One material, many ways to learn

Within the Montessori classroom, there are endless ways to work with the materials. Some of these ways are set out in the curriculum taught in the teacher training program, whereas others are improvised to match an interest on the part of the child. Several lessons with the colour tablets illustrate this.

Once the child is able to match the colour tablets (there are two of each colour), we try matching at a distance. This involves setting one set of colour tablets up all mixed up at our table, and the other set (the same colours) at a distant table. I set one colour tablet in front of the child and without saying the name of the colour, I ask the child to get the same colour from the other table – without taking the colour tablet along. At times, the child will come back for another look before finding the match. When the child comes back, I ask the child to put the tablet next to the one he/she was matching to and ask if it matches. It is important that the child decides if they match – I do not correct. This work builds the child’s working memory. There is often a distraction (conversation, interesting work to watch, etc.) along the way, which adds to the challenge.

Another lesson – and probably the most fun lesson from the child’s point of view – is matching to the environment (shown below). This activity involves setting one colour tablet in front of the child and asking him to find something in the environment that is the same colour and bring it to the table.  There are usually some very interesting choices of items!

To see if the child knows the names of all 11 colours, I ask the child to hand me the colours that he/she knows and tell me the name as he/she does so. If there are a few yet to learn, we do a 3-period lesson to help the child to learn the names of each colour.

Another way to work with these is labeling. Checking that the child knows the name of each colour, we set up a row of colours in front of the child. Often, I will select only one colour starting with each sound to make this work easier. This time, however, the child was very interested in using all of the colours, so we went ahead and used the entire set. Using the writing box (a narrow box with strips of paper, a pencil, and scissors), I write the name of one colour, cut the label, and place the label in front of the child. This work involves the child sounding out the name and then placing the label it in front of the colour to which it corresponds. This particular time, she was unsure about several labels that started with the same sound (green/grey, blue/black, and pink/purple), so I suggested that she set them aside for now. When all the others were done, she took these out and carefully sounded them out to match them to the appropriate colour. She was happy to bring these labels home to show to her family.

The point of sharing these lessons is to show how the same material can be used to match exactly where each child is in terms of language, working memory, and reading. In a number of cases, one child will watch the other working with a material and then ask to do the same thing, so my challenge is to refine the lesson to meet each child’s interest and ability.

Teri Courchene

Show, but don’t tell

A twist on the “show and tell” idea, Montessori favours “show, but don’t tell.” For children under 6, her method involves demonstrating an activity, but not giving verbal instructions. Discussion is certainly part of teaching, but not direct instruction. Why does this work for young children?

The answer lies with the mirror neurons. When a child is receiving a lesson, not only must the child inhibit movement (a topic for another blog), the child must also observe the teacher’s actions with the object of enacting them soon afterward. The activity of watching is not passive in the brain, as mirror neurons in the premotor cortex are at hard at work. Brain scanning has shown that when one observes another person performing a movement or series of movements, the observer’s brain goes through many of the motions that it would if the observer were performing the action. The brain is effectively preparing itself to replicate the movements. In research with monkeys, it was found that viewing of a goal-oriented action was required to get the mirror neurons to fire, not the viewing of the objects themselves. This neuron activity may help the monkeys to understand the goal of the observed action (Blakemore & Frith, 2005).

Does this mean that the teacher refrains from talking while presenting? Not necessarily. The focus is on the work, and the role of the Montessori teacher is to entice the child into the work…sometimes by talking, sometimes by altering the lesson to make it more suited to the child. Therein lies the challenge and the art of Montessori.

Teri Courchene

Blakemore, S., & Frith, U. (2005). The learning brain: Lessons for education. Oxford, UK: Blackwell.

Breaking the rules

The loudest, and in my view the most justified, criticism of Montessori programs is that they are rigid – the teacher shows “the right way” to do the work – and the children must conform. Thankfully, most Montessori schools don’t run this way (certainly not ours!), but there is definitely some rigidity in the program.

There is a fundamental conflict when a Montessori child becomes a Montessori teacher. A true Montessori child learns to question, think for himself or herself, and importantly, look inward instead of to others when making decisions. If such a child becomes a Montessori teacher (as I did), then he or she will be told what to teach, how to structure lessons, and instructed to adhere closely to a method that has been tried and true for more than 100 years. You can double the conflict by making a Montessori teacher out of a Montessori child who is also an economist (me again)! Evaluating choices and trade-offs/opportunity cost is at the core of economic thinking – not following set rules.

