# Square of Pythagoras – Mathematics

The Square of Pythagoras or the Decanomial Square is a first sensorial representation of the times tables. The colours correspond to the colours of the bead material and they represent 1×1 all the way up to 10×10. By carrying out this exercise, the children become familiar with algebraic patterns. The study of patterns in numbers is the key to algebraic thinking.

Later the children make the same Square of Pythagoras or the Decanomial Square with the beads. Even later still, this work is extended to replacing the numbers with the symbols A – J.  In this last stage, the white square (the 7×7 beadsbecomes G2.

# Movable Alphabet – Language

The Movable Alphabet is a beautiful wooden material, with all the letters of the alphabet in cursive script.  With this material, the children embark on a great journey of Word Study which begins straight away in the beginning of lower elementary.

Word study  helps to build vocabulary and aid spelling as it reinforces regularities and it highlights exceptions. Word study strengthens reading comprehension because the children learn the meanings of roots and affixes and they discover that knowing some roots and affixes already helps them to decode new words!

The children work with affixes:

suffixes,  and prefixes;

compound words;

and word families.

From this work, the root of words becomes very easily visible. Working with words in this way is fun and allows for a systematic build-up of vocabulary. All the while, the children are becoming accustomed to the formation of the letters in cursive script, and they are ‘collecting words’ and practicing spelling.

# Tone Bars – Music

Music, which is usually an ‘extra-curricular’ subject in other schools, is fully integrated into the Montessori classroom. A child may choose to work with the tone bars in music, or the notation boards (another post later) while other children work with math, geography, history, or any other materials.  Music is very close to my heart, as I was a music teacher for many years (violin, piano and flute), but what I am really excited about is how music becomes accessible to all children in the Montessori classroom, not just the lucky few.

As with all other areas of the curriculum, first the foundation is presented to the children upon which they can build, and the tone bars are used for this purpose – to build a foundation in the language of music. Although the set up of the tone bars replicates a piano keyboard, the difference between the tone bars and  a regular piano is that each ‘bar’ is movable!

This allows us to pull out the bars needed to make a major or minor scale, starting on any note. This also allows us to pull out the bars of only one key, giving us only the tone bars needed for that  great song we want to play or compose!

In this picture, the major scale of C is pulled out. This is the first set that the child works with – all white notes, no sharps or flats – and from here we build in complexity, as we do in all areas of the curriculum.

Have a listen to how the tone bars of the Montessori Elementary Schoolhouse sound!

# Pin Maps – Geography

This is what learning the countries, capitals and national flags of the countries of the world looks like if you attend the Montessori Elementary Schoolhouse. For each of the five continents there is a set of 4 maps, like this set of North America.

A trademark of Montessori education is the feature of the ‘built-in control of error’ in the materials. This means that the materials allow the child to correct his/her own work, without the intervention of an adult. Making mistakes is a natural part of learning, and it is essential to learning, and this self-correction helps the child to develop confidence.

For each continent, there is one working map and three control maps. When learning the names and position of the countries of the continent, the child works with the green country name flags, the pin flags are placed into the tiny holes of their corresponding country, and when the work is completed the child can check the work with the country name control map.

When learning the names of the capital cities, the child works with the red flags on the working map and the cities control map. With the flag control map, the child can also check whether the flags are matched with their respective countries!

The work is in the child’s hands and the correction too. This is the way the information can be internalized and a love for the subject matter developed.

This work follows on perfectly from the work with the puzzle maps from the Montessori 3-6 classroom. In fact, the knobs on the puzzle maps are placed in the exact position of the capital cities of each country! Everything has a purpose and everything is linked!

# Wooden Hierarchical Material

Not only is this one of my personal favourite materials in lower elementary, it is also a ‘Key Lesson’  which is presented to the 6 year olds in the first week of school, representing quantities of 1 – 1,000,000. It gives the children the ‘Key’  to the entire decimal system – the foundation for the rest of their work in mathematics and geometry over 6 years .  After this lesson, the foundation is laid for work in all four operations (+ – x /) with the large bead frame (next post).

Why is it one of my favourite materials?

• It is beautiful and precise. It appeals to the children; they want to work with it. It is shiny, and goes from teeny tiny and to very, very large, in precise proportions.
• The million cube, which is exactly 1,000,000 times bigger than the unit cube, appeals to the children; the children explore the interrelationships between the quantities and numbers.
• It is simple but at the same time it contains a wealth of information – a 3D mathematical experience with language.
• And we all know that 6 year olds LOVE big numbers!

