A Study - Outcomes of Montessori Fidelity

I recently had a chance to read this article:

Preschool children's development in classic Montessori, supplemented Montessori, and conventional programs
Angeline S. Lillard
Department of Psychology, University of Virginia, Charlottesville VA 22904-4400, USA


http://faculty.virginia.edu/ASLillard/PDFs/Lillard%20(2012).pdf


I put forth a particular paragraph that stands out for me:
It really says a lot about the Montessori Method - and the article goes on with more!

Theoretically, using Montessori materials would seem to exercise many aspects of executive function. For example, one of the first Montessori materials with which a child is presented is the Pink Tower, a set of 10 wooden pink blocks ranging in size from a 1-cm cube to a 10-cm cube, with each cube 1-cm larger on each face than the previous one. In using this material, the children's task is to carry the cubes one by one from a display to a rug that they have previously rolled out on the floor, then rebuild the tower. To do this task entails planning. Second, each time a child chooses a block, she or he must do so with reference to its relation to all the other blocks: Is there another one in between the size of this one and the last one placed on the tower? This step requires working memory. Third, the child must inhibit the prepotent tendency to grab the closest block, and fourth, the child must pay strict attention to how he or she places each block on the one below it, creating a symmetrical tower. After building the tower, the child takes it down, returns the blocks to their stand by the shelves (in the proper order), and then tightly rolls up the rug and returns it to its place. This step requires flexibility and task switching. Consider the difference between this and engaging with ordinary blocks. With ordinary blocks, one can do anything, without necessarily having any set plan, and one does not have to think about the blocks in relationship to each other. A preschool might not have a requirement that children put items away right after use (instead, there often is a single clean-up time right before going home), and there may well be no set way to arrange blocks when returning them to their place (often, they get put haphazardly into a large basket or box). The executive function demands are much reduced, and this difference in executive function demands applies across many other activities as well.

Music is Part of our Lives

Music is part of our every day lives. It is not something separate, to take to a different room and only experience with a "specialist". 

Music must be part of your everyday natural environment, incorporated into your classroom. 

In this regard, music is nothing special – it is a part of all of us. 

It is something every child should have a firm knowledge of, whether they take special instrument lessons or not. 

Yes, it can be noisy if the bells and tone bars are ringing throughout class, 

but it is well worth it. 

Montessori Cube Primer

There are many cubes in the Montessori environments :)


Found in Primary (3-6):

Geometric Solids

Bead Cabinet: cube for each number 1-10

Golden Beads: cubes of 1,000

Wooden Hierarchical Material: cubes of 1,000 and 1,000,000

Binomial Cube

Trinomial Cube


Each of those items are found in both primary and elementary.


What is just in elementary?

Power of 2 Cube

Hierarchical Trinomial Cube (also called "Arithmetic Trinomial Cube" and "Algebraic Trinomial Cube" - all three are the SAME thing) --- there is a story called "The Three Kings" that connects the Trinomial into this new Trinomial with new colors and new concepts.



But no matter the environment, the Trinomial Cube cannot be substituted for the Hierarchical Trinomial Cube - because they teach different things and are colored differently. Sorry!   The good news, the Hierarchical Trinomial Cube isn't just TOO expensive. ;)

Montessori Theory

doing a puzzle without a frame
(tessellations, that is the point;
Montessori details without the "big picture" - not so much)

When a person selects to attend a full-force Montessori training, they have a list of required readings. See this Montessori Nugget for a sampling of the required reading lists throughout AMI training centers in the United States.


And yet, every one of those training centers still require a theory album - to be created BY the trainee and submitted for review. Because the readings themselves don't yet bring it to a practical level of the day-to-day application of the method.

Yet there continues to be a resistance to accepting the importance (the crucial-ness) of theory album - at both primary and elementary levels. I would love to hear WHY this is the case :) Please comment if you have some input! Please share positive experiences, negative experiences, why you might not really "care" about having "another" theory source if you have/read all the books; or why you think some people might still be opposed to theory albums.


For further information:

• Please see this Montessori Nugget on the importance of theory albums.
• See this Montessori Nugget for the typical table of contents for primary Montessori albums and for elementary Montessori albums. 

Follow the Child

Let's juxtapose a few Montessori principles to see what they reveal :)

Follow the child.

Freedom and responsibility.

