Wednesday, December 22, 2010
Children's apps on iPad
I initially saw an article about 5 classic children's tales which were converted to the iPad (http://mashable.com/2010/12/12/childrens-books-ipad/) and followed it to watch the video of the two year old playing with the iPad (http://mashable.com/2010/04/06/2-year-old-girl-uses-ipad/) I've spent a bit of time to look at several applications designed for toddlers/preschoolers on the iPad. Many of them have or will be converted to the Android platform though. There are an ever increasing range of tablets available on the Android operating system. Although these applications below are free, many of them have a purchased version as well.
Lewis Gray indicated that his kids use his ipad all the time- mostly for UTube. "In addition to that, Matthew likes all the sports games, from Bowling to Arcade Hoops, Soccer and baseball. Both like Doodle Pad for drawing and we have another app for learning animals' names."
However, there is research that is currently showing that some of these apps are shown to be educationally beneficial.
"Are Preschoolers Learning from Mobile Device Apps?
A recent report from The Joan Ganz Cooney Center (http://www.joanganzcooneycenter.org/Reports-27.html) at Sesame Workshop documents the growing trend among young children to engage in play sessions using applications downloaded to mobile devices such as iPhones. The sessions, most often occurring when the devices are passed to the kids by siblings or adults, last between 5 and 20 minutes and consist primarily of playing games. The report says there is evidence the kids are learning, citing research on the Martha Speaks: Dog Party and Super Why apps that focus on literacy skills. Positive effects were found for children as young as age 3. The report also provides guidelines for app creators and family members with young children."
Source: NIEER newsletter.
1. "Alice Lite" for the iPad (listed in the Mashable article)
This app is very well done. The designers have essentially recreated the book and enhanced it. The enhancements take advantage of the functionality of the ipad. For example- on page starts with the text "So she was" the "SO" is half the page and a pocket watch is hanging from it. It can be moved by touch, hangs in orientation with the iPad, and swings with movement. Most of the embedded enhancements can be moved by touch.
Primary concern with this book is the ability to move objects in random directions by touch. It seems to be a very abstract ability for young children, especially since the object "follows" the finger.
2. "Peter Rabbit"
This is an electronic book created on the pop-up of the book form. The pop-ups/ pull tabs move in an identical pattern to the book. It is very similar to an actual book.
3. "Alice HDO"
I'm not sure if this is related to the initial Alice. It is a detailed hidden object picture game. Touching one of about five objects that are listed on the bottom of the screen causes them to fly forward and then disappear. There is no audio component to the words, only music. I'm not sure of the intended audience. The words are elaborate and sometimes archaic. For example - "Hooka, camomiles, diamond-ring"
4. "First Words Sampler" (Possibly shown in the video with the two year old)
There are simple words combined with cartoon images. There is audio component that pronounces the letter name when touched. The letters are to be dragged to their matching positions, and then the word is pronounced. The image spins and enlarges. This is a very basic application and not consistent with Montessori principles. It might help to increase vocabulary, but I doubt that any child that is able to play with a tablet is lacking opportunities for vocabulary development.
5. "Snake"
Puzzle matching game. The pieces must be dragged into position almost exactly in order to fit the puzzle. 1/4 inch is not accurate enough. The puzzle pieces can not be rotated.
6. "Animal Shape Puzzle"
This starts with a full screen of advertising and moves to a "Start" that is changing size and shape. It is also a puzzle matching activity. These are cartoon pictures of animals that are then segmented into puzzle pieces. The pieces can not be rotated and requires a high degree of accuracy in placement.
7. "Smart Baby Colors"
This application teaches colors through an initial screen of color swipes and the associated word. It is then followed by a realistic picture of an object in that color upon screen touch. It repeats with different colors. This application is similar to a book except for the audio component.
*My conclusions.*
Many of the best applications actually resemble a book. What are the benefits and disadvantages of moving to electronic books when this is something that is happening currently in the adult world? The ability of the touch screen to move objects and defy gravity without an obvious connection is something to think about. Puzzle piece and matching games do not allow a child to feel the piece or rotate it. This will diminish the ability to reason in three dimensional space. Other uses of the apps vary from videos to essentially traditional computer games uses.
Tuesday, November 2, 2010
NCLB and the 21st century
- Standards based education reform based on standards and standardized testing. Standards and tests were set by states. (This is changing as states adopt the National Core Standards)
- Considered to be "high-stakes" testing because if schools did not show student improvement federal funding could be jeopardized as well as other punitive measures.
General Goals of Education for the 21st Century
1. Basic skills mastery. This includes general content and is relevant to job preparation at all levels.
2. Critical thinking
3. Social skills and collaboration among diverse audience.
4. Development of a work ethic.
The testing requirements of NCLB have led to increased teaching time devoted to reading and mathematics. There have been very little improvements in reading and modest improvements in mathematics. Both subjects are frequently considered to be very dull and tedious with drill and kill approaches according to research with both students and teachers disliking them. Education time for science, social studies, art, music, PE, recess has dropped or even been eliminated. These changes are more pronounced in schools with a higher poverty level.
Student performance on standardized tests does not measure critical thinking skills. In fact, it's rarely taught. Project-based, inquiry-based, and problem- based collaborative projects are often not part of the curriculum. An emphasis on test scores has been shown to increase drop-out rates rather than increase a work ethic.
Thursday, September 16, 2010
Announcing the Montessori Book Club- with great delight!
This book is available online and free from Google books. It was published in 1915 and contains some unusual insights into what the early practice of Montessori education was like. One example was that the initial color tablets were spools of silk thread. Ms. Baily went to Rome in order to study the results of Montessori education. She observed the children themselves as well as had the opportunity to meet with Maria Montessori and listen to her lectures. It is primarily a study of the children of a Montessori environment. It is easy to read and very descriptive.
Maria Montessori: Her Life and Her Work by E.M. Standing
This book is technically a biography, but it contains a very dense summary of Montessori practice and philosophy. E.M. Standing worked closely with Maria Montessori in the writing of it and she read much of the manuscript. Although not written by Maria Montessori, much of it sounds as if it could be her words. This book is heavy on philosophy and includes elements that I have not previously seen in other books such as the sensitive periods for "Learning Good Manners" and "Grammar."
Amazon review
"This is the book that opened Montessori's theories and achievements to me in a way her own writing never managed to. The Standings are not unbiased, having worked with Dr. Montessori --- but they do an excellent job of weaving Montessori's life story with her teaching discoveries and methods. If someone is interested in learning about the Montessori method, and can only read one book, this is the one. There is another biography by Rita Kramer that looks good, but I haven't gotten to it yet. Good luck!"
Dr. Montessori's Own Handbook by Maria Montessori
This book is written by Maria Montessori and is easy to read. The Handbook is more about the didadic materials and the prepared environment rather than philosophy although any discussion on the Montessori method includes philosophy. There are extensive descriptions of the Children's House, sensorial, language and mathematical materials.
Amazon review
"This short book is like an Army basic training manual. Montessori teaching methods are described in detail, like recipes in a cookbook. An interesting section on food for children recommends large amounts of fat and sugar foods and therefore seems outdated. The systematic order achieved by the method is described as desirable while too much variety and child/teacher interaction is regarded as undesirable. The book warns that over-stimulating a child's imagination could cause him or her to miss the purpose of the lessons (tell that to Barney). The author's works have a ring of truth throughout and are valuable because of the spirit they convey even today."
Friday, September 3, 2010
An amazing morning!
Some other work that I saw-
-3 girls worked together to clean two wall length shelves. In the process they removed every item including several plants and all of the sandpaper letters. They traced many of the letters.
-Every child who was hungry served their own snack. First they got a cloth placemat. Second, they washed their hands. Third a glass plate. Fourth- using tongs they counted out 3 crackers and 2 apples based on the number in front of the bowl. Each and every child. If they were still hungry, they got seconds.
-Many children made necklaces or bracelets with a real needle and beads. The only thing the teacher did was tie a finishing knot.
- Beads were spilled all over the floor and picked up. Twice.
- Tables were washed.
- Plants were watered.
- Polygons were studied.
- Continents were built using puzzles and painted after being traced.
- Words were developed from practicing writing "sh"
- Children were learning about the concept of addition using the golden bead material. In the thousands.
All of these children were 3-6. Maybe only 3-5. It's only the third day of school for the entire group together.
Montessori Education at it's best. I loved it.
Tuesday, August 31, 2010
Maria Montessori's Morning Devotional
Morning Devotional ~
To respect children- in return to be worthy of their respect. To praise much and blame little. To emphasize their successes and minimize their failures
MAY LOVE AND UNDERSTANDING TEACH ME.
To make no promise to children that I cannot keep. To have unbounded faith in them. To know they have great potential. To have the patience and wisdom to bring it forth. To allow children the dignity of their own personality and individuality. To refrain from making them over to our desire.
MAY LOVE AND UNDERSTANDING HELP ME.
To be cheerful and ready to smile and often to laugh. Children love and thrive on cheer. As teachers, we have no right to inflict our moods on children. (Happiness is an outward sign of inward spiritual grace.)To have infinite patience with children and to make allowances, knowing there is so much for them to learn and knowing that I myself am not so very wise.
MAY LOVE AND UNDERSTANDING GUIDE ME.
To protect the child always from my nerves and from our own irritability, prejudice, pessimism, fears- showing and practicing in their presence only the opposites.
MAY LOVE AND UNDERSTANDING AID ME.
To help them choose their life's work that they are suited for. To stir up the gift that is in them. To discover the talent or talents that they truly have- the inner pattern they came with.
MAY REAL UNDERSTANDING LEAD ME.
To bring fresh energy into the schoolroom engaging all with keen alertness, interest and enthusiasm. To help children to meet life bravely, honestly, independently.
MAY LOVE AND UNDERSTANDING SHOW ME.
To give the children freedom and to never confuse liberty with license, as these two words are not synonymous ever. To show my friendly interest in each child. To consciously care for their progress, but to attain this by warmth and love rather than by rigid cold discipline. To manage children by the pleasantest of methods, with intelligence and affection and never by condemnation and fear.
MAY LOVE AND UNDERSTANDING TEACH ME.
To educate truly, by drawing out rather than spoon feeding. To guide them instead of driving them. To direct their energy instead of repressing it. To try always to understand them, instead of sitting in judgment of them: and through all misdemeanors, both trivial and serious, to let them know it is the action we deplore and never the child.
OH LEAD ME, OH TEACH ME, OH GUIDE ME.
- posted by Terri (Montessori online)
Friday, August 20, 2010
Going for a walk
I recently was reading one of the Karachi Lectures by Maria Montessori "When a child is walking, s/he is not merely walking, but is observing and learning. The adult takes a walk to walk but the child walks to observe the whole environment in its smallest details. The example of the tiny child with his/her back to the flower and marveling at the tiniest running spider should make us reflect what we need to know, to observe and to learn from the child."
It reminded me instantly that walking is the child's activity. When schools, directors and teachers set up a plan so that children can go for a morning walk every day, it's not the same. A walk on a prescribed path or at a certain time or when one is unallowed to explore is not a walk. It is exercise and it does not belong to the child, but an infringement of their choices.
I want to walk in the garden today with children, watch flowers or bugs and hummingbirds. Perhaps they will walk with me. Perhaps not.
And another one down for our school systems...
Written by Peter Gray. Read the complete article at... (This is abridged!) Posted: 19 Aug 2010 12:31 PM PDT My overriding point was that, because of the increased competitive and standardized nature of schooling, behaviors that in the past would have been regarded as within the range of normal are now considered to be abnormal. At present, in the United States, roughly 12% of boys and 4% of girls have been diagnosed with ADHD. What kind of a society are we if we consider 12% of boys (one out of every eight) to be mentally disordered in this way and in need of strong psychoactive drugs as treatment? Some people who commented on that post objected to my sociological analysis by referring to evidence that the brains of people diagnosed with ADHD are in some ways different from those of other people. To them, the evidence of a brain difference is somehow proof that ADHD is a "medical" or "biological" disorder and that a sociological analysis of it is out of place. But if you give it some thought, you will quickly realize that there is no contradiction at all between biological and sociological analyses of ADHD or any other condition referred to as a disorder. My goal in that essay was to explain the extraordinary increase in rate of ADHD diagnosis that has occurred over the last two or three decades. I don't think that increase is primarily due to a change in brain structures in the general population; I think it is primarily due to a change in social values and especially in the conditions of schooling. Today, as a society, we are far less tolerant of children who don't adapt well to our system of compulsory education than we were in the past, and so we diagnose them and give them drugs. The basic cognitive characteristic of ADHD appears to be high impulsiveness and reduced "executive control." According to the most widely accepted cognitive model of it, the fundamental problem in ADHD is not one of attention so much as one of impulsiveness.[1] By a wide variety of measures, people diagnosed with ADHD are more impulsive, less reflective and controlled, than other people. This impulsiveness is believed to underlie all or most of the distinguishing behavioral characteristics shown by such people. Impulsiveness leads them to be easily distractible, which is why they are seen as inattentive. It also leads them to be impatient and restless, unable to tolerate tedium or to sit still unless something truly grabs and retains their interest, which is why they may be seen as hyperactive. And it leads them to be highly emotionally reactive; they tend to respond immediately, emotionally, overtly, to stressful or otherwise arousing situations. Continuing reading at... |
Wednesday, August 18, 2010
Fantasy and Imagination
Note: The majority of this was written by Sharon Cauldwell of the Montessori Foundation. It was part of a larger post on fantasy and imagination on the Montessori_online yahoo group. There were a few key ideas that I wanted to pull out and add small notes of my own.