What is the solution? Understanding and believing in the Montessori approach means that one can stay with the essence of the lessons and yet break many of the so-called “rules.” A Montessori child takes particular pleasure in breaking rules for a good reason – trust me on that one.

Above is a lesson with the constructive triangles that I showed this morning. At the end of the lesson, the child wanted to structure a lesson for me: I had to recreate the design that he created (shown below). Not in the rule book, but definitely an important lesson nonetheless. The child did reassure me that I had done a good job even though I had difficulty recreating his design. Kindness is a rule that we adhere to happily.

Teri Courchene

Concentration

How do children learn to concentrate? To answer this, think of when you have seen a young child completely absorbed in an activity. It might be pouring water back and forth from one container to another or building a sandcastle.  These activities are purposeful and require all of the child’s attention. Providing the child with the freedom to engage in and stay with such activities supports the child’s development of the ability to concentrate.

In a Montessori classroom, there are dozens of purposeful activities that call to the child in such a way. For the youngest children, the button frame or pouring rice may be the activities that hold the attention the longest. As the child grows and becomes more capable of complex activities, it might be polishing, sewing on a button or care of plants.

What is the purpose of these activities? It is not the end result – having a polished dish or a perfectly sewn-on button. Through undertaking these activities, the child develops control and coordination of movement. Working through the many steps of polishing or sewing on a button calls on the child to determine which is the next logical step in the process. The child is the one who decides when the process is complete and returns the activity to the shelf.

In order to entice this wonderful focus in the child, the classroom is filled with beautiful, well-organized materials. The activities on the shelf should call to the child, the materials should be finely crafted and attractively arranged, and the activities should have an end result that the child can work towards (a button attached to a fabric square, or a shiny spoon, strips of cut paper).

Apart from the materials themselves, the other unique aspect of the Montessori approach compared to the pre-school or kindergarten approach is that Montessori allows for endless time – the child is free to repeat as much as he or she wishes. Sometimes I hear, “I want to do it again!” or look up to see that a child has cut 20 serpentine strips in a row.  When I see this, I smile to myself and look forward to all of the interesting work that lies ahead of us.

Teri Courchene

True or False?

Children have a wonderful sense of humour, especially at the ages of 4 and 5. Since they are so tuned into the language around them (they are picking up grammar, vocabulary, and complex sentence structure at an impressive pace), they find playing with language hilarious.

Early readers love to see their name in print. Sorry, dads, but the children’s next favourite word is often “Mom.” Even before children are reading many words, they learn to recognize the most important ones – the names of the people in their family.

One of the new games I have developed for the students is a True or False Sentence Game. It is both a reading and writing game and builds on the idea that children want to play games with reading and writing before they are fluent readers. Since there is considerable repetition, the children learn to recognize the words we are working with even though the children are (usually) at the early phonetic stage (sounding out individual letters in words).  We make a small pouch for the word labels and the children are excited to take the games home and play with their parents.

I was told these were true:

“Cooper has a toy”

“Carter has a toy”

“Dad has a toy”

But this one was false:

“Mom has a toy”

After I ask the child lots of questions about true and false and move lots of words around, I mix up all the words and ask the child to make some sentences.

This was Cooper’s first true sentence:

“Cooper has a Mom”

In this way, the students can create their own sentences before they can use a pencil and paper to write all the words from memory.  The joy the children get from this game is contagious…I am still smiling about the fun we had yesterday.

Teri Courchene

The Dice Race

This game has been used with great results at the University of Toronto’s Dr. Eric Jackman Institute of Child Study Laboratory School. It was introduced to me by Lab School Teachers – Julie Comay and Carol Stephenson in my OISE math course in the summer of 2011*. It has been modified a little to work in a Montessori classroom and it is now a standard part of the classroom, ready to take from the shelf when the children wish to use it.

(*The Early Learning in Mathematics course was taught by Dr. Joan Moss and Bev Caswell with support from the Robertson Program for Inquiry-Based Teaching in Mathematics.)

What is the game?

