About Us

The Patterns in Arithmetic series was written by Alysia Krafel, Suki Lueck Glenn, and Susan Carpenter, whose work together began in 1985 while they were all teaching at The Farm School, the University of California, Irvine’s laboratory school under the instruction of Prof. Michael Butler. The Farm School was founded on the principle that children learn best through direct experience, exploration, and meaningful engagement. In mathematics, this meant moving away from rote memorization and toward teaching for true understanding. Students were encouraged to investigate, question, and discover, developing their own ways of thinking and solving problems. This philosophy became the foundation of the Patterns in Arithmetic series.

Created for both homeschool families and classroom teachers, the lessons nurture a child’s natural curiosity and love of learning through exploration, experimentation, and creative problem-solving. Students encounter concepts such as addition, subtraction, place value, patterns, and logic by building models, playing games, observing relationships, and recording their discoveries in ways that make sense to them. Each learner is encouraged to move at their own pace while developing confidence and mathematical insight.

We are a publisher of elementary mathematics books designed to help children experience the beauty, creativity, and logic of numbers. Our approach is grounded in the belief that how mathematics is taught is just as important as what is taught.

Our curriculum uses a multi-sensory, inquiry-based, and constructivist approach that invites students to actively explore mathematical ideas rather than simply memorize procedures. Through hands-on discovery, they learn to recognize patterns, build models, test ideas, and develop a deeper understanding of how mathematics works.

Meet the Authors

Alysia Krafel

Alysia Krafel began her teaching career in 1975 at the Farm School, the University of California, Irvine’s lab school. There, under the direction of Prof. Michael Butler, math was taught in ways that generated understanding rather than through memorized procedures. This requirement was the genesis of Patterns in Arithmetic.

After moving to Northern California, Alysia homeschooled her two daughters. Since 1996, the Patterns in Arithmetic series has been field tested with homeschoolers and at Chrysalis Charter School, which she helped found to further develop this work. Chrysalis has used the program for over 18 years with excellent results.

Patterns in Arithmetic is the culmination of her many years of work in mathematics for children. Alysia also instructs teachers and parents through conferences, in-service trainings, and her popular Math for Moms classes.

Today, she offers one-on-one math tutoring in person in Northern California and online. Learn about her tutoring services.

Susan Carpenter

Susan holds a BS from Antioch College and an MST from the University of Chicago. After teaching in Chicago public schools, alternative schools, and Teacher Curriculum Work Centers, she spent fourteen years teaching mathematics to children in kindergarten through sixth grade at the Farm School.

For many years, Susan helped write and edit the Patterns in Arithmetic series and has been instrumental in bringing the project to completion. She now lives on her hand-built ship in Iowa and works with autodidacts of all ages.

Suki Glenn

Suki Lueck Glenn holds a BA, MA, and an elementary teaching credential from CSU Fullerton. She taught children ages five through seven at the UCI Farm Elementary School for seven years, where she also served as a consultant and mentor to teachers. Over the years, she has worked extensively with homeschool students.

She also taught for two years at Village Elementary School in Fallbrook, California, a school focused on constructivist learning. Her more than twenty-five years of teaching experience led her to a strong belief in individualized instruction and child-centered learning.

Suki has presented workshops at the Greater San Diego Mathematics Council Conference, the Christian Home Education Conference in Anaheim, and the Home Education Conference in Sacramento. She continues to learn through teaching, holding to the belief that children are our best teachers.

More About Our History...

The Farm School at the University of California, Irvine was an experimental elementary school established in 1969, which provided alternative education to children 5 to 12 years old. It was co-founded by UC Irvine professor Michael Butler along with other faculty who had become disenchanted with public education. Inhabiting three remodeled farmhouses that were originally part of the Irvine Ranch, the Farm School took around 50 students per year and provided a non-traditional ungraded learning environment that incorporated their rural surroundings. In Butler's own words, they "wanted a school where children would learn to do what finders and makers do, not just master more or less badly and mechanically, some scattered things they have worked out." Besides serving the community as a school, the Farm School also served the School of Social Sciences as an instructional and research site.

The math program developed there, and now used successfully for over thirty years is based on the insights, ideas, and teachings of Professor Michael Butler. The heart of the Farm School philosophy is learning by discovery and having meaningful conversations between a student and a teacher. A strength of home schooling is being able to interact one-on-one and have these productive dialogs.

"We wanted a school where children would learn to do what finders and makers do, not just master more or less badly and mechanically some scattered things they had worked out. The students would ideally acquire some of the skills and habits of mind of mathematicians and historians and writers and scientists and artists, and even learn to do what good thinkers do when they are thinking well, independent of a particular practice; and they would learn to find matters of interest in and around themselves, and to develop and sustain those interests, as creators of new art and knowledge must do. These were not the only aims of the school, called the Farm School, but they were central. In this sense we were elitist in our ambitions for children, but populist in our belief that most children could realize those ambitions."

- Prof. Emeritus Michael Butler

Mathematicians look for and use patterns—in numbers, shapes, and relationships—to understand the world. The goal of this program is to help students think like mathematicians, rather than simply memorize procedures. From the beginning, learners actively “do” mathematics through inquiry, experimentation, and discovery.

Students develop their own methods for solving problems and use concrete materials to build, test, and verify their thinking. They are encouraged to explore multiple approaches, leading to genuine understanding rather than rote learning. Along the way, they learn to recognize what understanding feels like, work through confusion, and develop perseverance.

Throughout the program, learners are encouraged to look for patterns, invent problems, estimate and predict, use problem-solving strategies, and explore relationships between ideas. Over time, they develop key mathematical habits of mind: recognizing when they understand, forming and testing conjectures, and refining their thinking.

The Parent/Teacher Guide supports this process through structured lessons that model these ways of thinking, helping students gradually take ownership of their learning.

Concepts are developed through a consistent progression: