working. 

Pink is a calming color - it brings the children into the primary environment at a very young age. It is attractive. If it is not attractive to boys, then we need to look at the programming done at home. At 3, pink is NOT a girl or boy color! If it's a girl color only, then the boys will never learn to write.... 

Because the sandpaper letters (used to introduce writing not reading) are pink too! Usually it is the consonants (the majority of the letters) but I've seen it reversed. Interestingly enough, the metal insets (used for.... drum-roll.... WRITING! -- the first time child a writes with a pencil and intended to focus on writing skills and letter-writing-directionality) are pink and blue too. The writing material coordinates. Hmm. And as it moves into reading, it becomes red and blue. I'm not sure why on that one. 

Why brown for the brown stair? Because it looks so nice coordinated with the pink cubes from the pink tower when doing extension work. If you're going to leave ONE thing natural, this would be it because it still goes along with the pink tower. But really - the solid smooth color is much better for the children than the grain of wood on this one (or the pink tower or red rods). 

Red rods? It stands out clearly against just about any material in the classroom - and since we use the rods as a measuring device, this would be a good thing! 

Oh, but the paint chips! Hint: I know Dr. Montessori originally said she allowed the children to be destructive - but then she spent some time in India. Under house arrest. Just because she was Italian. She went there for 2 weeks and came home something like FOUR YEARS later. Interesting how world history (World War 2 in this case) affects how we interpret someone's books on how we educate our children today. Yep. She changed her thinking AND her teaching on *anything* destructive. Kids like to knock their cups off their high chairs as babies - it can be cute in the moment but it leads to carelessness and destruction (and messes!) later, so we nip in the bud. 

The grain of the wood can detract from the visual impression of dimension that we are trying to emphasize with the children. Here is a YouTube video of a pink tower with the natural broad stair - beautifully done, but the knots on the broad stair didn't need to be there. 

Red fraction circles: the unit is red; the fraction circles and squares are dividing up a unit. 

Red and blue number rods - red is the unit; blue is a nice alternate color from the color wheel; it also avoids most color-blind issues. 

Place value for math and the colors of the number beads are rarely questioned - these seem to make natural sense for everyone. 

 Ask me about other colors!

Numerical Values of Squares by Montessori

Colors of the Numbers
1 - red
2 - green
3 - pink
4 -  yellow
5 - light blue
6 - purple
7 - white
8 - brown
9 - dark blue
10 - gold

Each number corresponds to the bead bars - there are boxes and sets of bead bars for various materials and works.


The numerical value of the squares: 
1, 4, 9, 16, 25, 36, 49, 64, 81, 100

Each square has a corresponding SHORT chain of that number of bead bars linked together to fold up to make the square. (so 8 bead bars are linked together so that the fold up to a square)
The short chain lays flat on a horizontal plane.


The numerical value of the cubes:


Each cube has a corresponding LONG chain of that number of bead bards, linked together to fold up to make a row of squares, with larger links to indicate the end of each square formation.
Each cube also has a corresponding number of squares which, when stacked, form the cube. These lay flat, behind the sections of the short chain laying down.


So when they hang in the bead cabinet, you see the squares of which the cube is composed, hanging down below that cube. When those squares are stacked up, you have the cube.

You can see the squares from across the room.
What a BEAUTIFUL visual! and preparation for later work. 

Grammar Boxes - Colors

Why did Dr. Montessori choose the colors for the grammar boxes? Why don't they match the grammar symbols like they do in primary?

Because if they matched, it becomes a mindless matching activity.

So why use color at all? To aid the child in sorting the multitude of cards into the proper compartments. Also to show during transposing that the "verb" just became a "noun" - without the color, the incongruence wouldn't show up as clearly; the grammar boxes "game" would be less fun, fewer patterns would be noted, and the fullness of the activity would be lost.

All reasons and many more riches are described in The Advanced Montessori Method available free online via Google Books.

Please do not change what Maria Montessori developed - when we don't understand the true depth, we can inadvertently take away the true beauty in the experience.

