Dr. Cotter on RightStart and Montessori

Most people have heard of Montessori, but often they are not sure what it’s all about.

The word Montessori refers both to a person and a method of education. Dr. Maria Montessori (1870-1952) was an Italian physician and educator. She is also the developer of the Montessori method of education. 

Dr. Montessori originally worked with children living in institutions and then continued with children in a housing project daycare. She introduced child-size tables and chairs and developed four categories of materials:

• exercises of practical life,
• sensorial materials,
• language activities, and
• math materials.

Exercises of Practical Life

Young children love to help maintain their space, which Montessori called a Children’s House. Therefore, a Montessori preschool provides small brooms, dustpans, and sinks. To teach dressing skills, there are frames for buttoning, zippering, shoe tying, and buckling. The children also have access to polishing and pouring activities.

After a child has been shown how to use a material, they are free to take it from its place on the shelf as desired, perform the activity, and return the material to the same place.

Sensorial Materials

To encourage the child to hone their senses, one activity requires matching Color Tablets and another, grading a set of tablets, for example, from dark blue to light blue.

There are other materials, usually ten items, to be placed in order from largest to smallest in one, two, and three dimensions.

Additionally, there are materials for matching weights and sounds.

Language Activities

Beginning language activities include the Sandpaper Letters that the child traces with their fingers in the direction they are written. The teacher uses them to teach the sound of the letters.

Also available is the Movable Alphabet box, a set of several copies of individual letters, enabling the child to compose simple phonetic words before reading.

For 5-year-olds, more advanced language materials are symbols for identifying parts of speech. Learning new vocabulary is an important part of language.

Puzzle maps provide a tactile means for teaching geography vocabulary while nomenclature cards showed geometrical terms.

The adult uses the three-period lesson, or name lesson, as follows: 

• This is. . . . (a triangle)
• Show me. . . . (the triangle)
• What is this?. . . . (a triangle)

Math Materials

The beginning Montessori math material is the Number Rods, a set of ten rods increasing in length from 10 cm to 100 cm (1 m). To make the rods countable, each 10 cm segment is painted in alternating colors of red and blue.

The classroom has many other materials designed for counting. Soon the child is introduced to tens, hundreds, and thousands with base-ten materials made with the ‘golden’ beads.

My Montessori Experience

I first heard of Montessori decades ago from reading a newspaper article. Dr. Montessori’s philosophy made sense to me and I read every book I could find about her and her method to teaching.

A few years later, I enrolled in the first Montessori training course offered in Minnesota and received my diploma from Mario Montessori, Maria’s son. I taught in Montessori schools for several years in the Minneapolis/St. Paul area, including one year as the special education teacher. I thoroughly enjoyed teaching those years.

While I love the way Montessori teaches reading, I slowly began to question the math progression for several reasons. Montessori used color frequently with the math materials; the ones are green, the tens are blue, and the hundreds are red, repeating in the thousands and millions. She seemed to be unaware that one out of twelve boys has some color deficiency, creating unexpected challenges for these children.

Also, Montessori wanted the children to be proficient at counting, possibly to pass the Italian basic competency test that required specific counting skills. She did not group by fives for quick quantity recognition. She provided bead bars ranging from one to ten, each in a different color, a forerunner of colored blocks, which doesn’t emphasize the critical grouping of fives; subitizing.

From the Bead Frame to the Cotter AL Abacus

I have been fascinated with abacuses for many years, even mastering adding and subtracting on the Japanese abacus.

Montessori’s version of an abacus, the Bead Frame, has four horizontal rows each with ten beads; the top row beads are green followed by rows of blue, red, and green. A strip along the left side indicates, 1, 10, 100, and 1000. Some children had difficulty writing the number represented by these quantities because of this sideways orientation.

When I presented the Bead Frame to the Montessori children, I found they had great difficulty in mastering it. To add 8 + 6, they counted out 8 beads; then to add 6, they counted 2 beads before reaching the end of the top row. At this point, they traded the row of 10 green beads for 1 blue bead, and then continued by moving 4 more green beads. Unfortunately, after the trade the children frequently forgot where they were in the count for 6.

This method of trading before completely combining the numbers does not correlate with the addition algorithm.

I felt a simpler abacus would better serve the children. I made a few abacuses with 100 beads, ten rows each with ten beads grouped in two colors, one dark and one light.

With this modified bead frame, the children didn’t need to count. They could use strategies to help them learn their facts.

To enable the children to perform trades, side 2 of this abacus used two columns of beads for the ones, tens, hundreds, and thousands. With this arrangement, both addends are present before trading. The children really enjoyed the modified Bead Frame, now called Cotter AL Abacus, and made great progress mathematically.

From the Cotter Abacus to RightStart Math

When the time came for me to decide on a topic for my doctoral dissertation, I chose to replicate features of primary mathematics as taught in other countries, especially in East Asia, combined with some Montessori principles. The lessons I wrote became RightStart Grade 1 and Level B, first edition.

The school where I conducted my research was amazed at the children’s progress and asked me to continue writing lessons for more grades, and thus was born RightStart Mathematics.