The child is the constructor of the man (loose translation).



Yes, we follow the child, but if the child is leading us toward a fugue, it is OUR responsibility to re-direct him. Immediately in the case of bad habits and of danger (physical, emotional, spiritual).
That applies to both primary and elementary - and all ages actually. We do NOT let babies stick their fingers in outlets, nor toddlers to stick knives in outlets - but we do allow elementary children to build electrical circuits - because we have given them a strong foundation in safety and good habits. THUS, the child's work is ENHANCED because we provided boundaries.


Freedom and responsibility. Your freedom ends where mine begins and my freedom ends where yours begins. We do not let babies pull on mother's hair just so they have freedom (that is actually called license and Montessori was adamant that license is NOT acceptable).
They learn these boundaries that we provide for them, so that later, let's say in elementary, the children learn that they have freedom to explore their interests, AND they have the responsibility to be genuine in their work - not just busy work; they also have the responsibility to meet any local educational standards.

Ultimately, they have societal freedom and responsibility as well. We can go anywhere we want on public sidewalks, but we do not have the freedom to walk through other people's gardens and yards without permission. We have freedom to visit local nature centers, and the responsibility to follow the rules set there. They have freedom to do many things in this world, but must always be aware of the local rules and laws and customs so as to be respectful of others and be a responsible human being.


The child is the constructor of the man - but it is the other adults who must provide the appropriate tools - whether these are material-goods or metaphysical realities.


A child who has difficulty telling the truth, cannot connect with reality, has imaginary friends to the detriment of making and keeping real friends - this child has a fugue and Maria Montessori provides the solutions for working these out. We do NOT follow this child down Imaginary Friend Lane, thereby keeping him from making real friends.

A child who just LOVES workbooks and worksheets should NOT be given a curriculum that is nothing but workbooks and worksheets. These things do not help the child to THINK, to CONNECT, to INTERACT. They can have their place, a very small place in the academic Montessori - and there will indeed be "worksheets" in the real world (tax forms come to mind!) - so knowing how to use them is fine.

A child who just LOVES candy, should NOT be followed to candy dish at every meal, in between every meal. A few small treats in balance is good for the soul. Too much candy leads to unhealthy mind and body AND soul.

What about a child with a keen academic interest and the work is truly deep? SURE! Keep it GOING! But don't let him stall there either. Slowly (slower than usual) still be providing other presentation, other learning. This will only serve to ENRICH his current work, encouraging new connections and sometimes integration of the new material with the current/past. It also provides additional work choices as the first main interest peters out. If a child steeped in nothing but ancient history studies that for 5 years and never gets ANY stories, tidbits, quick presentations on his local country's history - and never touches a lick of math? Is that healthy for the child? No. He's not a "literate citizen" at that point. He doesn't need a LOT of the other stuff when an intense interest is at hand - but does need continued "food" - continued balance - to promote continued studies. We are talking a small part of the week to present a few new things - nothing major - nothing distracting - just a bit of "here is something else you can save for later". But if we avoid adding in these little bits, we have an undernourished child.

We must also trust that children are capable of multiple interests at once as well. This does not mean we overwhelm them - it just means we observe - and respond. Continue our stories. Continue planting seeds so they have LOTS of time for germination as the child works to construct himself.





Follow the child.

Freedom and responsibility.

The child is the constructor of the man (loose translation).

It's just not working!

"it" - what IS "it"? That is your first question. Is "it" a subject area, certain materials, the environment, etc.

Your next question (and where you will find your solution) is "what foundational piece is missing for "it"?"

NO PROGRESS can truly be made, in any sort of joyful or even efficient manner, if the
FOUNDATION is MISSING. hint-hint ;)

If the problem is adult preparedness - you are the only who can fix that ;)

If the problem is the environment - consider what obstacles are in the environment that hinder the child's natural and proper development? This page has some ideas on that.


Let's look at the different subject areas regarding the foundation:

Mathematics: 
"it": the children are just not enjoying mathematics, they are not really working with it, they are either playing with it or ignoring it.
PRIMARY: Go back to the numerals 1-9 and 0. Play the basic change game with them. These are the foundational pieces for EVERYTHING in mathematics in our society. They don't even NEED the teens and tens (this is just vocabulary, not directly "math" - it is language).
ELEMENTARY: Well, same thing. Go back to make sure they understand place value. But one more thing: do you have cosmic education going? Did you tell the Story of Numbers? Do you have other stories in your environment that utilize mathematics? For younger children, Sir Cumference is great; Life of Fred for several ages; stories on early mathematicians; more.....


Geometry: 
"it": the children are not learning the names of the shapes, not exploring with the geometric cabinet and solids, or the volume work and geometric sticks.
PRIMARY: Go back to the early geometric cabinet presentations and begin again. Make it a GAME. Assure that you have albums with exercises for the 5 and 6 year olds as well. This will help keep you on track giving those early presentations early ;)
ELEMENTARY: Go back to the early presentations, and add in MORE nomenclature (roots words, language connections). But also - again - Cosmic Education - did you tell the story about the Ancient Egyptians? Do you tell stories of the early geometers? Do you have the children exploring shapes in the environment?


History: 
ELEMENTARY: COSMIC EDUCATION. Get those Great Lessons going; repeat them as needed and at least once a year!
Do you have and USE the History Question Charts?
Do you have timeline paper in various formats available, with resources on hand to entice interest?
Are you making trips to the library, to museums, to other outings, for further experiences?



Language: 
"it": the language area just isn't working. The children aren't really writing and/or they aren't really reading. There are children about to go elementary who just can't or refuse to read. There are elementary children who can't read, don't want to read.
PRIMARY: Go back to the beginning of the language album. Lay that strong foundation. Sound games - environment games - vocabulary building - experiences to talk about and eventually write about.
5 year olds should be reading. Period. There are VERY FEW children who cannot read at age 5, with ease and joy, when given the right tools at the right time. Those remaining children will read around age 8. Not to lay a guilt-trip! Just look at the tools provided, start at the beginning and work your way through. At this point, each step does not have the 100% perfect to move on because frankly, a 5 year old still working on the sandpaper letters is not having his/her developmental needs of the moment met (but still needs those foundational pieces to get to the point of access to materials that DO meet current developmental needs).

ELEMENTARY: Use the "remediation" sections in the language album. COSMIC EDUCATION: Story of Communication in Signs in particular - but ALL the Great Lessons. Give them books to read they WANT to read (but not junk books either - show them you value them by giving them real literature).
Remove the audio books if elementary children are not reading. Or listen to the first chapter and invite them to read the rest themselves. Or take turns reading a page or a paragraph.
Get them started on the grammar boxes - most of the words are basic enough, and the phrases start small and slowly build.
DO NOT MAKE THEM READ ALOUD. Provide written commands or other reading material that requires some action such that you can assess comprehension. And have some reading material that is just for enjoyment, so they're not feeling "tested" all the time.
PS Dr. Seuss books are great for reluctant readers!


BUT THE ENVIRONMENT IS NOT CARED FOR! 
Go back to the beginning of the year. Check into Grace and Courtesy.
Do the children know where the cleaning supplies are located?  How to use them? Who is responsible for the room? (hint: the children are!)
Control of movement (walking on the line, silence game) - is it being done? Daily? Really, truly daily???
How are you the adult behaving within the environment? Graceful movements? Two hands to carry one object? Completing your work cycle? If you said "yes", are you absolutely sure?



The point in all of this - if "it" isn't working, and you desire true success, don't just finish the album and mourn, stop where you are, go back and re-build that foundation. Likely a bit faster this time, but make sure all those pieces are there!

Planning Presentations and Materials

In non-Montessori environments, the tendency is to push towards minimal planning. In this way, the children are not given too much, too fast; parents and teachers do not feel "overwhelmed" if the plans weren't completed in a set timeframe (because now we need to move on to the new set of weekly plans, i.e. in an environment that centers on weekly themes).


WELL....

In Montessori we over-plan so that we are always prepared to meet a child's interests and needs.

Elementary: We don't know which presentation is going to incite a deep interest, so we present and present and present until something clicks - and then they are off. And we might not then present something new for several days - or we'll still drop little plant stories here and there for example, or recall a language-deep child back to geometry with a story about Pythagoras - just to keep it fresh.
The albums are not necessarily the easiest to organize by ages, because of the wide differences from one child to the next, but it is possible to focus on the most likely possibilities for one year at a time.