Freedom and Responsibility

Montessori is NOT anarchy. The children do not get to make every choice for themselves.

Sometimes we describe the freedom of Montessori as being "the adult sets the environment (making the ultimate choices), and the child chooses within this safety." This is accurate, but not the entire picture.


Montessori has been critiqued for being too free (the child has complete choice; child-led only; no adult guidance); and it has also been critiqued as being too restrictive (the child cannot use a material in any other way except the way presented - which isn't actually TRUE but could be done inappropriately in Montessori-in-name-only environments).
We know that neither of these extremes are true, but that is not the point to this Nugget :)


The point is the balance we provide. 



Let's look at some Montessori principles that are, indeed, universal principles:

Daniel Schwabauer (author and teacher of Once a Year Adventure Novel)

A principle of creativity that applies in every field: Boundaries actually inspire creativity, they don't hinder it.

Some people think creativity means a lack of boundaries.

He then quotes GK Chesterton:

G.K. CHesterton said, "Art consists of limitation. The most beautiful part of every picture is the frame."

This thoroughly applies throughout life.

It is healthy to set boundaries for our children. We also want them to explore. We work with them to create the right balance.

Grammar Boxes - when to present

This Montessori Nugget is previously discussed over at Montessori Trails.

Grammar Box Order of Operations:

NOTES:
1) There is no *ONE* right way – just as there is no identical child or experience.
2) There are many wrong ways:

• --don't follow the child
• --insist on waiting far too long (if it accidentally happens, it's fine)
• --insist on presenting too much too fast (unless the child is asking and is obviously capable)
• --requiring copywork of this material
• --following any one procedure for all children

3) the enclosed is based on AMI album pages and training

4) The enclosed is based on a child starting in 1^st grade at age 6, with primary experience. New children at older ages will just work at their own pace – pretty quickly through quite a bit of it; let them take their time wherever needed. 

       4B) The enclosed is a guideline - it is a general guideline so should be flexible enough for most situations. If it doesn't fit for you, adjust it. It's ok :)
5) FOLLOW THE CHILD



Oral and reading introduction as given in primary is ideal - all parts of speech, only receiving an explanation of function, not the name of the part of speech.
If the child is young enough, consider giving the primary style presentations first with the child doing an oral activity followed by the same activities in reading. We hope the children have done sentence analysis in primary as well, but it is not absolutely necessary.

ELEMENTARY - in no particular year, though suggestions noted - just start as soon as possible and move forward:

First - Oral Presentation of the Noun
Second - Grammar Box 2: the article

PARALLEL – keep the initial introduction of grammar boxes in order of one another; otherwise the exercises and personal work can overlap or keep cycling through: Continue to utilize filler boxes in Box 2 Definite and Indefinite Noun Number Noun Gender Classification of Nouns: Common and Proper Grammar Box 3 (could be introduced before the above noun items)      Adjective Command Cards and Classification      Comparison of Adjectives Grammar Box 4 – Verb      Verb Commands and Synonyms Grammar Boxes 5, 6, 7, 8, 9      follow each with appropriate command cards if available for that box After Grammar Box 7:      Personal Pronouns

The above is likely to be year 1, if you started at the beginning of the year and have a child who plugs right along in this and other work; it is very possible and highly likely there is additional work to do in the above areas in the 2^nd year. Just pick up where needed; everything reviews on previous knowledge, and all past presentations are available to the child (this may need to be reminded to them).

The following is almost always 2^nd year, could be end of the first year – and runs parallel with the above if the child is still working with the above --- 

Begin these at the appropriate age, regardless of the above work, just after introducing the noun:

Classification of Nouns: Concrete and Abstract (age 7-7 1/2)
Classification of Nouns: Material and Collective (age 7-7 1/2)
Classification of Nouns: Classification of Abstract (age 7-7 1/2)
Classification of Nouns Chart (all work with other classification of nouns - this is a consolidation)

WHENEVER READY: (could be any year, any age)

Additional Grammar Symbols

Generally, verb tenses will be done in the 3^rd year; with some children starting some of the work in the 2^nd year. Try to assure this work is at least presented in the 3^rd year, and the children may need to finish working in their 4th year. The only real pre-requisite here is that the child has done work with the personal pronouns.
VERB TENSES: (personal pronouns should be done; all grammar boxes are likely presented, even if the child is still working with them)

• Simple Tense: Present
• Simple Tense: Past
• Auxiliary Verbs
• Simple Tense: Future
• The Perfect Tenses
• The Infinitive and Moods
• Negative Form of the Verb

There is a lot going on in Language and in all the areas. Overlapping with the grammar boxes is Word Study; and you may or may not work with the earliest presentations in Logical Analysis before finishing up grammar. Follow the child on this overlap. There is plenty of time for Logical Analysis in 3^rd year and higher, but strong readers who are also adept at the grammar box work, may appreciate the extra challenge of the Logical Analysis work mixed in.

If the children have needed to do remedial language, the grammar box work will pick up orally while they are working with remedial language; but you might wait until they are comfortably reading to start the boxes themselves; sometimes the short phrases of the grammar boxes are a nice little encouragement to work on reading skills; so introduce them slowly, closely observing if they are a help or a hindrance until the child is comfortably reading.

(the child does not have to read these cards out loud – he just has to GATHER the materials – reading aloud is best for a struggling reader AFTER he has proven he knows what the card says (“get a pencil” for example – he brings the pencil, you say “yes” and he then reads the card))

FOLLOW THE CHILD.

Follow the child's interests and abilities. The child is using interjections and conjunctions every day, why wait until age 7 or 8 to introduce them? Why turn a fun interesting game such as the grammar boxes into a tedium of a series of exercises that may or may not be beneficial or any longer enjoyable because they are presented as such?

We want the children to LOVE language, to PLAY with language, to EXPLORE with language.


EXPLORE!

Have fun with it! 

Is not this a common mistake?

Apply this idea to what you know of Montessori, to what you know of the children you have, to what you know of life in general.

A great deal of time and intellectual effort are wasted in the world because what is false seems great and what is true seems slight. 

The Discovery of the Child By Maria Montessori Chapter 14

Elementary Montessori Materials

The main Montessori elementary material is a series of impressionistic charts. These charts are designed to entice the child's imagination without giving too much technical information - enough to fuel an interest to study more without giving all the answers. 

When selecting impressionistic charts - choose ones that are truly impressionistic - not cartoony, not "scientific" - but imaginative, beautiful, and to the point. 

Imagination allows for exploration of what cannot be physically explored or experienced. Our understanding of this power enables us to truly assist the children in our environments. Understanding of these concepts is one of the determinants as whether or not the adult is running a real Montessori environment, as opposed to a environment just using Montessori materials. If the adult does not understand the importance of appealing to the imagination, it is very easy to fall into the trap of using the materials and charts as teaching tools or props. Some teachers may use the charts as visual aids, but that is even not their true purpose. Their purpose is to help the imagination of the child work with the reasoning mind to come to a point of understanding. Our materials and charts are certainly important and do provide concrete provocation of the imagination so the child can go from using materials to understanding something in her mind that was not presented with the concrete materials. The child will come to understanding, to conclusions, utilizing the abstract. 

Practice on Mathematics Problems

Montessori builds repetition into the materials without requiring tedium.

When a child plays a 3-period-lesson game; or language games with the sensorial materials, with the language materials, with the interconnectedness of every area of the classroom and life. From laying out a Far Eastern place setting to the continent folders of that region - in primary; from all the timelines of elementary to all the peoples and events throughout history - OUR history.

Everyone seems to accept these sorts of connections and repetitions and reinforcements with ease and peace.


But what about mathematics?

