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, Dr. Maria Montessori (1870-1952), an Italian physician and educator, and the Montessori method of education she developed. 

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 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 room 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. Her philosophy made sense to me and I read every book I could find about Montessori and her method. 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. 

Also, Montessori did not group by fives for quick quantity recognition. She wanted the children to be proficient at counting, possibly to pass the Italian basic competency test that required counting. 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.

From the Bead Frame to the 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 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. Remember that algorithms do not trade before completely combining both numbers. 

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 and 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 AL Abacus, and made great progress mathematically.

From the AL 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.



  1. We are moving from a traditional AMI Montessori program to homeschooling and the similarities between Montessori and what I was reading in reviews about Right Start Math led me to google this combination and to this page.

    I have a 5 year old and 9 year old. I don’t think I understand Montessori math enough to duplicate everything my 9 year old has learned for my 5 year old so I’m looking for a comprehensive curriculum to follow.

    My question is…

    Do you feel that a 3rd grader would be confused by the differences between what he has been taught in Montessori if we move to Right Start, especially for my kindergartener? He has a very good working knowledge of what Montessori considers abstract concepts through division.

    Thank you,

    • Rachel Anderson says

      Hi, Michelle. My name is Rachel and I am happy to help you today.

      We have many children come into RightStart Math from a variety of programs. The first few lessons in the Lesson Manual are transition lessons helping you and your child learn how to use the manipulatives and strategies taught in the program.

      While RightStart Math has a unique way of teaching, for most children, this is very refreshing. 😉 The program uses hands-on materials to engage the student and help them learn – and more importantly – understand math concepts.

      In addition, practice is done through playing math card games – instead of worksheets. Now, RightStart Math does use worksheets, but does not use those worksheets to ‘drill’ the child. That makes the learning of math facts and other concepts less stressful to learn so the child learns them easier.

      Because your 3rd grade is coming from Montessori, I believe they will do very well in transition. Some of the manipulatives and methods of teaching are similar, so your 3rd grader will not have any trouble at all acclimating to the program.

      For your kindergartener, Level A is so much fun and engaging – your child is going to absolutely love it, even if they have a beginning foundation without using the manipulatives. While Level A is engaging for the child (all of my kids LOVED it), it covers all the math concepts. Level A will cover basic numeration, addition, subtraction, multiplication, division, fractions, time, money and geometry. I was absolutely amazed at the amount of material my kindergartner was learning! Just to give you an example, by the end of the level, my daughter was doing this problem: 1 – 3/5 = 2/5! I am not joking! Because of the approach, not only was my child able to do more complex equations for a kindergartner, but she understood the math!

      I hope that gives you the information you are looking for. If not, please feel free to email us at info@rightstartmath.com or you can post your questions here.

      Have a great day!

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