Distinguish between fantasy and imagination
"Maria Montessori believed that the creative imagination of art and science is based upon truth. In the context of Montessori education, the imagination is seen as the mind's power to form images based on what has previously been learnt through the senses. The imagination enables us to know and understand something which we cannot see and touch. This means that if we are to truly be able to use our potential for imaginative thought, we need a firm foundation of factual knowledge. Fantasy, on the other hand, is something untrue, an "illusory imagination, based upon credulity". By carefully observing children, Maria Montessori noticed that children in her schools derived a deep satisfaction from working within a realistic environment tailored to their needs.
Because she began with the Aristotelian belief that "nothing is in the intellect that was not first in the senses," the challenge for her was to understand how such basic sense impressions became the loftiest of human knowledge, knowledge which could issue in the great artistic, scientific and social achievements of humankind. She came to see imagination as the link between these lower and higher forms of knowledge.[1]
To fully grasp the importance of this, it is necessary to understand the extreme respect that the Montessori approach has for the developing child.She saw fantasy essentially, as lies concocted by the adult. At best these fabrications entertain and distract the child, but more often than not they
deliberately mislead the child, who trusts the adult implicitly.
Hence the difference between true imagination based on true images or ideas derived from reality and false imagination based on fancies and fantasies without any bearing on reality. True imagination forms an important part of human intelligence; but false imagination consists of disorderly movements
of the mind.[2]
Put very simply, imagination is an activity of the mind which is concerned with real things – both what is, and what could be. Fantasy is unreal and can never be real. It is a flight into worlds which could never be, populated by beings, not of a child's imagination, but of an adult's creation."
I've long reflected on this subject. Adults love imagination and telling stories. In fact, stories are part of every culture. Yet very young children often can not distinguish between reality and fiction. In these days of constant media and entertainment the younger children are often convinced in the reality of characters that they can not see. I believe that their brains are different and that they process thought differently. It's truly necessary to accept them where they are. Yet, I've often had young children tell me that "it was just pretend." I think the dividing line between imagination created by the child and that created by the adult as a way to enjoy time with the child is small. I think that even very young children know the difference between dishes that they eat from and those that they feed their doll. It is different type of activity than an adult imposed fiction that the child can not escape from.
Fantasy and behavior
"In essence, Montessori came to realize that "normal" children did not seek refuge in fantasy and pretend play. That when given the opportunity to use real objects, in real contexts, they wanted to do they same tasks they saw adults performing, and that when given the information they needed, they applied their active imaginations to exploring the limitless wonders of reality.
Observation shows that children reared on a diet of fantasy, and starved of reality, tend to turn inward. The inability to develop an orderly activity and consequent disorderly movement produce a disorderly mind or a confused mind. The confused mind may be vivacious; but it is a vivacity without a purpose or aim.[3] "
I no longer find this true when I observe children. Children of all ages, but particularly young children do engage in fantasy, pretend and role play.. How much is it the child's home life, the role of media, or the fact that children have changed over time.
[1] John Snyder, "Imagination: The child's key to the universe".
[2] Maria Montessori, *What You Should Know About Your Child*, p. 58.
[3] Maria Montessori, *What You Should Know About Your Child*, p. 58
Saturday, August 7, 2010
Education in the future and Online Education
By common consent, the first duty of the educator is that of doing no harm; first do no harm, a precept also accepted in the practise of medicine. To obey it to the letter is, indeed, impossible, because every method of scholastic education is in some way prejudicial to the normal development of the child. But the educator will seek to alleviate the injury which instruction necessarily entails." (op cite)
This was written about 100 years ago. (Maria Montessori, Spontaneous Activity in Education) and she was quoting noted educators of the day. Does it seem like a common refrain? The necessity of making education interesting. She worked very hard to do so. It's all about choice. As anyone who has ever been "taught" something compared to chosen to "learn" something knows- it's all about your own choice.
Recently there have been several online articles about the future of education and specifically some very influential individuals saying that education in the future will be online. At the Techonomy conference, Bill Gates said that he believes that in five years any of the best lectures in the world will be online, and that the idea of young adults needing to go to universities will go away. Marco Masoni wrote an article on Mashable about "Online Education needs to get social." In particular, "providers meet the challenge of satisfying the rising demand for online education by simply throwing courses up on the web and seeing what sticks" and "It’s not enough for a course to be accessible online, it must also be designed in a way that keys into the digital pulse of current events, trending topics and insider knowledge endemic to the web. The three-quarters of 18 to 29 year-olds who have profiles on social networks are likely wondering why online course offerings aren’t nearly as enticing as the content that they find on their favorite social websites." Again, we're talking about making education interesting and exciting.
Friends, social networks, games and current events as a method of education? Not everything will work that way. Education isn't interesting because of games though- it's interesting because of choice and following your own interests.
A great lecture is a fantastic way to learn about a particular subject. It may be exactly what you are looking for. Itunes University has a collection. There are other publishers that are currently marketing series of "Great Lectures. True education in a field often requires both breadth and depth- not all of it may be incredibly interesting just at the moment until you get to a more complicated or intricate task or the application of your learning. Real learning often takes place with the exchange of ideas through discussion, critical thinking and questions.
The ability to make interesting and real time use of the internet is limited. Courses have to be planned and can not rely on current events. Current events such as the BP oil spill become case studies most of the time. Internet usage has to be filtered for quality. A quality online course needs to have as much planning and development as any good educational course. It's the individual's interest that makes it work. Online education will have it's place in many ways, but not necessary to completely prepare one for many careers. Some educational careers will adapt very easily to online education styles.
What about the many different types of intelligence or learning styles? It's possible that a very well designed on-line course may meet many of them. It's not going to be the same to watch and listen to a video though as a dramatic reenactment yourself.
Montessori education is a program by choice. From the preschool level to the high school level children learn to choose their own learning activities.