Primary: We prepare ahead, but know that we will present and back-off. I love how primary albums can be reorganized into groups of 6 month spans. Within those 6 months, the child has a lot of space to explore but the adult can better focus for planning purposes.

But we also have to balance that over-planning with the recognition that a child's interests might take off and we set aside our plans for a time. Therefore *our* plans have no date on them. The elementary child's work-plan might have dates, and there is where we help to work through the planning process of what MUST be done within a time-frame and what can be put off while a new interest is being explored.

Primary Montessori Materials LIVE in the Elementary Classroom

(updated - 11/26/12 - math section!)

There is a sub-set of Montessori materials that is utilized at both primary and elementary. The presentations are different; the teaching concepts are different - and the material proves just how deep it can go!

Teacher in one level or the other and want to know which materials overlap levels?
Homeschool parent transitioning from primary Montessori to elementary Montessori?
Curious for another reason as to the depth of the Montessori materials?

Here goes!

Some items can be very useful if you still have them in elementary - the children may do further exploration (pink tower, brown stair and the like come to mind). But core materials?

Keep the following items:

Exercises of Practical Life: 

• Primary has care of the environment items on trays on the shelves; elementary has supply shelves, with empty trays to gather what they need. Same items - set up is different
• Many of the EPL supplies can also be used in the geography area in elementary for demonstrations and such.

Sensorial: 

• Geometry Cabinet (geometry in elementary)
• Constructive Triangles (geometry in elementary)
• Puzzle maps of the world/continents (could be used in elementary, but don't buy them just for elementary)
• Binomial Cube (mathematics in elementary; geometry in adolescence)
• Trinomial Cube (mathematics in elementary; geometry in adolescence)
• Bells (use initially in elementary, then transition to tone bars; but don't buy them if you are just starting elementary - just use the tone bars)
• Other stuff is great to have on hand, but if you must be budget/space-conscious, it is ok to let go ;)

Language: 

• small movable alphabets (at least 3 colors needed in elementary; letters and punctuation on tiles/cardstock and stored in a divided box - like a tacklebox)
• wooden grammar symbols (multiples of each symbol in a box)
• (NOTE: reading analysis material from primary is organized different, but you could use most of the same components and add the charts - see this post: Reading/Sentence/Logical Analysis)

Language Extensions: (AMI organization; other albums this includes biology)

• Plants and Animals
• (could keep the nomenclature material, but add more components to it - definition strips, more extensive definitions, blank material for the children to create their own)

Mathematics:

• Golden beads (9 thousands, 45 hundreds, 45 tens, 45 units is all that is needed for elementary)
• Bead cabinet (all short and long chains, cubes, squares)
• Fraction circles (metal circles)
• Large bead frame (short bead frame is primary; if starting your child in elementary, only use the large bead frame)
• "Decanomial bead bar box" (the set that has 55 of every bead bar, 1-10 - some boxes only have 45, some only have bars 1-9 - these smallers are handy in classrooms; not so useful in homeschools)
• Division with racks and tubes (short division in primary; short and long division in elementary)
• (additional math note: if you purchase the elementary negative snake game, you'll have all you need for the primary level snake games)

(note: this list does not include items that if a child "missed" primary, they might find useful as a bridge into elementary - such as the land/water and continent globes - useful but ok to use an on-the-fly adapted presentations with less expensive and spacious materials)



Let me know if I missed something :)

UPDATED THE MATH SECTION! (decanomial bead bar box --- and short/long division)

To Be

Children need free time.

Large blocks of free time.

To be bored.

To explore nature.

To find themselves.

To be in silence.

To be in company with others.

To be.


So do adults.


Make that time.

Trinomial Cube - LONG Life

I would like to introduce you to a long-time companion of mine - the Trinomial Cube:

The "big" cube in primary!

The Binomial Cube
The small guy in primary

He has a few buddies: 

The Algebraic Cube - Elementary

Power of Two Cube - Elementary

Binomial and Trinomial are beautiful puzzles in the primary environment. But the Trinomial - he goes places! While the binomial is also useful in the elementary class, the trinomial does most of the work. 

(a + b + c)^3 

The children are learning this sequence, sensorially at age 3 1/2, and it builds and grows from there. 

The children continue to use the material sensorially in elementary, then they start doing some squaring work with the lid (the lid has (a + b + c)^2). 