On a piece of grid paper 6 squares wide by 10 squares tall, the numbers 1 – 6 are written below each of the squares at the bottom of the page. When a child rolls the die into the basket, the number rolled is entered in the first square above that number. The first number to be rolled 10 times wins the game.

What can children get from playing the game?

  1. Subitizing – quickly recognizing number, i.e., that 4 dots on the die make the number 4.
  2. Practice writing numbers – when a number is rolled, the child writes that number in the square.
  3. Probability – when the child sees that one number has been rolled more than the others, the child understands that the number in the lead is likely to win. The child tends to be very surprised if the same number is rolled several times in a row.
  4. Graphing – the child sees how to represent which number is winning. The child essentially learns to read a graph by doing this.
  5. Addition and subtraction – the child sees how many squares are left to fill. Sometimes a child will laugh when he/she finds that “4 needs 4 more!” or “3 needs 3 more”.
  6. It is fun! Children start to cheer for certain numbers and often want to play again to see if a different number or their favourite number will the following time.
  7. No one loses! In contrast to many games, it is the numbers and not the children who win and lose.

This is a great addition to a Montessori classroom, since it is a hands-on way to enjoy a broad exposure to mathematical concepts. Children go beyond number sense into another strand of the mathematics curriculum – data management and probability – areas not generally covered within the Montessori mathematics curriculum for this age.

Teri Courchene

Real and breakable

To some, one of the most surprising differences between a Montessori classroom for ages 2-5 and a Kindergarten classroom for ages 4-5 is that the Montessori classroom has many breakable items: ceramic jugs for pouring rice, glasses for pouring from jug to 3 glasses, glass vases  – and many more items. Why are breakable items used for young children?

To answer this, I will give you an example of a very dear friend of mine who excitedly told me that she found amazing sunglasses for her 2-year-old daughter. These sunglasses could be bent every which way and would not break! When I looked askance at the sunglasses, she asked me what was wrong. Giving a child sunglasses that can be twisted and used roughly teaches a child that sunglasses can be twisted and used roughly. The next time that child picks up a real pair of sunglasses, the child will have learned to be very rough with them – and may break them.

This exact principle applies within a Montessori classroom. Surround the child with real – and at times, breakable – materials, and the child will learn to hold the items with care. We show a child how to hold materials with two hands, carry a tray level with two hands, pour with a jug, etc. When we hold and use items with care, the child learns to do so.  A Montessori teacher will not say “this is breakable, be careful” because there is no need to do so. A broken item is a learning experience, resulting in that set of materials being taken off the shelf. That is the consequence of the breakage – there is no reprimand, just the feeling that something must be taken away until it is repaired.

Do many items get broken? Surprisingly not. In seven years of operating my school, only one glass item was broken – and I did it. I was hurriedly vacuuming and bumped the vacuum into a wall shelf and knocked down a butterfly-shaped glass dish with a lid, breaking the glass lid. Hmmm…should have spent more time with breakable items as a child, I suppose…

The magic of the number line

It didn’t take long for me to step outside the traditional Montessori boundaries – this is only the third post! With due respect to Maria Montessori, she can be viewed as a pioneer in the use of number lines in the classroom – a look at the ticketed squared and cubed chains confirms that they are indeed number lines. However, a more traditional number line (from 1-10 or from 1-25) is not part of most Montessori classrooms.

Below is the ticketed 5-squared chain from the Montessori mathematics area:

Research into mathematics learning, particularly in the case of children lagging behind their peers and/or exhibiting learning disabilities, has proven that the use of number lines has been very effective.

The most compelling study is one by Siegler (2009), who investigated the case of low-income children lagging behind in numerical development. Interestingly, this study tested the impact of using a mathematically precise number line with the numerals 1-10 compared to a similar line with colours for each of the squares. With four sessions of 15 minutes each, the children using the number line with numerals were able to advance in mathematics learning to the level of their more well-off peers, while the children using the coloured line did not advance. The reason that the number line works is that children tend to have an internal number line that is logarithmic instead of linear and repeated exposure to a mathematically precise linear number line serves to “correct” their internal number line. What does it mean that their number line is logarithmic? If asked to place 5 on the number line, a child would place it close to 10 instead of in the middle.