Let me tell you about one project at one Montessori elementary school. The Great Brain Project. It's research based and involves several months. The children individually choose their topics, research them and prepare presentations. The style and the timelines of the presentations vary so there isn't huge pressure to finish by a particular day. They are using their own "Great Brains" to best determine how to share what they've learned. In one year children choose topics ranging from the incredibly general "plants" to Rosa Parks to atomic structure to Trilobytes.
This project initially came from Lynn Stoddard's vision, but was implemented by Aleta Ledendecker at the New Horizon Montessori School. Aleta's article was in the June 2010 issue of Montessori Leadership published by the Montessori Foundation.
My Buzz post linking to this post is here.
Wednesday, June 23, 2010
"Big Work" in the Montessori classroom.
Jacqueline M. Cossentino wrote "Big Work: Goodness, Vocation, and Engagement in the Montessori Method" Copyright 2006 The Ontario Instutue for Studies in Education of the University of Toronto. Curriculum Inquiry 36:1 (forgive me- full citation is not on printed copy.)
This is a great narrative piece where a formal educator, researcher and the parent of a young child attending a Montessori school examines the concept of "work" in a Montessori classroom as opposed to the traditional concept of "play" for young children. It takes the alien concept of "work" at the preschool level and explains both it's beauty and value. "Work and play are framed as either/or endeavors. Work is associated not with 'desire' but with 'productivity' and 'employments.' Play, by contrast, is 'the purest, most spirtual activity of man at this stage (childhood.)' (Froebel, 1892)" {all uncited quotes are direct from the article} This is attitude toward play is still very common of parents today. Children should PLAY...
Maria Montessori felt that the work of the child is to develop into an adult. This work is done through freely chosen activities involving real and meaningful tasks that allows for deep concentration on the part of the child.
Cossentino wanted to know what "work" means in the context of the Montessori classroom. Through the process of observation she recorded instances of dialogue where "work" was referred to. This included-
the beginning of the "work cycle"
parent visits for "cooking work"
trays of "work" for the children to use
sensorial "work", math ""work, geography "work"
"work"space, "work" rugs, the symbolic unrolling of rugs to signal the beginning of "work."
reminders to "find work now" or a gentle question, "are you choosing challenging work?"
Older children may remind younger ones, "someone may step on your work there."
"Work" is what is done in the Montessori classroom, and there are rituals to respect and not interrupt a child's work. As two elementary students clarified for Cossentino, "Play is when you get hot and tired outside; work is when you don't get tired," and "When you play, you get rid of energy. When you work, you keep your energy."
What a beautiful way to explain to parents why a child might not want a "Play-based" preschool...
Tuesday, June 8, 2010
Themes and Dual Curriculum in Montessori
In educational theory there are some commonly used terms. "Theme" and "Integrated Thematic Unit." A theme is a unifying element. An "integrated thematic unit" is a learning theory that is designed to integrate lessons across curriculum areas through the use of one theme.
Maria Montessori when observing children designed her classroom materials to be an integrated form of learning. One material will lead to and support another. The materials themselves are interconnected. This is true at the primary and the elementary levels.
A monthly "theme" is very common in Montessori preschools at the primary level. "Themes" are very common in other educational preschools. Examples of themes include - Dinosaurs, transportation, Spring, Volcanoes, Life Cycle of the Butterfly. Although well intentioned, themes interfere with a Montessori based education. When adults choose what children should learn, then the freedom of the child to grow and learn is hindered. In order, for these themed topics to be taught in a way that is consistent with Montessori philosophy, the classroom materials have to be designed for the children to use them independently and in a manner that is self-correcting. This is possible, but often isn't done correctly and requires a great deal of extra effort on the part of the teachers. Worksheets from Enchanted Learning for the children to color aren't Montessori and don't truly build their learning- only their fine motor skills.
From an administrative point of view, many schools feel that they must show their "curriculum" in terms of themes so that parents understand what is being "taught." I'm still trying to understand why, because it shows that the school is willing to accept that parents know best and cater to their desires.
Wednesday, June 2, 2010
3 - Part Cards
"I've been thinking recently about a book that I've been reading which talks
about creative thinking and right brain thinking. In my mind, the 3-part
cards are one of the dullest areas of the curriculum. Yes, the children
will use them, but I don't see them drawn to them as much as other things.
In our print rich world, and the age of computers, scrapbooking, page
layouts etc, part of me wonders if there isn't a better way.
The real question is can anyone point me to Maria Montessori's writings on three-part cards? I want to read what she actually wrote/said and why they were designed that way in the first place."
Miri knew exactly where Maria Montessori spoke of the cards.
In "The Discovery of the Child" Maria Montessori talks about promoting early reading in children, assisting them in their "insatiable desire for reading". She describes the Exercise with Classified Cards (pages 232-236), as"simple reading game" that "aims at arousing an interest in written word". It consists "in preparing a series of objects and a corresponding numbers of cards on which are written the names of the objects. After a child has read a card he places it near its corresponding object... When a child recognizes the name of a present object, he is as pleased as if he had discovered a secret; and he enjoys placing the card near the object and thus satisfying and rounding out his intimate activity. By now his inner drive has been aroused, interest enkindled, and a connection between the source of the life and the mastering of externals established".
Then she mentions the "reversing the purpose of the above exercise. Objects that are educationally important and assembled and marked by cards giving their respective names. Whereas in the first exercise the objects were know and the difficulties of learning were connected with words, here a child starts with a sufficient knowledge of the words to teach him the names of the objects which are grouped together for some educational purpose. In a developed form, this exercise has been extended to teaching the names of various materials used in our schools, for example, those of goods, fastenings, polygons and so forth. Finally, it has been applied to models of plants and animals. Scientific terms indicating their relative classifications are written on separate cards, and these must than be placed on the objects when they are recognized.
These last exercises, however, lead us down a different road from that which is of present interest, namely, learning how to read. They rather resemble the practice of botanists and gardeners who give the Latin names of various plants on tags which they attach to them"
Aleta mentioned how in her school they make books out of them and Cathie talked of the different levels that they can be used. (Picture matching, word discrimination, beginning reading, reading) Sharon mentioned how they shouldn't be dull. I think that she's right of course. That's what started my line of thinking, but teachers make 3-part cards for everything! There must be some discretion in how they are done.
When it comes to labeling the environment, I'm thinking of a set of three part cards that match the environment and the Montessori materials.