And one day, they hear of the Story of the Three Kings. Oh, no,  not THOSE 3 Kings - the OTHER Three Kings. These Kings: A-Cubed, B-Cubed, and C-Cubed. They were marching along happily in procession - and... there was a REVOLT! That revolt overturned the order of the procession! It was chaos! It was order! And the children learn algebra! And cubing!

And the Trinomial Cube has a new lease on life! 

And the children work with the trinomial cube; then expand into the algebraic cube; finally they work with the power of two cube - it all began with the trinomial cube and his little brother the binomial cube.

But the children have moved on. And the trinomial cube appears done. A wash-out. Used up. It's all over for him. 

----------------------------------------------------------------------------------

I recently read through an older NAMTA journal, on the topic of teaching geometry in adolescence, using Euclid's Book of the Elements (all 13 volumes are currently available in a set of 3 books).  

Guess who makes an appearance! The trinomial cube is truly an ever-present material for the children in Montessori environments. And a credence to the AMI stance that we don't need "more" materials - we need to go DEEP with the materials!
ETA: The adolescent Algebra Album available through NAMTA - lists it as one of the necessary materials ;) NICE! 

Just looking at it, consider for yourself: how deep does this material go for you? What uses could you see for your children, even if you don't have all the album pages for all the levels? What could your children experience with just this one piece of Montessori equipment? 

Cosmic Education at all Planes: An Aid to Life

Margaret Stephenson as quoted in NAMTA Journal 23:3 Summer 1997:

Underlying the Montessori idea of "an aid to life" is her vision of the child as the cosmic agent of humanity and its survival. The theme that runs through the four planes is putting the child in touch with the cosmic task of the world and its inhabitants in a manner that is fitted to the psychology of each discrete plane. If a child does not get the connection in one plane, he or she cannot move on to the next plane fully prepared. 

(end quote)

The child does move on to the next plane, just not fully prepared.

What is given at each plane:

1. This connection is made subconsciously yet concretely through the materials. 
2. This connection is made more consciously, through approaching Cosmic Education as a drama, not as a lifeless curriculum. This drama is the vision of Montessori. If this drama inspires the child of the second plane...,
3. then when that child reaches the third plane, he or she will be able to ask, "What is my role in this drama?"

Ms. Stephenson again:

Going Out is also important to give the Elementary child a complete vision of the universe, and a particularly valuable aspect of Going Out is community service. This is the basis for the service we've been talking about for the adolescents; it needs to begin earlier than adolescence (in order to reach its fullest fruits). 

Keys at Every Plane of Development

Consider how the following words apply to EVERY plane of development. 

John McNamara as quoted in NAMTA Journal 23:3 Summer 1997:

Like I did when I taught at the Elementary level, I am still trying to help the students' passage to abstraction, to stimulate their interest, to capture their imagination, to meet their need for group work, to respect their growing moral awareness, and to give precise keys so they can proceed to make discoveries on their own. 

He refers to the adolescent age, but how does this apply to every age?

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.

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.

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.

Montessori Large Bead Frame

The small bead frame and large bead frames (sometimes called the "Montessori abacus", which is  not entirely accurate, but it sure looks like one!) are a necessary yet often overlooked piece of Montessori mathematics material.

Large Bead Frame -
goes up to 10 million

They each allow for addition, subtraction and long multiplication and are a step towards abstraction in the process of carrying into new categories and in exchanging.

While this material can be used for 3 operations, the main focus of this material is its teaching of *Long Multiplication* - this IS the Montessori material that teaches all the steps in proper order. Other materials either prepare for it, or expect a child to have this experience tucked away already.

The small bead frame has four bars, going into the thousands (with 10 thousand-beads, it can go to 10-thousand).

The large bead frame, with 7 bars, is the child's first experience going into the MILLIONS. And they LOVE it!

The children also utilize lightness of touch, visual organization, proper order of steps, which is preparation for the division with racks and tubes (test tube division) which starts with short division (1-divisor with a 4-7 digit dividend) and goes into long division (2, 3, or 4-digit divisor into a 4, 5, 6, or 7-digit dividend).

Many primary level children will get to this work and the short division with racks and tubes - generally between 5 1/2 and 6. Whether they get in primary or not, this material is heavily utilized and crucial in lower elementary on their work with long multiplication.