Is the number line an effective teaching and learning tool? Absolutely! After reading about Siegler’s research in early 2011, I created a quilted number line for the classroom and the children and I have been using it frequently for the past year. The results are very encouraging.

Below is the quilted number line:

Here are three ways to play the number line game:

1. Play as a race from 1 to 25 with one die. We use buttons for pieces. Learning that four dots on the die means 4 is called subitizing – and this game helps the children learn to subitize very quickly. Children tend to learn to subitize before they learn the numerals 1-6. There are many variations on this game: the winner is the one to reach the end first; play until all reach the finish line; or one must roll the exact number to end on the final square of the number line.

2. Play the race with + and – cards. Using small cards with the numbers +0, +1, +2, +3, +4, +5, +6 and -1, -2, -3, -4, -5, -6 play in the same ways as above. To make these cards, I typically make 4 each of the cards except the -3, -4, -5, cards, of which I make only 2, and the +1 and +2 cards, of which I make 6. The children tend to be very interested in this, particularly in the way that the positions can change so quickly. Clearly this is a more advanced game than the one with the die, since children need to know the numbers 0-6 and understand the concept of + and -.

3. Building a number line to 25. I make tiles (using craft foam) for the numbers 1 to 25 and the children build their own number line from left to right with the tiles.  As a self-correcting tool/reference point, the quilted number line is set up a distance away. If a child is stumped as to which number comes next, he/she can walk over and count up the number line. This works very well to reinforce the patterns in our number system. When the child is done, the quilted number line can be brought over and each tile placed on the number line as a check.

The number line has facilitated mathematical learning in our classroom, particularly for children for whom the traditional Montessori materials did not provide enough of a bridge from the concrete (quantity) to the symbolic (numbers) for building an understanding of the numbers to 0-10.

Many of the parents in my school purchased one of the quilted number lines when I sold them as a fundraiser last year. If anyone is interested in purchasing one, please get in touch.

References:

Siegler, R. S. (2009), Improving the Numerical Understanding of Children From Low-Income Families. Child Development Perspectives, 3: 118–124.

Teri Courchene, Riverdale Montessori

The Pink Tower – What’s that about?

If there is a quintessential Montessori material, it is the Pink Tower: a set of 10 cubes, differing in 1 cm increments in size from 1cm cubed to 10cm cubed and stacked in a tower. This tower may look simple, but it embodies the preparation for mathematical thinking in young children.

 

How can this tower help to prepare for math?

  1. Precision: the cubes are mathematically precise, and based on the metric system. Each cube differs from the next one by 1 cm in all dimensions and the children are shown how to move the 1 cm cube around each “step”of the tower to build an understanding of this relationship.
  2. Isolation: the cubes are all of the same material and colour, and are therefore differentiated only by size. The children are therefore differentiating by size when building this tower.
  3. Exploration: children learn to build it by mixing up the cubes and building it themselves. If they are not able to differentiate and build it in descending order of cube size, they do not have an understanding of size differences and need to spend more time on this before moving on to the next activity of differentiation. Children also get the chance to build the tower in different ways – some more stable than others…
  4. How they build reveals their learning: the teacher will see that if a child is able to build the tower in descending order of size, the child is ready for the next step – building the Brown Stair, which involves differentiation in only two dimensions.  Each prism is 20 cm in breadth, but ranges from 1cm to 10 cm squared in the other 2 dimensions.  This is more complex to build in descending order of size than the Pink Tower. Once the child can build the Brown Stair, the child moves to the Red Rods, which are differentiated in 10 cm increments in length alone (from 10cm to 1m).

But why is it pink? To be attractive to the eye and to appeal to the child. Montessori started her work in 1907, well before pink became a “girls’ colour” in 1940. At the turn of the century, pink was seen as a strong colour and was more closely identified with boys than with girls.

Comments? I would like to hear from you.

Teri Courchene

teri@riverdalemontessori.ca

My Montessori Journey

The launch of this blog marks a turning point in my Montessori journey.  This journey started at the age of 3 in a Chicago Montessori school, continued when each of my three children (ages 22, 18 and 11) attended Montessori, became a full-time passion when I trained as a Montessori teacher then set up my own school 7 years ago, and has now come full circle, as I turn to research and writing in the area of education. This latest phase brings in my education (BA, MA Economics) and professional experience (economist, media spokesperson, research director for 13 years).