Tuesday, June 1, 2010
Reflections on exploration from 2007
One is that materials should be used only after the child is presented with a lesson, and used in an appropriate manner only. Lessons are presented only when a child is developmental ready to successfully work with a material. The other is that a child is allowed to explore materials freely. The teacher presents individual lessons to the level of the child that bring the material down to the level of the child. In this environment, the child never feels thwarted from a material. An example would be a child that chooses the hundred board before true recognition of numbers alone, is presented with a lesson about counting or number recognition because he/she choose the material. {I'm not sure what AMS official position on this practice is, but I know the concept of exploration exists in AMS training centers.}
If a child spends more time exploring the pink cubes or brown prisms and working with them, they are developing a deeper understanding of the materials and a greater sensory perception. They are allowed to repeat and self correct their own usage. They can learn which sizes can be stacked or built on top of others and which formations are unstable. If they are trying to follow pattern cards, they are building visual perception skills, and eye hand coordination. If they are limited to only the patterns that we present, then we are limiting their ability to construct and explore fully.
If the goal of the metal insets is to work on fine motor control and they are exploring the material with fine and controlled lines, and repeating, then why should we stop them because they are not following a prescribed pattern? For example - they traced the square, but then continued to make a house. Isn't this an expansion into creativity? If a child is taking the oval, making an Easter Egg with several different patterns, cutting it out and gluing it to another piece of paper, they are exploring their own creativity, extending the use of the material, and extending their own skills. Why should we stop them? If they are at the stage of combining skills, we should not limit them to just one.
However, the freedom to explore materials should not extend to the use of materials becoming merely imaginative props or toys. When a child takes the pink cubes and brown prisms and builds a fence to surround them there is neither proper exploration or proper use of materials. The child is no longer learning anything appropriately.
Monday, May 31, 2010
Books - admin note
Reflections
Thinking about practical life that should be meaningful work to the child. I remember the joy of teaching children to sew with a real needle. Then watch their parents assume they can't carry their lunchbox or put on their coat. Schools buy screwdriver boards, but never actually let the boys use real wood, hammers or nails. What about hanging small pictures? It's only holes. Spackle anyone? Paint? Surely one board in the classroom could be set aside for sanding and real house maintenance...
I am still trying to write a post about my thoughts about using Montessori materials as a "supplement" to a traditional curriculum. That just makes no sense to me- completely ignores the philosophy, but it will take more time than I want to spend right now!
Then there is the list of 50 must read Montessori blogs. I'm honored to be on it, but more, I want to explore everyone else on it! There is always something to learn. Always something to do.
I asked for a laminator for my birthday. On the grounds that making materials is my new hobby. Apparently, I'll have to purchase that myself. I need to find a way to finance my own school!
Sensorial Extensions - revised
If you consider the properties of the sensorial materials that are not "education of the senses", use of the sensorial material is even more important. Gradation and sorting are pre-math skills. The development and extension of patterns, The ability to use one object as a unit of measurement. What about creativity and thinking of something from an artistic point of view.
Sensorial Extensions.
This was created by one of my students, Carter. He was surrounded by students working together on contingent maps. I recall how he had to work a bit to maintain his working area against the hustle of so many continent maps moving about the room. He was tremendously proud of himself for creating this balanced work of art using the red knobless cylinders. We took a picture and he wanted to make sure that I showed others. He told me how he needed to move this piece and that piece. I loved his concentration, but more I can see what he learned about weight, height and balance!

The robot is taken from a blog called The Montessori Goldmine. She initially got it from the Sunrise Learning Lab. The original picture reflects a picture of her son, and was edited by the Montessori Goldmine.
This pink tower and brown stair extension was located at Con La Cabeza en Las Nubes.

From the classroom at the Montessori School of Holmes Run in Falls Church, VA. We call it the Grand Sensorial Layout.
by Stevanne
Pink Tower Extension by BMMontessori!
I know that I have a picture of an extension called "The Grand Pagoda" and one that resembles a "Christmas Tree", but not on this computer. The idea that I like the most though isn't to copy an extension, but to create your own and become part of a book that shows possibilities!
Additional links with Sensorial extension pictures -
Montessori with Myra
Matt Bronsil
Montessori online photo album
Saturday, May 15, 2010
Small bead bars
When the children are still learning to count objects below 10, they really, really need to learn to order those objects. With the bead bars (bead stair) these objects are naturally formed into a line. Yet they are still distinct objects that can in fact be counted. In a traditional Montessori classroom you move from the bead stair to the teens. (There is the snake game, but...)
It seems to me that a child would benefit so much from having a classroom with several sets of the bead bars. They can use them for addition and extended counting activities. Better than dinosaurs! This material can stay small and manageable.
Saturday, May 8, 2010
Mothers Day - success and fail!
I decided to make a Handprint card with their picture.
"Sometimes you get discouraged
Because I am so small,
And always leave my fingerprints
On furniture and walls.
But everyday I'm growing,
I'll be grown up someday,
And all these tiny handprints
Will simply fade away.
So here's a final handprint
Just so you can recall,
Exactly how my fingers looked
When I was very small."
I had so much fun painting the children's hands! They would sit absolutely still - even a child that is extraordinarily hyper most of the time, but they almost all still wanted to hold control of their hands. When they relaxed and turned their hand so that I could brush paint on their little fingers- it tickled or was cold, etc. They watched with fascination as we made handprints. Most of them had to hold their hands out toward someone like Frankenstein as we went to the sink. "LOOK AT MY HANDS!"
Then came taking the pictures. Trying to find a place, taking several so that I could preview them later. I used photoshop and briefly adjusted the color and used a octagon crop before printing the. I did all the cutting of the pictures and the gluing.
Each card was beautiful. Their was a handprint in the upper right and left corners. The child's picture in the center and the handprint poem offset to the left or the right. I added a second piece of construction paper to add color and an additional frame that matched the paint.
I also did all the wrapping in tissue paper, and this is where I fail. If I'd set this up a week before it would have been such a perfect opportunity for the children to learn to wrap the presents for their moms themselves. The way that I was wrapping was very simple. One large piece of tissue paper. Another folded in half in the center. Card face down on the 2nd piece of tissue paper. Fold long sides. Fold short sides and tape. The children could have accomplished that. They SHOULD have made the cards that said "To MOM and from ...."
It would have been a great practical life exercise. They would have understood a complete cycle of work. Ah well, it is my own reflections and where I am as well. I practiced repetition and learned what I can do better as well!
Sunday, April 25, 2010
Walking Backwards
They did this for about 15 minutes. I watched and listened to them. They were excited having fun, and talking about how hard this was and quite a challenge. I was wondering if it would disturb the child working on the hundred board - it certainly would have disturbed me to be constantly circled! She didn't seem to mind except when they came a bit close to her rug. Gentle words of caution not to get to close.
Silliness reigned after about 15 minutes. A third child joined them and one of the first started to yell and giggle. They started to move faster and faster. I cautioned them once, and then suggested that it was perhaps time to find another work.