The main thing with this material is the connection to the writing. There is long bead frame paper that goes along with this material, for the children to begin their writing out of long multiplication - one sized for the short bead frame; the other sized for the large bead frame.

They are introduced to the bead frame with nomenclature first; then addition and subtraction just to get a feel for how it works and how the writing on the paper works.

Then they are introduced basic multiplication - 52 taken 3 times for example. They are writing the steps on paper and doing it on the bead frame, so they understand what they are writing and when they are exchanging, WHY they are exchanging or carrying. At this point, they might do a number such as 54 taken 3 times.

Once they are comfortable, they are given longer and longer multiplication examples, until they are making up their own (our goal is for them to create their own numbers, so that they own those numbers and will pay more attention to how they work, what are the patterns, what are the results).

And they begin to add zeroes into their writing.

Before you know it, they are writing out long multiplication problems without the use of the bead frame or a calculator.

AND they are prepared for the greater task of long division!



UPDATED TO ADD due to a small number of private messages received: Yes, there are a couple (?) of album sets you can purchase that do not introduce this material until the 3rd year of lower elementary and seem to indicate that it is an upper elementary work. AMI albums sit this material firmly at 5-8 years of age for normally functioning children, with the children working with it as long as they need (through any age). The fact is, upper elementary children are getting "less fiddly with the beads" (as quoted by one of my AMI trainers) and should really be far beyond the introductory stages to this material if they have had Montessori math since at least 5 1/2; still working with it as needed, but not JUST receiving it at age 8. If just getting it at age 8, they won't be doing LONG division until at least age 9, perhaps even 10, long after kids in the public schools have already started it; and Montessori has prepared them from the time they were 3 if they've been with Montessori that long - even starting at 5 1/2, there will be minimal slowing down in the early mathematics presentations. The big question is, if they're not doing long multiplication stages and long division stages at age 6 and 7, what have they been doing?
NEW children (starting Montessori after age 6 1/2 or 7) and children with severe learning impairments will follow a later schedule. THAT IS OKAY - but they are the exception and their needs should be considered when "Following the Child".

Montessori Music - An Article on Maccheroni's Book

Man's Spiritual Expressions: Language and Music, 1956

(click above)

This article was written in 1956 by Mario Montessori, Maria Montessori's son,  to announce the publication of one of the booklets made by Anna Maccheroni about the Montessori music material.

OUTLINE: 

• MAN'S SPIRITUAL EXPRESSIONS: LANGUAGE AND MUSIC
• Some facts about small children
• Dr. Montessori and the child.
• Music for children

Click above or here for the article. 

Normalization - Walking on the Line and Silence Game

Walking on the Line is the point of departure for the process of normalization. 

It brings children into a state of normalization.

It should be done consistently from the beginning of the primary experience, and is useful even in elementary.
(have ADHD kids? set up a permanently available walking on the line)


The Silence Game is the point of arrival. 

It cannot be done by children who have not yet been prepared.

It should not be done on the first day of class with new children. Some of the children can do it, but it's not because they yet have a state of normalization. They just know to obey the new teacher. Gain their trust first, because we want them to be open to a light touch on their shoulder or cheek; this sort of touch is not appropriate for a new adult in their lives.


Have a class or a group of children with a mixed state of readiness? The ones not ready can take a short walk with an assistant (or an older sibling) while the other children play the Silence Game.

Normalization: The Signs

Characteristics, or signs, of Normalized Children: 

1. Love of work, love of activity
2. Concentration on an activity
3. Self-discipline
4. Sociability or joyful work

All four characteristics must be present for us to say that a normalized type common to the whole of mankind is appearing—no matter how brief the appearance of the characteristics. The process is usually invisible to us because the process of normalization is hidden by characteristics not proper to the child. (The Absorbent Mind, p. 202)

Normalization in a Nutshell: Definition

Let's define our terminology so that we are discussing the same thing when we use particular words:

Normal: how things typically are in any given situation. This sense of normal can be good or bad.
Synonym: Typical. Ordinary. Usual. What is expected based on past experience.

Normalized: the state of being complete, whole, reaching one's potential, utterly fulfilled. This sense of "normal" is a beautiful and wonderful experience!
Synonym: Peaceful. Fulfilled.

Normalization: the process of becoming normalized.

Normalization is the single most important result of our work. 

(The Absorbent Mind, p. 204)