Written by Al Cotter

February 14, 2006

My wife, Joan, did not set out to develop the AL Abacus. Her objective was to improve the way we teach children math. Her passion is teaching! Before we were married we discussed how we wanted our children to develop a work ethic, to have the best education possible, and to join us in a lifetime of learning. We both believed that is the foundation for a happy and useful life.

I imagine we started to teach counting like other parents, but Joan soon recognized that counting is about language, not math. To teach math, you must teach about quantity and measurement, which leads to understanding and application.

The path to the AL Abacus started shortly after the birth of Kathleen, and like all paths that Joan travels, the first steps were paved with research. This era started in the mid-1960s when research information was obtained by going to the library. After checking out several books, Joan found a book Children Discover Arithmetic written by Catherine Stern in the Minneapolis Public Library.[1]

In this book Joan discovered Stern rods, more commonly known as colored rods. These rods, as designed by Catherine Stern, have been and are the basis for several math programs, including programs by Georges Cuisenaire developer of Cuisenaire rods, Mortensen Math, and Math-U-See.[2]

As dutiful husband, I made a copy of Stern rods for Joan to teach our now two daughters. After some experimentation we purchased a complete set of Stern rods and Joan proceeded to teach our children. While this worked, something was missing. When using "the rods," non-math information was also taught. If eight is orange (or brown), this is hard for a child to remember.

Joan was also very interested in teaching reading, as well as teaching every day living skills. There again she was led to the library and more research, which led her to Montessori and Montessori math. This method of teaching so fascinated Joan that she took the training to become a Montessori teacher. She continued to develop her concepts. Then, in 1977, she made the first AL Abacus using a picture frame with wooden beads stained two shades of brown. The first abacus had ten wires with five dark and five light beads on all rows. Later, the AL Abacus beads were rearranged into four quarters using two bright and distinct colors. This gave a better visual image of the entire abacus.

Joan now had a tool to teach young children their basic addition facts visually without relying on counting. Because a child is already familiar with their five fingers, this was a natural transition to a computing tool.

As Joan used her new tool in the Montessori classroom in 1982, she determined that a better way to teach trading abstractly was needed. The Montessori materials includes a bead frame, but it was difficult for the children to use. That is how the second side of the AL Abacus was developed. On the back side, a new layout is presented to demonstrate trading. It is much easier to use and transfers exactly to paper and pencil work.

In a span of 8 years of classroom development and research, Joan developed a unique tool to teach children arithmetic and introduce advanced mathematical concepts. This required a manual, prompting Joan to write Activities for the AL Abacus: A Hands On Approach to Arithmetic, first published in 1986.

As I started to look forward to retirement, I asked Joan what she wanted to do. During our marriage, every time my company asked me to relocate, Joan had to set up a new household, which included finding and adjusting to a new house in a new neighborhood, attending new schools, and joining a new church. This transition became her responsibility as I immediately became consumed in new professional responsibilities. So the question, "What do you want to do?" was only appropriate. Her response, "I want to earn my Ph.D. so I can do some thorough research on the AL Abacus."

In 1996, Joan earned her Ph.D. in mathematics education and early childhood with her thesis, Constructing a Multidigit Concept of Numbers: A Teaching Experiment in the First Grade. To do this research she wrote a first grade curriculum, now known as RightStart Mathematics First Grade for schools, or RightStart Mathematics Level B Lessons for home-schooled children. The test results of the experimental class were considerably higher than the control class. A summary of this research can be reviewed.

There have been several developments of the AL Abacus, the most significant being the overhead abacus. The National Council Teachers Mathematics (NCTM) also has an electronic version of the AL Abacus on their website. This illustration has both sides of the AL abacus. It is noteworthy that Joan's research paper was published on the NCTM web site and in a professional journal (Cotter, Joan. "Using Language and Visualization to Teach Place Value." Teaching Children Mathematics 7 (October, 2000): 108-114.)

When Joan designed the front side of the AL Abacus she thought she was doing original work. That may not be completely correct. Joan and I vacationed in Europe in 1992. While visiting a museum in Munich, Germany, we saw an old abacus with the same configuration as the AL Abacus. It was large abacus, about a meter by a meter. We purchased a book to learn more, but even after translation, we do not have its history, or an idea of how it was used.

A couple years ago, Professor Linda Bonne of Wesley University in New Zealand e-mailed Joan that she knew of another abacus configured like the AL Abacus, front side only, called the Slavonic abacus. My own search found the earliest reference in 2001.

I did make another discovery while researching for this paper. Whenever Joan would talk about Catherine Stern, she seemed to have a special bond with her. This is best illustrated the last time she had the first edition of the book Children Discover Arithmetic checked out of the library. She put a note in the library pocket offering to purchase the book if it was ever sold. Both editions of this book are now out of print.

Catherine Stern was a Montessori teacher! She developed the Stern Rods based on her classroom experience. However, she did not reveal her Montessori background in her books. Joan also has made only passing reference to her Montessori background. I believe Dr. Catherine Stern and Dr. Joan Cotter have so much respect for Dr. Maria Montessori that neither wanted to acknowledge they found improvements in the Montessori math.

This is not the end of the AL Abacus story; it is the beginning. Because of the AL Abacus, Activities for Learning, Inc. was established to publish curriculum. The stated mission of the company is a simple desire where Joan's journey began "To help children understand, apply, and enjoy mathematics."

[1] This is a testimonial to Joan's persistent research. The Minneapolis Library was over 30 miles from our home in the days of single car families.

[2] Cuisenaire rods are different in that they are not segmented as Stern, Mortensen Math and Math-U-See rods are.