The delightful part for me was that about 20 minutes later one of the children came to me and told me how much he had enjoyed walking backwards. "There is no place at home where I could walk backwards, and it was so much fun."
He was refreshed, energetic, so excited and happy. Walking backwards in a circle is not a lesson that was in my training. Yet, it falls in the principles of follow the child. Not everything is materials and academics. This child needed to move at the moment. They walked and talked and were happy. They did not disturb another child. I adored them...
Saturday, April 10, 2010
The pink block experiment
Mindful that this child was not actually enrolled-
I encouraged him to carry each pink cube one at a time to "keep them safe." (and of course as a way to feel the weight of each cube and hold the space in his hands!) I remembered in the Montessori handbook how she talks of the joy of a child in building the pink cubes in order to knock them down again- just so that he can rebuild them.
I LET him KNOCK down the pink tower!
Repetition. He worked on the pink tower for about 25 minutes! CONCENTRATION. He's not even 3, but I don't know his age. I wonder what age Maria Montessori designed the pink tower for. Was she worried about the cost at that point? Or looking at what the young children wanted to do.
Respect for the materials is critical. He was little. The blocks fell. Most were on the rug, a few off the rug. They didn't fly across the room, or hit anyone. All along his mother sat next to him, and tried to get him to find the "biggest" cube. He was, of course, building it completely out of size order. I have no idea if he has ever been given a lesson/example on the perfection of this material. He wouldn't care right now.
Should he work with anyone right now? NOPE, I don't think so. It was perfect for just his hands.
An older child needs to work on perfection and order and gradation.
I wonder...
How many schools ever allow children to knock down blocks - respectfully?
The pink cube is a unit of metric measurement that is systemic through many Montessori materials. The metric system is not used in the United States. Should some of these materials be revisited in their design? Isn't it more important to concretely understand what a 1/4 inch, 1/2 inch, inch etc. are than 10CM? (That has to be one of the most useless measurements I can concretely measure!)
Sunday, February 28, 2010
Knobless Cylinders and the mathematical mind
Bee Pape is the expert here, and a search for her documents is well worth the time. She has extensive extensions with the knobless cylinders. She's been teaching for a long time in a Montessori school, done research with early number development. She also knows the work of Piaget and Constance Kamii. Many of my own thoughts are generated from a workshop of hers that I attended combined with my own research. I found her delightful, because I've read and understood so much of the same material.
Jean Piaget was 26 years younger than Maria Montessori. His developmental theories were also based on the observation of children and many interesting and experiments. These included conversations with the children about what they were thinking. He was familiar with the ideas of Maria Montessori and was at one point president of the Swiss Montessori society. One of his fundamental beliefs is that children construct their own knowledge through interaction with the world. In many ways, this is similar to Maria Montessori (and many current educational theories) that young children learn best through concrete materials and actual experiences.
Jean Piaget observed an interesting phenomenon called "conservation." There is "Conservation of liquid," "conservation of number" and several more. These are a developmental stage that children go through where they can only hold one attribute of a physical material in their mind at a time. For example, in "conservation of liquid" once a child agrees that the liquid in two equal shaped glasses is equal, if one glass is poured into either a wide/short glass or a taller/thinner glass the amount of liquid is no longer the same. The same thing is true with "conservation of number." If a child agrees that two rows of similar materials (poker chips) have exactly the same amount, if you stretch out one line – then they are no longer the same. There are many reasons for this. Sometimes the child will say that the longer line has more, sometimes the shorter, sometimes they will provide an answer that is difficult to explain. The result is consistent and has been shown many times. Young children do not recognize that quantity is consistent regardless of spatial arrangement.
This developmental understanding of number only comes with actual experience (in many forms) with things to manipulate. Experience with objects to count, adding or subtracting one, matching, all promote learning about equality, greater than and less than. What do you do if there is one more doll than you have a bed for?
If you look at current educational research and activities for children, you see seriation, ordering, pattering, matching, and measurement. Maria Montessori was brilliant. How many people remember their training that a child should truly spend time with and master many of the sensorial materials before being introduced to mathematics? In my training, the knobless cylinders were one of the last materials that were introduced to a child because there is no control of error except visual. The knobless cylinders are a set of 40 with 4 subsets in different colors. You have a few pieces that are actually identical. A child can sort them by color. A child can sort them by size. A child can sort them by height. If one is missing, because they are sitting on it – they have a problem to solve and a interesting learning lesson about quantity. They can explore relationships. You can even set up logic puzzles that are designed for the youngest child and visually based. Find me a piece that is this height and this color (or not this color…)
100 Words
There is a Montessori group that is having a discussion recently. How would you describe Montessori in 100 words or less. I wrote two different versions from two perspectives in my own head. One is that of a director of a school and meant at least at some level either as recruitment or advertising. The other is more personal from my experiences as a teacher in some poor schools and my experiences as a parent with my children in high quality Montessori schools. Neither one is truly adequate. It turns out that 100 words does not offer much scope for the depth of what Montessori is and what I truly believe about it. It is about the individual in so many ways and allowing a child to explore their own interests. I have a child right now that is my own 12 year old's terms is "the most off-task." He's brilliant. I've evaluated him. He has conservation of number at age 4. Rare, and I've done the research! He turned a wooden cylinder which was meant as a sewing job into a yo-yo. He came up to me one day and said that he wanted to write a book. There weren't enough books… and he started dictating the entire story of the three little pigs- a story that we have not read in class. He also recently went up to the school office and started to touch everything to the point the director wanted to know who this child was! A teacher should know better, but I love this child. I fear for him. He will either find the teachers that will nurture him, or he will find the teachers that will destroy him. Is it really my place to say that he "must" study this now, when his brain is concrete and he's fascinated by how things move? No- that's for some "other" form of education. Montessori finds a way to accept where he is and still teach him everything that he needs to know to move forward.
#1
An individual has their own unique interests, talents, skills and obsessions. When learning comes from an individual's own interest it is joyful and will be deeper and better retained. Ideas and questions will be generated and facts related to current knowledge. Projects may be designed and undertaken with because of sheer captivation in learning with great enthusiasm. Montessori education is designed to spark a child's individual imagination and allow them to direct their own learning process within guidelines while developing specific skills. Children are nurtured for the wonderful individuals they are with unlimited potential.
#2
Montessori education aims to first teach the child independence. A child develops a sense of organization as a prerequisite to successful work. This forms the basis of further work with language, mathematics and the development of the senses. Each child is able to work at their own individual pace exploring in depth what skills they are currently motivated to learn. For the young child this may be learning to use a spoon or scissors or writing about sharks! It is not a mandatory curriculum where everyone completes the same task at the same time.