Golden bead material:
Addition - when a child is adding 2957 + 3495 - he is really doing 4 addition problems. More when you consider the carrying.
Subtraction? Same deal. 4824 - 3604 - the child has 4 subtraction problems in ONE.
Multiplication? We start with numbers such as 1242 taken twice. And quickly move into 4958 taken 4 times. LOTS of carrying.
Division? Same idea.

These are 4 year olds.

As they work with the materials, they get the patterns because they're not just writing it out, they're DOING it. Then they have the stamp game, bead frames, racks and tubes for short division and other tools to continue working with BIG numbers; and the memorization boards to start memorizing the basic math facts in each operation.

Let's consider a short division problem: 5,496,284 divided by 2. There are SEVEN division problems in that one problem alone.

And that is primary level. 


By elementary, they are getting into long division, intense fractions work, decimal fractions, squaring and cubing - and again, we are working with real numbers with real materials so that the child, even by manipulating the material, gains an understanding of what is going on.

If a child starts in the middle of the elementary with no Montessori background, he still gains from the experience, because he is still working with the material, surrounded by children who already "get it" and who are joyful to help him just where he is, without doing the work for him. Bank game, long division, and fractions are fantastic materials for new-to-Montessori elementary children.


Repetition is built in. Use the materials; use language and other games to get the materials out and put them away; provide real math problems; invite the children to think of their own (they always want to work with something harder than we provide anyway - LET them!). And they have joy in their work.

Binomial Cube and Trinomial Cube

What do these represent?

First, let's consider the lid of the binomial:
Look at each side and label each section a or b - so the length of each side is a + b
To find the area of the whole thing, we would multiply the length times the height (a + b)*(a+b)
We can also write that as (a+b)squared

Ok, so let's multiply that out - we end up with these pieces:
a-squared + ab + ab + b-squared

And that is what we have: a red square, 2 rectangles representing a times b, and a blue square.


But we have a CUBE.
So we multiply length by height by depth - (a + b)*(a+b)*(a+b)
Multiplying this out, we end up with a component for each prism within the binomial cube box.

Each piece represents a mathematical principle. 




The same concept applies for the trinomial cube, except there are 3 factors: a, b, c


As the children proceed through other mathematical experiences, they will begin seeing these same images in SO many other places. Because these principles surround us.

And most of you only remember those formulas from high school algebra, right!? ;)

Cursive or Print - 4

When choosing between print or cursive at any age, consider Montessori's own words in response to a popular method at her time of teaching capital print letters first:

This method for teaching one how to write illustrates the tortuous ways we follow in teaching because of our tendency to complicate matters. It resembles the tendency that we have to put a high value only on complicated things. ... Will not a child have to make an effort to forget printed, in order to learn cursive letters? And would it not be simpler to begin with the latter?

The Discovery of the Child by Dr. Maria Montessori, chapter 14

Third Plane of Development - Characteristics

Some online resources for Adolescence:

Comparison of Late Childhood and Adolescence

Third Plane of Development

Adolescent Characteristics

Characteristics of Early Adolescence

Calculators in Montessori

What calculators do we use in Montessori?

We have a lot - at various ages - but here there are all lumped together:

• bead bars
• someone else's eyes
• built-in control of error (anything where the pieces won't finish going in if one answer is wrong)
• figuring the problem two ways
• the human brain (which is mathematically designed)
• experience
• intuition developed through experience
• studying mathematics in history and culture
• graphing calculator - middle school; could be introduced as a future tool in upper elementary

Montessori mathematics develops perception and intuition; the children learn their facts through the consistent use of the Montessori mathematics materials. The fact is, they don't *need* a calculator. 

Any child or adult with experience in mathematics can figure out how to USE one. So it's not about "teaching them the tools they'll need in the future" - they'll figure it out when they get there. 

Graphing calculators are a handy tool - but to gain the maximum benefit, sufficient understanding of the concepts must be applied. Graphing calculators can be useful in middle and high school. Perhaps introduce in upper elementary, but it's not necessary. They have so much else to learn, why hinder them with using a tool that just gets in the way?