This material shows three families of numbers:

• the simple family – the family of units (1 -green), tens (10 – blue) and hundreds (100 – red).
• the family of thousands – units of thousand (1,000 – green), tens (10,000 – blue) of thousands and hundreds of thousands (100,000 – red).
• the family of millions – units of millions (1,000,000 – green).

Looking at it another way:

• the hierarchy of units (1; 1,000; 1,000,000 – all green)
• the hierarchy of tens (10; 10,000 – both blue)
• the hierarchy of hundreds (100, 100,000 – both red)

Here is a video of the material in action:

Wooden Hierarchical Material

# Microscope

Want to know what leaf veins look like? Let’s look at them up close!

Want to see what shape a salt crystal really is up close? We can find out!

What does a cell really look like? It is so, so small, but we can see it if we look here!

We are studying rocks and minerals. Can we see what components are visible in each of them?

Yes we can!

The Microscope is an important material and there is at least one available in a Montessori elementary classroom that the children can use for exploration. Yes! Even 6-year-old children have access to a microscope to examine the world up close. What a gift for the curious mind!

# Historical Art

The Montessori Elementary Schoolhouse received its first gift – Historical Art – dedicated to Maria Montessori. Today, I think its display could be categorized as art, but back in the day when I was an elementary student, it was official currency in Italy. This piece of historical art, a 1000 Lira note, has traveled from Italy to the Netherlands and now to Aruba, not to mention what a life it led while it was in Italy.

Most recently, this 1000 Lira note was gifted by dear friends of the Montessori Elementary Schoolhouse in Aruba, not to spend wisely on materials (1000 Lira = \$0.71 US or Afl. 1.27), but to display in the classroom as a dedication to Maria Montessori and as an inspirational piece of historical art from which uncountable avenues of exploration will be embarked upon: currency exchange calculations, international currencies, art on currency, history of education, where/how money is made, the origin and function of money… to name but a few!

In 1990, the Italian Government honoured Dr. Montessori by putting her image on the 1000 Lira note, with an image of two children on the back side of the note.

# Research Materials

A great part of elementary education is the pursuit of answers to the burning questions the children have about our universe, our cultures, the nature that surrounds us and the workings of the world, to mention but a few things in broad strokes. The greatest talent of the Montessori Elementary teacher is to give the children just enough to capture their attention and spark their interest in an area of study, intriguing them enough so that they will pursue further study of the subject, either through practice with the tactile Montessori materials in the classroom or through collaborative research projects, called ‘great works’ with the research materials.

A foundation research material that is essential in the Elementary classroom is a quality Encyclopedia series. The Montessori Elementary Schoolhouse already has its World Book Encyclopedia, as well as a beautifully illustrated Dutch ‘Wereld Geschiedenis’ series waiting in the wings to adorn the bookshelves when they are ready. The book collection is being lovingly compiled and it awaits to provide a wealth of answers to the children.

“The bottom line is, if you’re not the one who’s controlling your learning, you’re not going to learn as well,” Joel Voss, a neuroscientist at Northwestern University.

# The Checkerboard

This material is used in the Montessori lower elementary classroom with children between 6-9 years of age).

With the Checkerboard and bead bars (representing numbers 1-9) the children learn long multiplication (2, 3, 4, or more digit numbers). In the problem in Photograph 1, a five digit number was multiplied by a two digit number. The multiplicand is on the bottom horizontal line (in Photograph 2, it is 3,212) and the multiplier is on the vertical line. The children multiply each digit of the multiplicand by each digit of the multiplier and place corresponding bead bars in the corresponding coloured square. Each coloured square represents one level of the hierarchy of numbers: units (green), tens (blue), hundreds (red), units of thousands (green), tens of thousands (blue), and hundreds (red) etc. and this goes up in this way to hundreds of millions. After multiplying each digit of the multiplicand by each digit of the multiplier, and placing the corresponding bead bars in their coloured squares, the children exchange the bead bars to have only one bead bar in each square on the bottom line of squares, representing the answer.

With repeated work using this material, the children come to understand (deeply) the concept of long multiplication and, with time, alongside the tactile work with the material, the children also learn to extract this long multiplication process onto paper, and eventually they work on long multiplication in the abstract, only on paper and without the checkerboard.
The number (the answer) that is on the board in Photograph 1 represents 1,979,191. In Photograph 2, it will end up being 40,756.