Monday, February 22, 2010
Montessori something....
Stupid workbooks. One page per day. I have a child that just doesn't get them. We need to work on rhyming words. Other children that need to work on basic sounds. Most of them need to explore numbers. Stupid workbooks so they can make progress. Make consistent progress talking to each other, getting help from the teachers just to read the picture understand the sound in the first place. Some of these children can't even write there their own name! There sense of accomplishment is in finishing a worksheet.
Just a random rant and rave. There is only so much time in the classroom and in life. Especially with the commute. I know what most of the schools near me are like though. I already decided that my real priority is to open my own school. I'm just not sure if I want to NOT accept any position, not remodel the kitchen (possibly indefinitely) in order to have one year to fully develop a functional business plan and location options. CA is expensive and you need to cover the cost of the real estate.
My first step is a complete mission statement. The second would be an employee manual that would help to match it. I also need the financial breakdown and break even points. Those are the steps that I can do at home.
Thursday, February 18, 2010
Thinking about the Hundred Board
- Maria Montessori, AMS Triangle Magazine 1946/or 1947 (located via internet)
What happened to follow the child in the political correctness of giving the lesson the absolutely right way? What happened to scaffolding and the concept of the zone of proximal development? The idea that there is a place between what you know and what you don't know that is ideal for learning, particularly if it is structured to provide just the ideal amount of support. This makes sense - nothing too easy and nothing so challenging as to be impossible or perpetually frustrating.
These concepts are inherent in Montessori philosophy. The materials are designed to move from one to the next in a progression of concepts, building confidence and support as needed. They aren't perfect though. Sometimes a child just isn't interested in the "right" material, sometimes it needs to be demonstrated in a different way. Sometimes... whatever.
The Hundred Board.
In my training, I learned a presentation method where each group of ten numbers was in it's own box and the child worked with ten numbers at a time. There was no control chart. They learned how to carefully put it away for the next child.
At the next school that I worked with the child had the option of working on a hundred board that was preprinted as a matching or a blank board. They also had the option of completing a paper extension. (In that school it seemed as if the paper extension was the true goal of the children!)
I've heard and seen of schools where the hundred board had all 100 tiles in a box and randomly spread on the rug. I've also seen where the first 40 tiles where in one box and the remaining 60 in a second box. (I don't know the logic of that division...)
Yet children approach the hundred board from all different levels and can learn from it. The other day I watched two girls absolutely euphoric about going to the calendar realizing they needed "a one and a three" and finding "31" for "13" and continuing all through the teens. When they were done, I had them actually write the numbers that they might have seen if they had a control chart and they were still excited. (They were doing this job because they "had a lesson, and were volunteering to clean it up.)
Some children need to match the numbers and can find the hundred board and opportunity for learning numbers and the patterns inherent in building the hundred board. Some children can work independently from a control chart. Many children when they first begin the hundred board will have difficulty with a hundred tiles spread on the rug and will need to find a way to organize their work. "Scaffolding" may include sorting the pieces by the tens, but I've never heard of a formal training presentations that include that. I do, the children need it. It's no different than organizing the pieces of the trinomial cube.
Order is fundamental in many math aspects.
Tuesday, February 16, 2010
New Curriculum
Yet, the environment is not static. Changes are made to reflect the season, to try to regenerate interest in a material that is not being used. Changes are often made to reflect current holidays or teaching themes.
The more connections that you can make between current knowledge and new knowledge there will be a higher possibility of longer term retention. (It was only recently that I actually learned the dimensions of the knobless cylinders, but I was willing to guess they were in metric units!)
If we ARE teaching to current holidays, perhaps it is the ideal time to incorporate the geographic history and related significant figures over time. If we ARE teaching about the rain forest, perhaps we should also teach about the people in the rain forest- not just the animals. If we ARE teaching about dinosaurs, perhaps we should look up significant locations of fossil remains and teach about geography.
What would you change about the curriculum if you could start from scratch?
Sunday, February 14, 2010
Wild and untamed!
"My heart is still racing thinking of what this boy has accomplished. What was he thinking? THAT he was thinking is the key. Push the boundaries, turn over new ground - make, create, innovate. I'll bet this kid wasn't put on Ritalin.
- Mark"
I too am amazed at where he is right now and the concentration that he showed. He broke rules. He probably wasn't always easy to manage. We've all had the children in our classes that when very young march to their own drum - rather insistently. They can usually steal our hearts. For me this is a reminder of what they may accomplish!
Saturday, February 13, 2010
Online and thinking again.
Comcast has now replaced everything from the pole on the street to the junction at my computer and we replaced the cable modem as well.
I need to fix the picture, and I won an award! Thanks.
In the meantime, I've started a temporary job...
I want to make a new section on the blog - one that is a resource for known albums. It is a useful reference, even though I will not vouch for the quality.
Once again I'm thinking about a more coherent curriculum for preschool children rather than the entire theme based approach that many schools use and I want to investigate a new book on teaching science to preschoolers. It's based on research by Rutgers. Science is one of the areas that I do not feel Maria Montessori truly provided enough for children. They can do more, and many schools actually demand more. It's all about taking the philosophy and the right approach and the correct implementation.
Tuesday, January 26, 2010
Concentration
This reminds me of the Montessori work cycle and false fatigue. In my training program we learned about long work periods and false fatigue. How children settle into the concentrated work only after working on the easier or relaxing work, and they go through a period of unsettled behavior midway through the work period. I've seen this so many times. I've observed in schools with work periods as short as 45 minutes and so many transitions. Practical life is a huge draw for the children there.
In my own classroom, I was able to stretch the work period to over two hours and most of the advanced work was in the last 45 minutes. I always wanted to make it longer still. On the rare days that I did, it was fantastic!
What in the world is it that makes adults think that children can not concentrate? Have you watched a child with an art project? Or working on making a book or a puzzle? In the Montessori classroom there are a number of jobs - spelling with the movable alphabet, pinpunching shapes, the hundred board that can easily take much longer than ten minutes and these are by the littlest children!
What about when an older child reads a book? Yesterday one child sat enjoying her math assignment. It was just the right amount of difficulty to be a puzzle for her. My other daughter decided to clean - she concentrated on cleaning and organizing the bathroom for close to two hours.
We should encourage concentration - not assume they can't!
Sunday, January 24, 2010
Montessori Cosmic...
Dr. Montessori was first and foremost a scientist prior to an educator. Her system of education was built systematically based on observation and experiment. In the Montessori Handbook there is a very clear distinction that the nomenclature comes only after the child has had the opportunity for use. The child develops a very specific vocabulary which allows him to make observations, classifications, to discriminate, categorize and order his thoughts and impressions.
I've been also reading The World in the Palm of Her Hand by Tim Seldin. It's a book about introducing History and Geography to the young child. One section talks specifically about the different levels of abstraction of knowledge. There are three spheres - the outermost which consists of things that we have never seen and never heard, the next sphere is the sphere of knowledge - we know something but we have no real understanding or experience, the innermost sphere is that which we truly understand and know. Knowledge is usually gained through hands on experience.
A young child will find wavelengths of light to be in the outer level of knowledge, but they will have personal knowledge of a rainbow.
In order for knowledge to be useful for the very young child we must provide a way for knowledge to be both personal, and connected to other knowledge. The child must be able to make some sense of the knowledge.
Friday, January 15, 2010
Of course preschoolers understand math!
Said best at Montessori Matters and reprinted with permission... I loved this. It fits in so well with my thesis! I still need to send her a copy of it...
Yesterday, the most popular article on the New York Times website discussed a recent finding in the field of cognitive neuroscience.
Brace yourselves Montessorians!!! Contrary to long-held beliefs in the highest echelons of scientific research, the cognitive neuroscience community has discovered that children as young as four can grasp fundamental math concepts.
*pause for effect*
Uh, we could’ve told them that.
So, maybe we should!
Dear cognitive neuroscientists,
Congratulations on your ground-breaking discoveries in the field of pedagogy. You must have been quite pleased when you found out that young children can understand basic math concepts before the age of six. I’m so glad you finally put your expensive Harvard Ph.Ds to good use!
I hate to burst your bubble (actually, I quite enjoy it), but I thought you might want to know that a woman named Maria Montessori figured this out 100 years ago. Talk about arriving late to the party!
It is my pleasure to introduce you to the Primary Montessori classroom, where pre-schoolers have been actively working with math concepts – from numbers and quantities to long division and fractions – for over a century.
Maria Montessori believed that children have a natural curiosity for mathematical concepts, and look for order and patterns in the world around them. She called it the “mathematical mind”. However, because the concepts of math (the value of numbers, arithmetical operations, geometry, etc.) are not instantly recognizable to the untrained eye, Dr. Montessori deemed it necessary to create a curriculum where children could use concrete representations to discover these mathematical abstractions.
In other words, for children to understand what a number represents, what addition is about, or why we need to borrow during subtraction, they need to involve their senses, and we need to isolate the concept being introduced. These are two of the (many) reasons why traditional math education has never worked, and why so-called experts thought that young children were incapable of learning math.
Traditional approaches to teaching math have been truly uninspired and frankly insulting to a child’s intelligence. Using a pizza slice to illustrate the concept of a triangle is one of the dumbest things I’ve ever read about, and yet according to the NYT article, this technique is used in many children’s books (among many other equally idiotic tactics). And speaking of dumb techniques, why should pre-schoolers be using books to learn math, in the first place???
In Montessori, children start working with mathematical concepts around the age of three, when they are exposed to fractions, geometry, algebra, equivalences, and base-ten from a sensorial perspective (this means they’re using their senses to explore mathematically-precise materials without knowing they’re learning about math). By the time they’re 3 1/2, if they’ve been in the Montessori environment for at least six months, many are ready to begin their formal math education.
Yes, 3 1/2. I’ll give you a moment to pick yourself off the floor and climb back into your ergonomically-correct office chair. Ready? Let’s continue.
Montessori students move at their own pace through the math curriculum, first exploring quantities through the use of the number rods, then learning to identify symbols (aka, numbers 0-9), and then associating the symbol with the quantity.
Guide a child through this process, and voila! She can clearly understand that “5″ is not just a hard-to-write squiggle named “five”, but is an actual quantity she has carried, counted, and compared to other quantities. Deny a child the right to understand this concept clearly, and you’re setting her up for a lifetime of struggle and confusion.
Within a few weeks of commencing their formal math education, Montessori children will have learned about quantities, odds & evens, and the concept of zero as an empty space. Then it’s on to the decimal system, where – hold on to your lab coats! – children who just turned four learn how to work with four-digit numbers.
I bet you’ve never witnessed a four-year old who sees the number 8,657, says “eight thousand, six hundred, and fifty-seven”, AND represents the quantity accurately using golden beads. I know you’ve never seen this because, in the article, you were excited about children who could touch their nose seven times. You guys sure do have low standards for what children are capable of.
At the same time our students are discovering the joys of arithmetic, they’re also developing a clear understanding of what the numbers 11-99 represent, through the use of several beautiful, precise, and engaging materials. Skip-counting is also introduced, and the concepts of carrying and borrowing are practiced extensively.
As before, we follow a specific method of presenting the information to the children: first the quantity, then the symbol, and finally the association of the quantity and the symbol.
Yes, you mention this ground-breaking process in your article… Guess it’s not so ground-breaking after all.
Throughout this entire time, the children are free to move at their own pace, revisiting concepts as they see fit and staying with a particular material as long as necessary. If we, as guides, see that a particular concept has not been clearly understood by a child, we have the ability to bring him back to the appropriate material. We’ll gladly spend quality time re-presenting the concept and encouraging repetition through one-on-one games and small group activities.
Only when the above-mentioned concepts are clearly established in the child’s mind, will we guide her towards the memorization of tables. After all, what good is it to regurgitate 3+4=7, 3+5=8, etc. if there’s no understanding of what the concept means, and thus no way of applying it to daily life?
Oh, wait, I forgot. Traditional schools educate children to succeed on tests, so regurgitation is not only sufficient, it is required.
Well, here’s the thing: we, as Montessorians, would rather prepare children to succeed in life.
And speaking about preparing a child for life… If a child is fortunate enough to remain in the Montessori environment for her Kindergarten year, she will continue learning the arithmetic tables (always through the use of materials she can manipulate). Little by little, she will wean herself off the materials, as her brain matures and she learns to apply the knowledge she acquired in the first two years in the classroom. Upon solving an arithmetic problem without the use of the materials, it is not unusual for a five-year old Montessori child to remark: “I don’t know why I know, but I know.” If that doesn’t build self-esteem, I don’t know what does!
After reading the NYT article, it sounds to me like you guys are just re-inventing the wheel. Fortunately, you are starting to discover that you under-estimated children’s abilities (and over-estimated your own). Stop wasting time pretending your theories are ground-breaking, do some real research, and use your soapbox to give children the type of education they really deserve and are desperate for.
Welcome to Montessori. It matters more than you think.

